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Finish a first draft

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Bradlee Speice
2024-12-14 16:55:54 -05:00
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blog/2024-11-15-playing-with-fire/2-transforms/index.mdx
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@ -180,9 +180,23 @@ import FlamePost from "./FlamePost";
## Final transforms
Our last step is to introduce a "final transform" ($F_{final}$) that is applied
regardless of which transform function we're using. It works just like a normal transform
regardless of which transform the chaos game selects. It works just like a normal transform
(composition of affine transform, variation blend, and post transform),
but it doesn't change the chaos game state:
but it doesn't change the chaos game state.
With that in place, our chaos game algorithm changes slightly:
$$
\begin{align*}
&(x, y) = \text{random point in the bi-unit square} \\
&\text{iterate } \{ \\
&\hspace{1cm} i = \text{random integer from 0 to } n - 1 \\
&\hspace{1cm} (x,y) = F_i(x,y) \\
&\hspace{1cm} (x_f,y_f) = F_{final}(x,y) \\
&\hspace{1cm} \text{plot}(x_f,y_f) \text{ if iterations} > 20 \\
\}
\end{align*}
$$
import chaosGameFinalSource from "!!raw-loader!./chaosGameFinal"
@ -198,4 +212,4 @@ Variations are the fractal flame algorithm's first major innovation over previou
Blending variation functions and post/final transforms allows us to generate interesting images.
However, the images themselves are grainy and unappealing. In the next post, we'll clean up
the quality and add color.
the image quality and add some color.