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<!doctype html><html lang=en dir=ltr class="blog-wrapper blog-post-page plugin-blog plugin-id-default" data-has-hydrated=false><meta charset=UTF-8><meta name=generator content="Docusaurus v3.6.1"><title data-rh=true>Playing with fire: Tone mapping and color | The Old Speice Guy</title><meta data-rh=true name=viewport content="width=device-width,initial-scale=1.0"><meta data-rh=true name=twitter:card content=summary_large_image><meta data-rh=true property=og:url content=https://speice.io/2024/11/playing-with-fire-log-density><meta data-rh=true property=og:locale content=en><meta data-rh=true name=docusaurus_locale content=en><meta data-rh=true name=docusaurus_tag content=default><meta data-rh=true name=docsearch:language content=en><meta data-rh=true name=docsearch:docusaurus_tag content=default><meta data-rh=true property=og:title content="Playing with fire: Tone mapping and color | The Old Speice Guy"><meta data-rh=true name=description content="So far, our plot() function has been 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class="container margin-vert--lg"><div class=row><aside class="col col--3"><nav class="sidebar_re4s thin-scrollbar" aria-label="Blog recent posts navigation"><div class="sidebarItemTitle_pO2u margin-bottom--md">All posts</div><div role=group><h3>2024</h3><div role=group><h4>Playing with fire</h4><ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2024/11/playing-with-fire>The fractal flame algorithm</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2024/11/playing-with-fire-transforms>Transforms and variations</a><li class=sidebarItem__DBe><a aria-current=page class="sidebarItemLink_mo7H sidebarItemLinkActive_I1ZP" href=/2024/11/playing-with-fire-log-density>Tone mapping and color</a></ul></ul></div></div><div role=group><h3>2022</h3><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2011/11/webpack-industrial-complex>The webpack industrial complex</a></ul></div><div role=group><h3>2019</h3><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/12/release-the-gil>Release the GIL</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/09/binary-format-shootout>Binary format shootout</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/06/high-performance-systems>On building high performance systems</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/05/making-bread>Making bread</a></ul><div role=group><h4>Allocations in Rust</h4><ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/understanding-allocations-in-rust>Foreword</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/the-whole-world>Global memory</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/stacking-up>Fixed memory</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/a-heaping-helping>Dynamic memory</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/08/compiler-optimizations>Compiler optimizations</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2019/02/summary>Summary</a></ul></ul></div></div><div role=group><h3>2018</h3><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/12/allocation-safety>QADAPT - debug_assert! for allocations</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/12/what-small-business-really-means>More "what companies really mean"</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/10/case-study-optimization>A case study in heaptrack</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/09/isomorphic-apps>Isomorphic desktop apps with Rust</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/09/primitives-in-rust-are-weird>Primitives in Rust are weird (and cool)</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/06/dateutil-parser-to-rust>What I learned porting dateutil to Rust</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/05/hello>Hello!</a></ul><div role=group><h4>Captain's Cookbook</h4><ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/01/captains-cookbook-part-1>Project setup</a><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2018/01/captains-cookbook-part-2>Practical usage</a></ul></ul></div></div><div role=group><h3>2016</h3><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/11/pca-audio-compression>PCA audio compression</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/10/rustic-repodcasting>A Rustic re-podcasting server</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/06/event-studies-and-earnings-releases>Event studies and earnings releases</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/05/the-unfair-casino>The unfair casino</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/04/tick-tock>Tick tock...</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/03/tweet-like-me>Tweet like me</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/03/predicting-santander-customer-happiness>Predicting Santander customer happiness</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/02/profitability-using-the-investment-formula>Profitability using the investment formula</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/02/guaranteed-money-maker>Guaranteed money maker</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/01/cloudy-in-seattle>Cloudy in Seattle</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2016/01/complaining-about-the-weather>Complaining about the weather</a></ul></div><div role=group><h3>2015</h3><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2015/12/testing-cramer>Testing Cramer</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2015/11/autocallable>Autocallable Bonds</a></ul><ul class="sidebarItemList_Yudw clean-list"><li class=sidebarItem__DBe><a class=sidebarItemLink_mo7H href=/2015/11/welcome>Welcome, and an algorithm</a></ul></div></nav></aside><main class="col col--7"><article><header><h1 class=title_f1Hy>Playing with fire: Tone mapping and color</h1><div class="container_mt6G margin-vert--md"><time datetime=2024-12-16T21:32:00.000Z>December 16, 2024</time> · <!-- -->7 min read</div><div class="margin-top--md margin-bottom--sm row"><div class="col col--12 authorCol_Hf19"><div class="avatar margin-bottom--sm"><div class="avatar__intro authorDetails_lV9A"><div class=avatar__name><span class=authorName_yefp>Bradlee Speice</span></div><div class=authorSocials_rSDt><a href=https://github.com/bspeice target=_blank rel="noopener noreferrer" class=authorSocialLink_owbf title=GitHub><svg viewBox="0 0 256 250" width=1em height=1em class="authorSocialLink_owbf githubSvg_Uu4N" style=--dark:#000;--light:#fff preserveAspectRatio=xMidYMid><path d="M128.001 0C57.317 0 0 57.307 0 128.001c0 56.554 36.676 104.535 87.535 121.46 6.397 1.185 8.746-2.777 8.746-6.158 0-3.052-.12-13.135-.174-23.83-35.61 7.742-43.124-15.103-43.124-15.103-5.823-14.795-14.213-18.73-14.213-18.73-11.613-7.944.876-7.78.876-7.78 12.853.902 19.621 13.19 19.621 13.19 11.417 19.568 29.945 13.911 37.249 10.64 1.149-8.272 4.466-13.92 8.127-17.116-28.431-3.236-58.318-14.212-58.318-63.258 0-13.975 5-25.394 13.188-34.358-1.329-3.224-5.71-16.242 1.24-33.874 0 0 10.749-3.44 35.21 13.121 10.21-2.836 21.16-4.258 32.038-4.307 10.878.049 21.837 1.47 32.066 4.307 24.431-16.56 35.165-13.12 35.165-13.12 6.967 17.63 2.584 30.65 1.255 33.873 8.207 8.964 13.173 20.383 13.173 34.358 0 49.163-29.944 59.988-58.447 63.157 4.591 3.972 8.682 11.762 8.682 23.704 0 17.126-.148 30.91-.148 35.126 0 3.407 2.304 7.398 8.792 6.14C219.37 232.5 256 184.537 256 128.002 256 57.307 198.691 0 128.001 0Zm-80.06 182.34c-.282.636-1.283.827-2.194.39-.929-.417-1.45-1.284-1.15-1.922.276-.655 1.279-.838 2.205-.399.93.418 1.46 1.293 1.139 1.931Zm6.296 5.618c-.61.566-1.804.303-2.614-.591-.837-.892-.994-2.086-.375-2.66.63-.566 1.787-.301 2.626.591.838.903 1 2.088.363 2.66Zm4.32 7.188c-.785.545-2.067.034-2.86-1.104-.784-1.138-.784-2.503.017-3.05.795-.547 2.058-.055 2.861 1.075.782 1.157.782 2.522-.019 3.08Zm7.304 8.325c-.701.774-2.196.566-3.29-.49-1.119-1.032-1.43-2.496-.726-3.27.71-.776 2.213-.558 3.315.49 1.11 1.03 1.45 2.505.701 3.27Zm9.442 2.81c-.31 1.003-1.75 1.459-3.199 1.033-1.448-.439-2.395-1.613-2.103-2.626.301-1.01 1.747-1.484 3.207-1.028 1.446.436 2.396 1.602 2.095 2.622Zm10.744 1.193c.036 1.055-1.193 1.93-2.715 1.95-1.53.034-2.769-.82-2.786-1.86 0-1.065 1.202-1.932 2.733-1.958 1.522-.03 2.768.818 2.768 1.868Zm10.555-.405c.182 1.03-.875 2.088-2.387 2.37-1.485.271-2.861-.365-3.05-1.386-.184-1.056.893-2.114 2.376-2.387 1.514-.263 2.868.356 3.061 1.403Z"/></svg></a></div></div></div></div></div></header><div id=__blog-post-container class=markdown><p>So far, our <code>plot()</code> function has been fairly simple: map a fractal flame coordinate to a specific pixel,
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and color in that pixel. This works well for simple function systems (like Sierpinski's Gasket),
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but more complex systems (like the reference parameters) produce grainy images.</p>
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<p>In this post, we'll refine the image quality and add color to really make things shine.</p>
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<h2 class="anchor anchorWithStickyNavbar_LWe7" id=image-histograms>Image histograms<a href=#image-histograms class=hash-link aria-label="Direct link to Image histograms" title="Direct link to Image histograms"></a></h2>
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<div class="theme-admonition theme-admonition-note admonition_xJq3 alert alert--secondary"><div class=admonitionHeading_Gvgb><span class=admonitionIcon_Rf37><svg viewBox="0 0 14 16"><path fill-rule=evenodd d="M6.3 5.69a.942.942 0 0 1-.28-.7c0-.28.09-.52.28-.7.19-.18.42-.28.7-.28.28 0 .52.09.7.28.18.19.28.42.28.7 0 .28-.09.52-.28.7a1 1 0 0 1-.7.3c-.28 0-.52-.11-.7-.3zM8 7.99c-.02-.25-.11-.48-.31-.69-.2-.19-.42-.3-.69-.31H6c-.27.02-.48.13-.69.31-.2.2-.3.44-.31.69h1v3c.02.27.11.5.31.69.2.2.42.31.69.31h1c.27 0 .48-.11.69-.31.2-.19.3-.42.31-.69H8V7.98v.01zM7 2.3c-3.14 0-5.7 2.54-5.7 5.68 0 3.14 2.56 5.7 5.7 5.7s5.7-2.55 5.7-5.7c0-3.15-2.56-5.69-5.7-5.69v.01zM7 .98c3.86 0 7 3.14 7 7s-3.14 7-7 7-7-3.12-7-7 3.14-7 7-7z"/></svg></span>note</div><div class=admonitionContent_BuS1><p>This post covers sections 4 and 5 of the Fractal Flame Algorithm paper</div></div>
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<p>One problem with the current chaos game algorithm is that we waste work
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because pixels are either "on" (opaque) or "off" (transparent).
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If the chaos game encounters the same pixel twice, nothing changes.</p>
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<p>To demonstrate how much work is wasted, we'll count each time the chaos game
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visits a pixel while iterating. This gives us a kind of image "histogram":</p>
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<!-- -->
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<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> randomBiUnit </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/randomBiUnit"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> randomChoice </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/randomChoice"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> Props </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">as</span><span class="token plain"> ChaosGameFinalProps </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../2-transforms/chaosGameFinal"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> camera</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> histIndex </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/camera"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> quality </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">10</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> step </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">100_000</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">type</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">Props</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> ChaosGameFinalProps </span><span class="token operator" style="color:hsl(221, 87%, 60%)">&</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function-variable function" style="color:hsl(221, 87%, 60%)">paint</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> histogram</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=></span><span class="token plain"> ImageData</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">chaosGameHistogram</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> transforms</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> final</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> paint</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> Props</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixels </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> width </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> iterations </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> quality </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> hist </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token generic-function function" style="color:hsl(221, 87%, 60%)">Array</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token generic-function generic class-name builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)">></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">fill</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token function-variable function" style="color:hsl(221, 87%, 60%)">plotHist</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> x</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> y</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=></span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> pixelY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">camera</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelX </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelX </span><span class="token operator" style="color:hsl(221, 87%, 60%)">>=</span><span class="token plain"> width </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelY </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelY </span><span class="token operator" style="color:hsl(221, 87%, 60%)">>=</span><span class="token plain"> height</span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> hIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">histIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixelX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> pixelY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">hIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomBiUnit</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomBiUnit</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> iterations</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i</span><span class="token operator" style="color:hsl(221, 87%, 60%)">++</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">_</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> transform</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomChoice</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">transforms</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">transform</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">finalX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> finalY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">final</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">></span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">20</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">plotHist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">finalX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> finalY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">%</span><span class="token plain"> step </span><span class="token operator" style="color:hsl(221, 87%, 60%)">===</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">yield</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paint</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">yield</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paint</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<p>When the chaos game finishes, we find the pixel encountered most often.
|
||
Finally, we "paint" the image by setting each pixel's alpha (transparency) value
|
||
to the ratio of times visited divided by the maximum:</p>
|
||
<!-- -->
|
||
<!-- -->
|
||
<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paintLinear</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hist</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> img </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">new</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">ImageData</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> hMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> value </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">of</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">max</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hMax</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> value</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">length</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i</span><span class="token operator" style="color:hsl(221, 87%, 60%)">++</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">4</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> alpha </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token plain"> hMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> alpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<!-- -->
|
||
<center><center><div style=width:75%;aspect-ratio:1/1></div></center></center>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=tone-mapping>Tone mapping<a href=#tone-mapping class=hash-link aria-label="Direct link to Tone mapping" title="Direct link to Tone mapping"></a></h2>
|
||
<p>While using a histogram reduces the "graining," it also leads to some parts vanishing entirely.
|
||
In the reference parameters, the outer circle is still there, but the interior is gone!</p>
|
||
<p>To fix this, we'll introduce the second major innovation of the fractal flame algorithm: <a href=https://en.wikipedia.org/wiki/Tone_mapping target=_blank rel="noopener noreferrer">tone mapping</a>.
|
||
This is a technique used in computer graphics to compensate for differences in how
|
||
computers represent brightness, and how people actually see brightness.</p>
|
||
<p>As a concrete example, high-dynamic-range (HDR) photography uses this technique to capture
|
||
scenes with a wide range of brightnesses. To take a picture of something dark,
|
||
you need a long exposure time. However, long exposures lead to "hot spots" (sections that are pure white).
|
||
By taking multiple pictures with different exposure times, we can combine them to create
|
||
a final image where everything is visible.</p>
|
||
<p>In fractal flames, this "tone map" is accomplished by scaling brightness according to the <em>logarithm</em>
|
||
of how many times we encounter a pixel. This way, "cold spots" (pixels the chaos game visits infrequently)
|
||
are still visible, and "hot spots" (pixels the chaos game visits frequently) won't wash out.</p>
|
||
<details class="details_lb9f alert alert--info details_b_Ee" data-collapsed=true><summary>Log-scale vibrancy also explains fractal flames appear to be 3D...</summary><div><div class=collapsibleContent_i85q><p>As mentioned in the paper:<blockquote>
|
||
<p>Where one branch of the fractal crosses another, one may appear to occlude the other
|
||
if their densities are different enough because the lesser density is inconsequential in sum.
|
||
For example, branches of densities 1000 and 100 might have brightnesses of 30 and 20.
|
||
Where they cross the density is 1100, whose brightness is 30.4, which is
|
||
hardly distinguishable from 30.</p>
|
||
</blockquote></div></div></details>
|
||
<!-- -->
|
||
<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paintLogarithmic</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hist</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> img </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">new</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">ImageData</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> histLog </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">map</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">log</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> hLogMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token number" style="color:hsl(35, 99%, 36%)">Infinity</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> value </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">of</span><span class="token plain"> histLog</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> hLogMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">max</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">hLogMax</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> value</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> hist</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">length</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i</span><span class="token operator" style="color:hsl(221, 87%, 60%)">++</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">4</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// red</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// green</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// blue</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> alpha </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> histLog</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token plain"> hLogMax </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> alpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<!-- -->
|
||
<center><center><div style=width:75%;aspect-ratio:1/1></div></center></center>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=color>Color<a href=#color class=hash-link aria-label="Direct link to Color" title="Direct link to Color"></a></h2>
|
||
<p>Now we'll introduce the last innovation of the fractal flame algorithm: color.
|
||
By including a third coordinate (<span class=katex><span class=katex-mathml><math><semantics><mrow><mi>c</mi></mrow><annotation encoding=application/x-tex>c</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">c</span></span></span></span>) in the chaos game, we can illustrate the transforms
|
||
responsible for the image.</p>
|
||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=color-coordinate>Color coordinate<a href=#color-coordinate class=hash-link aria-label="Direct link to Color coordinate" title="Direct link to Color coordinate"></a></h3>
|
||
<p>Color in a fractal flame is continuous on the range <span class=katex><span class=katex-mathml><math><semantics><mrow><mo stretchy=false>[</mo><mn>0</mn><mo separator=true>,</mo><mn>1</mn><mo stretchy=false>]</mo></mrow><annotation encoding=application/x-tex>[0, 1]</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:1em;vertical-align:-0.25em></span><span class=mopen>[</span><span class=mord>0</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord>1</span><span class=mclose>]</span></span></span></span>. This is important for two reasons:</p>
|
||
<ul>
|
||
<li>It helps blend colors together in the final image. Slight changes in the color value lead to
|
||
slight changes in the actual color</li>
|
||
<li>It allows us to swap in new color palettes easily. We're free to choose what actual colors
|
||
each value represents</li>
|
||
</ul>
|
||
<p>We'll give each transform a color value (<span class=katex><span class=katex-mathml><math><semantics><mrow><msub><mi>c</mi><mi>i</mi></msub></mrow><annotation encoding=application/x-tex>c_i</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.5806em;vertical-align:-0.15em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span></span></span></span>) in the <span class=katex><span class=katex-mathml><math><semantics><mrow><mo stretchy=false>[</mo><mn>0</mn><mo separator=true>,</mo><mn>1</mn><mo stretchy=false>]</mo></mrow><annotation encoding=application/x-tex>[0, 1]</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:1em;vertical-align:-0.25em></span><span class=mopen>[</span><span class=mord>0</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord>1</span><span class=mclose>]</span></span></span></span> range.
|
||
The final transform gets a value too (<span class=katex><span class=katex-mathml><math><semantics><mrow><msub><mi>c</mi><mi>f</mi></msub></mrow><annotation encoding=application/x-tex>c_f</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.7167em;vertical-align:-0.2861em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span></span></span></span>).
|
||
Then, at each step in the chaos game, we'll set the current color
|
||
by blending it with the previous color:</p>
|
||
<span class=katex-display><span class=katex><span class=katex-mathml><math display=block><semantics><mtable rowspacing=0.25em columnalign="right left" columnspacing=0em><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mo stretchy=false>(</mo><mi>x</mi><mo separator=true>,</mo><mi>y</mi><mo stretchy=false>)</mo><mo>=</mo><mtext>random point in the bi-unit square</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mi>c</mi><mo>=</mo><mtext>random point from [0,1]</mtext></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mtext>iterate </mtext><mo stretchy=false>{</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mspace width=2.8453em /><mi>i</mi><mo>=</mo><mtext>random integer from 0 to </mtext><mi>n</mi><mo>−</mo><mn>1</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mspace width=2.8453em /><mo stretchy=false>(</mo><mi>x</mi><mo separator=true>,</mo><mi>y</mi><mo stretchy=false>)</mo><mo>=</mo><msub><mi>F</mi><mi>i</mi></msub><mo stretchy=false>(</mo><mi>x</mi><mo separator=true>,</mo><mi>y</mi><mo stretchy=false>)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mspace width=2.8453em /><mo stretchy=false>(</mo><msub><mi>x</mi><mi>f</mi></msub><mo separator=true>,</mo><msub><mi>y</mi><mi>f</mi></msub><mo stretchy=false>)</mo><mo>=</mo><msub><mi>F</mi><mrow><mi>f</mi><mi>i</mi><mi>n</mi><mi>a</mi><mi>l</mi></mrow></msub><mo stretchy=false>(</mo><mi>x</mi><mo separator=true>,</mo><mi>y</mi><mo stretchy=false>)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mspace width=2.8453em /><mi>c</mi><mo>=</mo><mo stretchy=false>(</mo><mi>c</mi><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo stretchy=false>)</mo><mi mathvariant=normal>/</mi><mn>2</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mrow/></mstyle></mtd><mtd><mstyle scriptlevel=0 displaystyle=true><mrow><mrow/><mspace width=2.8453em /><mtext>plot</mtext><mo stretchy=false>(</mo><msub><mi>x</mi><mi>f</mi></msub><mo separator=true>,</mo><msub><mi>y</mi><mi>f</mi></msub><mo separator=true>,</mo><msub><mi>c</mi><mi>f</mi></msub><mo stretchy=false>)</mo><mtext> if iterations</mtext><mo>></mo><mn>20</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel=0 displaystyle=true><mo stretchy=false lspace=0em rspace=0em>}</mo></mstyle></mtd></mtr></mtable><annotation encoding=application/x-tex>\begin{align*}
|
||
&(x, y) = \text{random point in the bi-unit square} \\
|
||
&c = \text{random point from [0,1]} \\
|
||
&\text{iterate } \{ \\
|
||
&\hspace{1cm} i = \text{random integer from 0 to } n - 1 \\
|
||
&\hspace{1cm} (x,y) = F_i(x,y) \\
|
||
&\hspace{1cm} (x_f,y_f) = F_{final}(x,y) \\
|
||
&\hspace{1cm} c = (c + c_i) / 2 \\
|
||
&\hspace{1cm} \text{plot}(x_f,y_f,c_f) \text{ if iterations} > 20 \\
|
||
\}
|
||
\end{align*}</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:13.5em;vertical-align:-6.5em></span><span class=mord><span class=mtable><span class=col-align-r><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:7em><span style=top:-9.16em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-7.66em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-6.16em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-4.66em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-3.16em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-1.66em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:-0.16em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:1.34em><span class=pstrut style=height:3em></span><span class=mord></span></span><span style=top:2.84em><span class=pstrut style=height:3em></span><span class=mord><span class=mclose>}</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:6.5em><span></span></span></span></span></span><span class=col-align-l><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:7em><span style=top:-9.16em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mopen>(</span><span class="mord mathnormal">x</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=mclose>)</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class="mord text"><span class=mord>random point in the bi-unit square</span></span></span></span><span style=top:-7.66em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class="mord mathnormal">c</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class="mord text"><span class=mord>random point from [0,1]</span></span></span></span><span style=top:-6.16em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class="mord text"><span class=mord>iterate </span></span><span class=mopen>{</span></span></span><span style=top:-4.66em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mspace style=margin-right:2.8453em></span><span class="mord mathnormal">i</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class="mord text"><span class=mord>random integer from 0 to </span></span><span class="mord mathnormal">n</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span><span class=mord>1</span></span></span><span style=top:-3.16em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mspace style=margin-right:2.8453em></span><span class=mopen>(</span><span class="mord mathnormal">x</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=mclose>)</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class=mord><span class="mord mathnormal" style=margin-right:0.13889em>F</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:-0.1389em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mopen>(</span><span class="mord mathnormal">x</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=mclose>)</span></span></span><span style=top:-1.66em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mspace style=margin-right:2.8453em></span><span class=mopen>(</span><span class=mord><span class="mord mathnormal">x</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0359em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mclose>)</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class=mord><span class="mord mathnormal" style=margin-right:0.13889em>F</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.1389em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span><span class="mord mathnormal mtight">ina</span><span class="mord mathnormal mtight" style=margin-right:0.01968em>l</span></span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mopen>(</span><span class="mord mathnormal">x</span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=mclose>)</span></span></span><span style=top:-0.16em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mspace style=margin-right:2.8453em></span><span class="mord mathnormal">c</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span><span class=mopen>(</span><span class="mord mathnormal">c</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>+</span><span class=mspace style=margin-right:0.2222em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mclose>)</span><span class=mord>/2</span></span></span><span style=top:1.34em><span class=pstrut style=height:3em></span><span class=mord><span class=mord></span><span class=mspace style=margin-right:2.8453em></span><span class="mord text"><span class=mord>plot</span></span><span class=mopen>(</span><span class=mord><span class="mord mathnormal">x</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0359em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mclose>)</span><span class="mord text"><span class=mord> if iterations</span></span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>></span><span class=mspace style=margin-right:0.2778em></span><span class=mord>20</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:5em><span></span></span></span></span></span></span></span></span></span></span></span>
|
||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=color-speed>Color speed<a href=#color-speed class=hash-link aria-label="Direct link to Color speed" title="Direct link to Color speed"></a></h3>
|
||
<div class="theme-admonition theme-admonition-warning admonition_xJq3 alert alert--warning"><div class=admonitionHeading_Gvgb><span class=admonitionIcon_Rf37><svg viewBox="0 0 16 16"><path fill-rule=evenodd d="M8.893 1.5c-.183-.31-.52-.5-.887-.5s-.703.19-.886.5L.138 13.499a.98.98 0 0 0 0 1.001c.193.31.53.501.886.501h13.964c.367 0 .704-.19.877-.5a1.03 1.03 0 0 0 .01-1.002L8.893 1.5zm.133 11.497H6.987v-2.003h2.039v2.003zm0-3.004H6.987V5.987h2.039v4.006z"/></svg></span>warning</div><div class=admonitionContent_BuS1><p>Color speed isn't introduced in the Fractal Flame Algorithm paper.<p>It is included here because <a href=https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/variations.c#L2140 target=_blank rel="noopener noreferrer"><code>flam3</code> implements it</a>,
|
||
and because it's fun to play with.</div></div>
|
||
<p>Next, we'll add a parameter to each transform that controls how much it changes the current color.
|
||
This is known as the "color speed" (<span class=katex><span class=katex-mathml><math><semantics><mrow><msub><mi>s</mi><mi>i</mi></msub></mrow><annotation encoding=application/x-tex>s_i</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.5806em;vertical-align:-0.15em></span><span class=mord><span class="mord mathnormal">s</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span></span></span></span>):</p>
|
||
<span class=katex-display><span class=katex><span class=katex-mathml><math display=block><semantics><mrow><mi>c</mi><mo>=</mo><mi>c</mi><mo>⋅</mo><mo stretchy=false>(</mo><mn>1</mn><mo>−</mo><msub><mi>s</mi><mi>i</mi></msub><mo stretchy=false>)</mo><mo>+</mo><msub><mi>c</mi><mi>i</mi></msub><mo>⋅</mo><msub><mi>s</mi><mi>i</mi></msub></mrow><annotation encoding=application/x-tex>c = c \cdot (1 - s_i) + c_i \cdot s_i</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.4306em></span><span class="mord mathnormal">c</span><span class=mspace style=margin-right:0.2778em></span><span class=mrel>=</span><span class=mspace style=margin-right:0.2778em></span></span><span class=base><span class=strut style=height:0.4445em></span><span class="mord mathnormal">c</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span></span><span class=base><span class=strut style=height:1em;vertical-align:-0.25em></span><span class=mopen>(</span><span class=mord>1</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>−</span><span class=mspace style=margin-right:0.2222em></span></span><span class=base><span class=strut style=height:1em;vertical-align:-0.25em></span><span class=mord><span class="mord mathnormal">s</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mclose>)</span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>+</span><span class=mspace style=margin-right:0.2222em></span></span><span class=base><span class=strut style=height:0.5945em;vertical-align:-0.15em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span><span class=mspace style=margin-right:0.2222em></span><span class=mbin>⋅</span><span class=mspace style=margin-right:0.2222em></span></span><span class=base><span class=strut style=height:0.5806em;vertical-align:-0.15em></span><span class=mord><span class="mord mathnormal">s</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3117em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.15em><span></span></span></span></span></span></span></span></span></span></span>
|
||
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|
||
<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">mixColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> color1</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> color2</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colorSpeed</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> color1 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">-</span><span class="token plain"> colorSpeed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> color2 </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> colorSpeed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<p>Color speed values work just like transform weights. A value of 1
|
||
means we take the transform color and ignore the previous color state.
|
||
A value of 0 means we keep the current color state and ignore the
|
||
transform color.</p>
|
||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=palette>Palette<a href=#palette class=hash-link aria-label="Direct link to Palette" title="Direct link to Palette"></a></h3>
|
||
<p>Now, we need to map the color coordinate to a pixel color. Fractal flames typically use
|
||
256 colors (each color has 3 values - red, green, blue) to define a palette.
|
||
The color coordinate then becomes an index into the palette.</p>
|
||
<p>There's one small complication: the color coordinate is continuous, but the palette
|
||
uses discrete colors. How do we handle situations where the color coordinate is
|
||
"in between" the colors of our palette?</p>
|
||
<p>One way to handle this is a step function. In the code below, we multiply the color coordinate
|
||
by the number of colors in the palette, then truncate that value. This gives us a discrete index:</p>
|
||
<!-- -->
|
||
<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">colorFromPalette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colorIndex</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> numColors </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">length </span><span class="token operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> paletteIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">floor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colorIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">numColors</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">paletteIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// red</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">paletteIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// green</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">paletteIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token comment" style="color:hsl(230, 4%, 64%)">// blue</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<details class="details_lb9f alert alert--info details_b_Ee" data-collapsed=true><summary>As an alternative...</summary><div><div class=collapsibleContent_i85q><p>...you could interpolate between colors in the palette.
|
||
For example, <code>flam3</code> uses <a href=https://github.com/scottdraves/flam3/blob/7fb50c82e90e051f00efcc3123d0e06de26594b2/rect.c#L483-L486 target=_blank rel="noopener noreferrer">linear interpolation</a></div></div></details>
|
||
<p>In the diagram below, each color in the palette is plotted on a small vertical strip.
|
||
Putting the strips side by side shows the full palette used by the reference parameters:</p>
|
||
<!-- -->
|
||
<div style=width:100%;height:40></div>
|
||
<h3 class="anchor anchorWithStickyNavbar_LWe7" id=plotting>Plotting<a href=#plotting class=hash-link aria-label="Direct link to Plotting" title="Direct link to Plotting"></a></h3>
|
||
<p>We're now ready to plot our <span class=katex><span class=katex-mathml><math><semantics><mrow><mo stretchy=false>(</mo><msub><mi>x</mi><mi>f</mi></msub><mo separator=true>,</mo><msub><mi>y</mi><mi>f</mi></msub><mo separator=true>,</mo><msub><mi>c</mi><mi>f</mi></msub><mo stretchy=false>)</mo></mrow><annotation encoding=application/x-tex>(x_f,y_f,c_f)</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:1.0361em;vertical-align:-0.2861em></span><span class=mopen>(</span><span class=mord><span class="mord mathnormal">x</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord><span class="mord mathnormal" style=margin-right:0.03588em>y</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:-0.0359em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mpunct>,</span><span class=mspace style=margin-right:0.1667em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span><span class=mclose>)</span></span></span></span> coordinates. This time, we'll use a histogram
|
||
for each color channel (red, green, blue, alpha). After translating from color coordinate (<span class=katex><span class=katex-mathml><math><semantics><mrow><msub><mi>c</mi><mi>f</mi></msub></mrow><annotation encoding=application/x-tex>c_f</annotation></semantics></math></span><span class=katex-html aria-hidden=true><span class=base><span class=strut style=height:0.7167em;vertical-align:-0.2861em></span><span class=mord><span class="mord mathnormal">c</span><span class=msupsub><span class="vlist-t vlist-t2"><span class=vlist-r><span class=vlist style=height:0.3361em><span style=top:-2.55em;margin-left:0em;margin-right:0.05em><span class=pstrut style=height:2.7em></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style=margin-right:0.10764em>f</span></span></span></span><span class=vlist-s></span></span><span class=vlist-r><span class=vlist style=height:0.2861em><span></span></span></span></span></span></span></span></span></span>)
|
||
to RGB value, add that to the histogram:</p>
|
||
<!-- -->
|
||
<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> Props </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">as</span><span class="token plain"> ChaosGameFinalProps </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../2-transforms/chaosGameFinal"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> randomBiUnit </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/randomBiUnit"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> randomChoice </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/randomChoice"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> camera</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> histIndex </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"../src/camera"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> colorFromPalette </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"./colorFromPalette"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> mixColor </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"./mixColor"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">import</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"> paintColor </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">from</span><span class="token plain"> </span><span class="token string" style="color:hsl(119, 34%, 47%)">"./paintColor"</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> quality </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">15</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line code-block-hidden" style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> step </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">100_000</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">type</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">TransformColor</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> color</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colorSpeed</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">type</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">Props</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> ChaosGameFinalProps </span><span class="token operator" style="color:hsl(221, 87%, 60%)">&</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colors</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> TransformColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalColor</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> TransformColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">chaosGameColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> transforms</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> final</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> colors</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalColor</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> Props</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixels </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> width </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> imgRed </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token generic-function function" style="color:hsl(221, 87%, 60%)">Array</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token generic-function generic class-name builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)">></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">fill</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> imgGreen </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token generic-function function" style="color:hsl(221, 87%, 60%)">Array</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token generic-function generic class-name builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)">></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">fill</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> imgBlue </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token generic-function function" style="color:hsl(221, 87%, 60%)">Array</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token generic-function generic class-name builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)">></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">fill</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> imgAlpha </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token generic-function function" style="color:hsl(221, 87%, 60%)">Array</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token generic-function generic class-name builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token generic-function generic class-name operator" style="color:hsl(221, 87%, 60%)">></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">fill</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token function-variable function" style="color:hsl(221, 87%, 60%)">plotColor</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> x</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> y</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> c</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=></span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> pixelY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">camera</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelX </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelX </span><span class="token operator" style="color:hsl(221, 87%, 60%)">>=</span><span class="token plain"> width </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelY </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">||</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> pixelY </span><span class="token operator" style="color:hsl(221, 87%, 60%)">>=</span><span class="token plain"> width</span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> hIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">histIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">pixelX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> pixelY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">r</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> g</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> b</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">colorFromPalette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">palette</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> c</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgRed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">hIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+=</span><span class="token plain"> r</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgGreen</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">hIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+=</span><span class="token plain"> g</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgBlue</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">hIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+=</span><span class="token plain"> b</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgAlpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">hIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomBiUnit</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomBiUnit</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> c </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">random</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> iterations </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> quality </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> iterations</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i</span><span class="token operator" style="color:hsl(221, 87%, 60%)">++</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">transformIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> transform</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">randomChoice</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">transforms</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">transform</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> transformColor </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> colors</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">transformIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> c </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">mixColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> c</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> transformColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">color</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> transformColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">colorSpeed</span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">finalX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> finalY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">final</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">x</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> y</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> finalC </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">mixColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> c</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">color</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">colorSpeed</span><br></span><span class="token-line theme-code-block-highlighted-line" style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">></span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">20</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">plotColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalX</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalY</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> finalC</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">if</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">%</span><span class="token plain"> step </span><span class="token operator" style="color:hsl(221, 87%, 60%)">===</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">yield</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paintColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgRed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgGreen</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgBlue</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgAlpha</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">yield</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paintColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgRed</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgGreen</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgBlue</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> imgAlpha</span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
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<p>Finally, painting the image. With tone mapping, logarithms scale the image brightness to match
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how it is perceived. With color, we use a similar method, but scale each color channel
|
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by the alpha channel:</p>
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<div class="language-typescript codeBlockContainer_Ckt0 theme-code-block" style="--prism-background-color:hsl(230, 1%, 98%);--prism-color:hsl(230, 8%, 24%)"><div class=codeBlockContent_biex><pre tabindex=0 class="prism-code language-typescript codeBlock_bY9V thin-scrollbar" style="background-color:hsl(230, 1%, 98%);color:hsl(230, 8%, 24%)"><code class=codeBlockLines_e6Vv><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token keyword" style="color:hsl(301, 63%, 40%)">export</span><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">function</span><span class="token plain"> </span><span class="token function" style="color:hsl(221, 87%, 60%)">paintColor</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> width</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> height</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> red</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> green</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> blue</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> alpha</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> </span><span class="token builtin" style="color:hsl(119, 34%, 47%)">number</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token operator" style="color:hsl(221, 87%, 60%)">:</span><span class="token plain"> ImageData </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixels </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> width </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> img </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">new</span><span class="token plain"> </span><span class="token class-name" style="color:hsl(35, 99%, 36%)">ImageData</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">width</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">,</span><span class="token plain"> height</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">for</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token keyword" style="color:hsl(301, 63%, 40%)">let</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)"><</span><span class="token plain"> pixels</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"> i</span><span class="token operator" style="color:hsl(221, 87%, 60%)">++</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">{</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> scale </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> Math</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token function" style="color:hsl(221, 87%, 60%)">log10</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">alpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">/</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">(</span><span class="token plain">alpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1.5</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">)</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> i </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">4</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> rVal </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> red</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> scale </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> rVal</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> gVal </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> green</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> scale </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">1</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> gVal</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> bVal </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> blue</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> scale </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">2</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> bVal</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">const</span><span class="token plain"> aVal </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> alpha</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">i</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> scale </span><span class="token operator" style="color:hsl(221, 87%, 60%)">*</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">0xff</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">.</span><span class="token plain">data</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">[</span><span class="token plain">pixelIndex </span><span class="token operator" style="color:hsl(221, 87%, 60%)">+</span><span class="token plain"> </span><span class="token number" style="color:hsl(35, 99%, 36%)">3</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">]</span><span class="token plain"> </span><span class="token operator" style="color:hsl(221, 87%, 60%)">=</span><span class="token plain"> aVal</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain" style=display:inline-block></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"> </span><span class="token keyword" style="color:hsl(301, 63%, 40%)">return</span><span class="token plain"> img</span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">;</span><span class="token plain"></span><br></span><span class=token-line style="color:hsl(230, 8%, 24%)"><span class="token plain"></span><span class="token punctuation" style="color:hsl(119, 34%, 47%)">}</span><br></span></code></pre><div class=buttonGroup__atx><button type=button aria-label="Copy code to clipboard" title=Copy class=clean-btn><span class=copyButtonIcons_eSgA aria-hidden=true><svg viewBox="0 0 24 24" class=copyButtonIcon_y97N><path fill=currentColor d="M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z"/></svg><svg viewBox="0 0 24 24" class=copyButtonSuccessIcon_LjdS><path fill=currentColor d=M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z /></svg></span></button></div></div></div>
|
||
<p>And now, at long last, a full-color fractal flame:</p>
|
||
<!-- -->
|
||
<center><center><div style=width:75%;aspect-ratio:1/1></div></center></center>
|
||
<h2 class="anchor anchorWithStickyNavbar_LWe7" id=summary>Summary<a href=#summary class=hash-link aria-label="Direct link to Summary" title="Direct link to Summary"></a></h2>
|
||
<p>Tone mapping is the second major innovation of the fractal flame algorithm.
|
||
By tracking how often the chaos game encounters each pixel, we can adjust
|
||
brightness/transparency to reduce the visual "graining" of previous images.</p>
|
||
<p>Next, introducing a third coordinate to the chaos game makes color images possible,
|
||
the third major innovation of the fractal flame algorithm. Using a continuous
|
||
color scale and color palette adds a splash of excitement to the image.</p>
|
||
<p>The Fractal Flame Algorithm paper goes on to describe more techniques
|
||
not covered here. For example, image quality can be improved with density estimation
|
||
and filtering. New parameters can be generated by "mutating" existing
|
||
fractal flames. And fractal flames can even be animated to produce videos!</p>
|
||
<p>That said, I think this is a good place to wrap up. We went from
|
||
an introduction to the mathematics of fractal systems all the way to
|
||
generating full-color images. Fractal flames are a challenging topic,
|
||
but it's extremely rewarding to learn about how they work.</div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Blog post page navigation"><a class="pagination-nav__link pagination-nav__link--prev" href=/2024/11/playing-with-fire-transforms><div class=pagination-nav__sublabel>Older post</div><div class=pagination-nav__label>Playing with fire: Transforms and variations</div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href=#image-histograms class="table-of-contents__link toc-highlight">Image histograms</a><li><a href=#tone-mapping class="table-of-contents__link toc-highlight">Tone mapping</a><li><a href=#color class="table-of-contents__link toc-highlight">Color</a><ul><li><a href=#color-coordinate class="table-of-contents__link toc-highlight">Color coordinate</a><li><a href=#color-speed class="table-of-contents__link toc-highlight">Color speed</a><li><a href=#palette class="table-of-contents__link toc-highlight">Palette</a><li><a href=#plotting class="table-of-contents__link toc-highlight">Plotting</a></ul><li><a href=#summary class="table-of-contents__link toc-highlight">Summary</a></ul></div></div></div></div></div><footer class=footer><div class="container container-fluid"><div class="footer__bottom text--center"><div class=footer__copyright>Copyright © 2024 Bradlee Speice</div></div></div></footer></div> |