Post/final transform implementation

blog/2024-11-15-playing-with-fire/1-introduction/GasketWeighted.tsx

@@ -28,8 +28,8 @@ export default function GasketWeighted() {
 
     const weightInput = (title, weight, setWeight) => (
         <>
-            <div className={styles.inputDiv}>
+            <div className={styles.inputElement}>
-                <p><TeX>{title}</TeX> weight:<span style={{float: 'right'}}>{weight}</span></p>
+                <p><TeX>{title}</TeX> weight: {weight}</p>
                 <input type={'range'} min={0} max={1} step={.01} style={{width: '100%'}} value={weight}
                     onInput={e => setWeight(Number(e.currentTarget.value))}/>
             </div>
@@ -38,7 +38,7 @@ export default function GasketWeighted() {
 
     return (
         <>
-            <div style={{paddingTop: '1em', display: 'grid', gridTemplateColumns: 'auto auto auto'}}>
+            <div className={styles.inputGroup} style={{display: 'grid', gridTemplateColumns: 'auto auto auto'}}>
                 {weightInput("F_0", f0Weight, setF0Weight)}
                 {weightInput("F_1", f1Weight, setF1Weight)}
                 {weightInput("F_2", f2Weight, setF2Weight)}

blog/2024-11-15-playing-with-fire/2-transforms/CoefEditor.tsx

@@ -0,0 +1,48 @@
+import TeX from "@matejmazur/react-katex";
+import {Coefs} from "../src/coefs";
+
+import styles from "../src/css/styles.module.css";
+
+export interface Props {
+    title: String;
+    isPost: boolean;
+    coefs: Coefs;
+    setCoefs: (coefs: Coefs) => void;
+}
+export const CoefEditor = ({title, isPost, coefs, setCoefs}: Props) => {
+    return (
+        <div className={styles.inputGroup} style={{display: 'grid', gridTemplateColumns: 'auto auto auto'}}>
+            <p className={styles.inputTitle} style={{gridColumn: '1/-1'}}>{title}</p>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\alpha</TeX> : 'a'}: {coefs.a}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.a}
+                       onInput={e => setCoefs({...coefs, a: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\beta</TeX> : 'b'}: {coefs.b}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.b}
+                       onInput={e => setCoefs({...coefs, b: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\gamma</TeX> : 'c'}: {coefs.c}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.c}
+                       onInput={e => setCoefs({...coefs, c: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\delta</TeX> : 'd'}: {coefs.d}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.d}
+                       onInput={e => setCoefs({...coefs, d: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\epsilon</TeX> : 'e'}: {coefs.e}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.e}
+                       onInput={e => setCoefs({...coefs, e: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <p>{isPost ? <TeX>\zeta</TeX> : 'f'}: {coefs.f}</p>
+                <input type={'range'} min={0} max={2} step={0.01} style={{width: '100%'}} value={coefs.f}
+                       onInput={e => setCoefs({...coefs, f: Number(e.currentTarget.value)})}/>
+            </div>
+        </div>
+    )
+}

blog/2024-11-15-playing-with-fire/2-transforms/FlameBlend.tsx

@@ -1,15 +1,7 @@
 import {useContext, useEffect, useState} from "react";
-import { blend } from "./blend";
-import { applyCoefs, Coefs } from "../src/coefs"
-import {randomBiUnit} from "../src/randomBiUnit";
-import {linear} from "../src/linear";
-import {julia} from "../src/julia";
-import {popcorn} from "../src/popcorn";
-import {pdj} from "../src/pdj";
-import {Variation} from "../src/variation";
 import {Transform} from "../src/transform";
 import {
-    pdjParams,
+    identityCoefs,
     xform1Coefs,
     xform1Weight,
     xform2Coefs,
@@ -17,26 +9,15 @@ import {
     xform3Coefs,
     xform3Weight
 } from "../src/params";
-import {randomChoice} from "../src/randomChoice";
-import {plotBinary} from "../src/plotBinary"
 import {PainterContext} from "../src/Canvas"
-
+import {buildBlend, buildTransform} from "./buildTransform"
-import styles from "../src/css/styles.module.css"
+import {chaosGameFinal} from "./chaosGameFinal"
-
+import {VariationEditor, VariationProps} from "./VariationEditor"
-type VariationBlend = {
-    linear: number,
-    julia: number,
-    popcorn: number,
-    pdj: number
-}
 
 export default function FlameBlend() {
-    const quality = 2;
-    const step = 5000;
-
     const {width, height, setPainter} = useContext(PainterContext);
 
-    const xform1Default: VariationBlend = {
+    const xform1Default: VariationProps = {
         linear: 0,
         julia: 1,
         popcorn: 0,
@@ -44,7 +25,7 @@ export default function FlameBlend() {
     }
     const [xform1Variations, setXform1Variations] = useState(xform1Default)
 
-    const xform2Default: VariationBlend = {
+    const xform2Default: VariationProps = {
         linear: 1,
         julia: 0,
         popcorn: 1,
@@ -52,7 +33,7 @@ export default function FlameBlend() {
     }
     const [xform2Variations, setXform2Variations] = useState(xform2Default)
 
-    const xform3Default: VariationBlend = {
+    const xform3Default: VariationProps = {
         linear: 0,
         julia: 0,
         popcorn: 0,
@@ -60,80 +41,21 @@ export default function FlameBlend() {
     }
     const [xform3Variations, setXform3Variations] = useState(xform3Default)
 
-    function buildTransform(coefs: Coefs, variations: VariationBlend): Transform {
+    // Cheating a bit here; for purposes of code re-use, use the post- and final-transform-enabled chaos game,
-        return (x: number, y: number) => {
+    // and swap in identity components for each
-            const [varX, varY] = applyCoefs(x, y, coefs);
+    const identityXform: Transform = (x, y) => [x, y];
-            const varFunctions: [number, Variation][] = [
-                [variations.linear, linear],
-                [variations.julia, julia],
-                [variations.popcorn, popcorn(coefs)],
-                [variations.pdj, pdj(pdjParams)]
-            ]
 
-            return blend(varX, varY, varFunctions);
+    useEffect(() => setPainter(chaosGameFinal(width, height, [
-        }
+        [xform1Weight, buildTransform(xform1Coefs, buildBlend(xform1Coefs, xform1Variations))],
-    }
+        [xform2Weight, buildTransform(xform2Coefs, buildBlend(xform2Coefs, xform2Variations))],
-
+        [xform3Weight, buildTransform(xform3Coefs, buildBlend(xform3Coefs, xform3Variations))]
-    const image = new ImageData(width, height);
+    ], identityXform)), [xform1Variations, xform2Variations, xform3Variations]);
-    function* chaosGame() {
-        let [x, y] = [randomBiUnit(), randomBiUnit()];
-        const transforms: [number, Transform][] = [
-            [xform1Weight, buildTransform(xform1Coefs, xform1Variations)],
-            [xform2Weight, buildTransform(xform2Coefs, xform2Variations)],
-            [xform3Weight, buildTransform(xform3Coefs, xform3Variations)]
-        ]
-
-        const iterations = quality * image.width * image.height;
-        for (let i = 0; i < iterations; i++) {
-            let [_, transform] = randomChoice(transforms);
-            [x, y] = transform(x, y);
-
-            if (i > 20)
-                plotBinary(x, y, image);
-
-            if (i % step === 0) {
-                console.log(`Checking in; iterations=${i}`)
-                yield image;
-            }
-        }
-
-        yield image;
-    }
-    useEffect(() => setPainter(chaosGame()), [xform1Variations, xform2Variations, xform3Variations]);
-
-    const variationEditor = (title, variations, setVariations) => {
-        return (
-            <>
-                <p style={{gridColumn: '1/-1'}}>{title}:</p>
-                <div className={styles.inputDiv}>
-                    <p>Linear: {variations.linear}</p>
-                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.linear}
-                           onInput={e => setVariations({...variations, linear: Number(e.currentTarget.value)})}/>
-                </div>
-                <div className={styles.inputDiv}>
-                    <p>Julia: {variations.julia}</p>
-                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.julia}
-                           onInput={e => setVariations({...variations, julia: Number(e.currentTarget.value)})}/>
-                </div>
-                <div className={styles.inputDiv}>
-                    <p>Popcorn: {variations.popcorn}</p>
-                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.popcorn}
-                           onInput={e => setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/>
-                </div>
-                <div className={styles.inputDiv}>
-                    <p>PDJ: {variations.pdj}</p>
-                    <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.pdj}
-                           onInput={e => setVariations({...variations, pdj: Number(e.currentTarget.value)})}/>
-                </div>
-            </>
-        )
-    }
 
     return (
-        <div style={{paddingTop: '1em', display: 'grid', gridTemplateColumns: 'auto auto auto auto'}}>
+        <>
-            {variationEditor("Transform 1", xform1Variations, setXform1Variations)}
+            <VariationEditor title={"Transform 1"} variations={xform1Variations} setVariations={setXform1Variations}/>
-            {variationEditor("Transform 2", xform2Variations, setXform2Variations)}
+            <VariationEditor title={"Transform 2"} variations={xform2Variations} setVariations={setXform2Variations}/>
-            {variationEditor("Transform 3", xform3Variations, setXform3Variations)}
+            <VariationEditor title={"Transform 3"} variations={xform3Variations} setVariations={setXform3Variations}/>
-        </div>
+        </>
     )
 }

blog/2024-11-15-playing-with-fire/2-transforms/FlameFinal.tsx

@@ -0,0 +1,64 @@
+import {useContext, useEffect, useState} from "react";
+import {Coefs} from "../src/coefs"
+import {
+    xform1Coefs,
+    xform1Weight,
+    xform1Variations,
+    xform1CoefsPost,
+    xform2Coefs,
+    xform2Weight,
+    xform2Variations,
+    xform2CoefsPost,
+    xform3Coefs,
+    xform3Weight,
+    xform3Variations,
+    xform3CoefsPost,
+    xformFinalCoefs as xformFinalCoefsDefault,
+    xformFinalCoefsPost as xformFinalCoefsPostDefault,
+} from "../src/params";
+import {PainterContext} from "../src/Canvas"
+import {buildBlend, buildTransform} from "./buildTransform";
+import {transformPost} from "./post";
+import {chaosGameFinal} from "./chaosGameFinal"
+import {VariationEditor, VariationProps} from "./VariationEditor";
+import {CoefEditor} from "./CoefEditor";
+import {Transform} from "../src/transform";
+
+export default function FlameFinal() {
+    const {width, height, setPainter} = useContext(PainterContext);
+
+    const [xformFinalCoefs, setXformFinalCoefs] = useState<Coefs>(xformFinalCoefsDefault);
+
+    const xformFinalVariationsDefault: VariationProps = {
+        linear: 0,
+        julia: 1,
+        popcorn: 0,
+        pdj: 0
+    }
+    const [xformFinalVariations, setXformFinalVariations] = useState<VariationProps>(xformFinalVariationsDefault);
+
+    const [xformFinalCoefsPost, setXformFinalCoefsPost] = useState<Coefs>(xformFinalCoefsPostDefault);
+
+    useEffect(() => {
+        const transforms: [number, Transform][] = [
+            [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)],
+            [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)],
+            [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)]
+        ];
+
+        const finalBlend = buildBlend(xformFinalCoefs, xformFinalVariations);
+        const finalTransform = buildTransform(xformFinalCoefs, finalBlend);
+        const finalPost = transformPost(finalTransform, xformFinalCoefsPost);
+
+        setPainter(chaosGameFinal(width, height, transforms, finalPost));
+    }, [xformFinalCoefs, xformFinalVariations, xformFinalCoefsPost]);
+
+    return (
+        <>
+            <CoefEditor title={"Final Transform"} isPost={false} coefs={xformFinalCoefs} setCoefs={setXformFinalCoefs}/>
+            <VariationEditor title={"Final Transform Variations"} variations={xformFinalVariations}
+                             setVariations={setXformFinalVariations}/>
+            <CoefEditor title={"Final Transform Post"} isPost={true} coefs={xformFinalCoefsPost} setCoefs={setXformFinalCoefsPost}/>
+        </>
+    )
+}

blog/2024-11-15-playing-with-fire/2-transforms/FlamePost.tsx

@@ -0,0 +1,46 @@
+import {useContext, useEffect, useState} from "react";
+import {Coefs} from "../src/coefs"
+import {Transform} from "../src/transform";
+import {
+    xform1Coefs,
+    xform1Weight,
+    xform1Variations,
+    xform1CoefsPost as xform1CoefsPostDefault,
+    xform2Coefs,
+    xform2Weight,
+    xform2Variations,
+    xform2CoefsPost as xform2CoefsPostDefault,
+    xform3Coefs,
+    xform3Weight,
+    xform3Variations,
+    xform3CoefsPost as xform3CoefsPostDefault
+} from "../src/params";
+import {PainterContext} from "../src/Canvas"
+import {chaosGameFinal} from "./chaosGameFinal"
+import {CoefEditor} from "./CoefEditor"
+import {transformPost} from "./post";
+import {buildTransform} from "./buildTransform";
+
+export default function FlamePost() {
+    const {width, height, setPainter} = useContext(PainterContext);
+
+    const [xform1CoefsPost, setXform1PostCoefs] = useState<Coefs>(xform1CoefsPostDefault);
+    const [xform2CoefsPost, setXform2PostCoefs] = useState<Coefs>(xform2CoefsPostDefault);
+    const [xform3CoefsPost, setXform3PostCoefs] = useState<Coefs>(xform3CoefsPostDefault);
+
+    const identityXform: Transform = (x, y) => [x, y];
+
+    useEffect(() => setPainter(chaosGameFinal(width, height, [
+        [xform1Weight, transformPost(buildTransform(xform1Coefs, xform1Variations), xform1CoefsPost)],
+        [xform2Weight, transformPost(buildTransform(xform2Coefs, xform2Variations), xform2CoefsPost)],
+        [xform3Weight, transformPost(buildTransform(xform3Coefs, xform3Variations), xform3CoefsPost)]
+    ], identityXform)), [xform1CoefsPost, xform2CoefsPost, xform3CoefsPost]);
+
+    return (
+        <>
+            <CoefEditor title={"Transform 1 Post"} isPost={true} coefs={xform1CoefsPost} setCoefs={setXform1PostCoefs}/>
+            <CoefEditor title={"Transform 2 Post"} isPost={true} coefs={xform2CoefsPost} setCoefs={setXform2PostCoefs}/>
+            <CoefEditor title={"Transform 3 Post"} isPost={true} coefs={xform3CoefsPost} setCoefs={setXform3PostCoefs}/>
+        </>
+    )
+}

blog/2024-11-15-playing-with-fire/2-transforms/VariationEditor.tsx

@@ -0,0 +1,42 @@
+import styles from "../src/css/styles.module.css"
+
+export interface VariationProps {
+    linear: number;
+    julia: number;
+    popcorn: number;
+    pdj: number;
+}
+
+export interface Props {
+    title: String;
+    variations: VariationProps;
+    setVariations: (variations: VariationProps) => void;
+}
+
+export const VariationEditor = ({title, variations, setVariations}: Props) => {
+    return (
+        <div className={styles.inputGroup} style={{display: 'grid', gridTemplateColumns: 'auto auto auto auto'}}>
+            <p className={styles.inputTitle} style={{gridColumn: '1/-1'}}>{title}</p>
+            <div className={styles.inputElement}>
+                <span>Linear: {variations.linear}</span>
+                <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.linear}
+                       onInput={e => setVariations({...variations, linear: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <span>Julia: {variations.julia}</span>
+                <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.julia}
+                       onInput={e => setVariations({...variations, julia: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <span>Popcorn: {variations.popcorn}</span>
+                <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.popcorn}
+                       onInput={e => setVariations({...variations, popcorn: Number(e.currentTarget.value)})}/>
+            </div>
+            <div className={styles.inputElement}>
+                <span>PDJ: {variations.pdj}</span>
+                <input type={'range'} min={0} max={1} step={0.01} style={{width: '100%'}} value={variations.pdj}
+                       onInput={e => setVariations({...variations, pdj: Number(e.currentTarget.value)})}/>
+            </div>
+        </div>
+    )
+}

blog/2024-11-15-playing-with-fire/2-transforms/blend.ts

@@ -1,7 +1,10 @@
 // hidden-start
-import { Variation } from "../src/variation"
+import {VariationBlend} from "../src/variationBlend";
 // hidden-end
-export function blend(x: number, y: number, variations: [number, Variation][]): [number, number] {
+export function blend(
+    x: number,
+    y: number,
+    variations: VariationBlend): [number, number] {
     let [finalX, finalY] = [0, 0];
 
     for (const [weight, variation] of variations) {

blog/2024-11-15-playing-with-fire/2-transforms/buildTransform.ts

@@ -0,0 +1,26 @@
+import {applyCoefs, Coefs} from "../src/coefs";
+import {VariationProps} from "./VariationEditor";
+import {Transform} from "../src/transform";
+import {linear} from "../src/linear";
+import {julia} from "../src/julia";
+import {popcorn} from "../src/popcorn";
+import {pdj} from "../src/pdj";
+import {pdjParams} from "../src/params";
+import {blend} from "./blend";
+import {VariationBlend} from "../src/variationBlend";
+
+export function buildBlend(coefs: Coefs, variations: VariationProps): VariationBlend {
+    return [
+        [variations.linear, linear],
+        [variations.julia, julia],
+        [variations.popcorn, popcorn(coefs)],
+        [variations.pdj, pdj(pdjParams)]
+    ]
+}
+
+export function buildTransform(coefs: Coefs, variations: VariationBlend): Transform {
+    return (x: number, y: number) => {
+        [x, y] = applyCoefs(x, y, coefs);
+        return blend(x, y, variations);
+    }
+}

blog/2024-11-15-playing-with-fire/2-transforms/chaosGameFinal.ts

@@ -0,0 +1,29 @@
+// hidden-start
+import { randomBiUnit } from "../src/randomBiUnit";
+import { randomChoice } from "../src/randomChoice";
+import { plotBinary as plot } from "../src/plotBinary"
+import {Transform} from "../src/transform";
+const iterations = 500_000;
+const step = 1000;
+// hidden-end
+export function* chaosGameFinal(width: number, height: number, transforms: [number, Transform][], final: Transform) {
+    let image = new ImageData(width, height);
+    let [x, y] = [randomBiUnit(), randomBiUnit()];
+
+    for (let i = 0; i < iterations; i++) {
+        const [_, transform] = randomChoice(transforms);
+        [x, y] = transform(x, y);
+
+        // highlight-start
+        [x, y] = final(x, y);
+        // highlight-end
+
+        if (i > 20)
+            plot(x, y, image);
+
+        if (i % step === 0)
+            yield image;
+    }
+
+    yield image;
+}

blog/2024-11-15-playing-with-fire/2-transforms/index.mdx

@@ -37,12 +37,14 @@ the general format. For example:
 $$
 \begin{align*}
 F_0(x,y) &= \left({x \over 2}, {y \over 2}\right) \\
-&= (a_0 \cdot x + b_0 \cdot y + c_o, d_0 \cdot x + e_0 \cdot y + f_0) \\
+&= (a_0 \cdot x + b_0 \cdot y + c_0, d_0 \cdot x + e_0 \cdot y + f_0) \\
 & a_0 = 0.5 \hspace{0.2cm} b_0 = 0 \hspace{0.2cm} c_0 = 0 \\
 & d_0 = 0 \hspace{0.2cm} e_0 = 0.5 \hspace{0.2cm} f_0 = 0
 \end{align*}
 $$
 
+TODO: Explain the applyCoefs function
+
 However, these transforms are pretty boring. We can build more exciting images by using additional functions
 within the transform. These "sub-functions" are called "variations":
 
@@ -79,10 +81,10 @@ $$
 r &= \sqrt{x^2 + y^2} \\
 \theta &= \text{arctan}(x / y) \\
 \Omega &= \left\{
-    \begin{array}{lr}
+\begin{array}{lr}
-    0 \hspace{0.4cm} \text{w.p. } 0.5 \\
+0 \hspace{0.4cm} \text{w.p. } 0.5 \\
-    \pi \hspace{0.4cm} \text{w.p. } 0.5 \\
+\pi \hspace{0.4cm} \text{w.p. } 0.5 \\
-    \end{array}
+\end{array}
 \right\} \\
 
 V_{13}(x, y) &= \sqrt{r} \cdot (\text{cos} ( \theta / 2 + \Omega ), \text{sin} ( \theta / 2 + \Omega ))
@@ -123,8 +125,7 @@ import pdjSrc from '!!raw-loader!../src/pdj'
 
 Now, one variation is fun, but we can also combine variations in a single transform by "blending."
 Each variation receives the same $x$ and $y$ inputs, and we add together each variation's $x$ and $y$ outputs.
-We'll also give each variation a weight ($v_j$) that scales the output, which allows us to control
+We'll also give each variation a weight ($v_{ij}$) to control how much it contributes to the transform:
-how much each variation contributes to the transform:
 
 $$
 F_i(x,y) = \sum_{j} v_{ij} V_j(a_i \cdot x + b_i \cdot y + c_i, \hspace{0.2cm} d_i \cdot x + e_i \cdot y + f_i)
@@ -136,7 +137,10 @@ import blendSource from "!!raw-loader!./blend";
 
 <CodeBlock language={'typescript'}>{blendSource}</CodeBlock>
 
-And with that in place, we have enough to render a first full fractal flame:
+And with that in place, we have enough to render a first full fractal flame.
+The sliders below change the variation weights for each transform (the $v_{ij}$ parameters);
+try changing them around to see which parts of the image are controlled by
+each transform.
 
 import BrowserOnly from "@docusaurus/BrowserOnly";
 import Canvas from "../src/Canvas";
@@ -145,3 +149,28 @@ import FlameBlend from "./FlameBlend";
 <Canvas width={500} height={500}>
     <BrowserOnly>{() => <FlameBlend/>}</BrowserOnly>
 </Canvas>
+
+## Post transforms
+
+After variation blending, we apply a second set of transform coordinates.
+
+The fractal flame below starts with the same initial transforms/variations as the previous fractal flame,
+but allows modifying the post-transform coefficients.
+
+$$
+P_i(x, y) = (\alpha_i x + \beta_i y + \gamma_i, \delta_i x + \epsilon_i y + \zeta_i)
+$$
+
+import FlamePost from "./FlamePost";
+
+<Canvas width={500} height={500}>
+    <BrowserOnly>{() => <FlamePost/>}</BrowserOnly>
+</Canvas>
+
+## Final transform
+
+import FlameFinal from "./FlameFinal";
+
+<Canvas width={500} height={500}>
+    <BrowserOnly>{() => <FlameFinal/>}</BrowserOnly>
+</Canvas>

blog/2024-11-15-playing-with-fire/2-transforms/post.ts

@@ -0,0 +1,7 @@
+// hidden-start
+import {Coefs} from "../src/coefs";
+import {Transform} from "../src/transform";
+import {applyCoefs} from "../src/coefs";
+// hidden-end
+export const transformPost = (transform: Transform, coefs: Coefs): Transform =>
+    (x, y): [number, number] => applyCoefs(...transform(x, y), coefs)

blog/2024-11-15-playing-with-fire/src/coefs.ts

@@ -3,7 +3,7 @@ export interface Coefs {
     d: number, e: number, f: number
 }
 
-export function applyCoefs(x: number, y: number, coefs: Coefs) {
+export function applyCoefs(x: number, y: number, coefs: Coefs): [number, number] {
     return [
         (x * coefs.a + y * coefs.b + coefs.c),
         (x * coefs.d + y * coefs.e + coefs.f)

blog/2024-11-15-playing-with-fire/src/css/styles.module.css

@@ -1,4 +1,23 @@
-.inputDiv {
+.inputGroup {
+    padding: .5em;
+    margin: .5em;
+    border: 1px solid;
+    border-radius: var(--ifm-global-radius);
+    border-color: var(--ifm-color-emphasis-500);
+}
+
+.inputTitle {
+    border: 0 solid;
+    border-bottom: 1px solid;
+    border-color: var(--ifm-color-emphasis-500);
+    margin-bottom: .5em;
+}
+
+.inputElement {
     padding-left: .5em;
     padding-right: 1em;
 }
+
+.inputElement > p {
+    margin: 0
+}

blog/2024-11-15-playing-with-fire/src/julia.ts

@@ -3,11 +3,14 @@ import { Variation } from './variation'
 // hidden-end
 export const julia: Variation = (x, y) => {
     const r = Math.sqrt(Math.pow(x, 2) + Math.pow(y, 2));
+
     const theta = Math.atan2(x, y);
     const omega = Math.random() > 0.5 ? 0 : Math.PI;
 
+    const sqrtR = Math.sqrt(r);
+    const thetaVal = theta / 2 + omega;
     return [
-        r * Math.cos(theta / 2 + omega),
+        sqrtR * Math.cos(thetaVal),
-        r * Math.sin(theta / 2 + omega)
+        sqrtR * Math.sin(thetaVal)
     ]
 }

blog/2024-11-15-playing-with-fire/src/params.ts

@@ -4,11 +4,11 @@
  */
 
 import { Coefs } from './coefs';
+import {VariationBlend} from "./variationBlend";
 import { linear } from './linear'
 import { julia } from './julia'
 import { popcorn } from './popcorn'
 import {pdj, PdjParams} from './pdj'
-import {Variation} from "./variation"
 
 export const identityCoefs: Coefs = {
     a: 1, b: 0, c: 0,
@@ -25,7 +25,7 @@ export const xform1Coefs = {
     d: 1.381068, e: -1.381068, f: 0,
 }
 export const xform1CoefsPost = identityCoefs;
-export const xform1Variations = [
+export const xform1Variations: VariationBlend = [
     [1, julia]
 ]
 export const xform1Color = 0;
@@ -39,7 +39,7 @@ export const xform2CoefsPost = {
     a: 1, b: 0, c: 0.241352,
     d: 0, e: 1, f: 0.271521,
 }
-export const xform2Variations = [
+export const xform2Variations: VariationBlend = [
     [1, linear],
     [1, popcorn(xform2Coefs)]
 ]
@@ -51,7 +51,7 @@ export const xform3Coefs = {
     d: 0.740356, e: -1.455964, f: -0.362059,
 }
 export const xform3CoefsPost = identityCoefs;
-export const xform3Variations = [
+export const xform3Variations: VariationBlend = [
     [1, pdj(pdjParams)]
 ];
 export const xform3Color = 0.349;
@@ -61,7 +61,7 @@ export const xformFinalCoefs = {
     d: 0, e: 2, f: 0
 }
 export const xformFinalCoefsPost = identityCoefs;
-export const xformFinalVariations = [
+export const xformFinalVariations: VariationBlend = [
     [1, julia]
 ]
 export const xformFinalColor = 0;

blog/2024-11-15-playing-with-fire/src/variationBlend.ts

@@ -0,0 +1,2 @@
+import {Variation} from "./variation";
+export type VariationBlend = [number, Variation][];