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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Generative Design</title>
<link rel="stylesheet" href="style.css">
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
<script type="text/javascript" id="MathJax-script" async
src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js">
</script>
<script src="pan_zoom_canvas.js"></script>
<script src="mandelbrot_webgl/fractal_webgl.js"></script>
<script src="colormaps.js"></script>
<script src="random_walk.js"></script>
<script src="unstable.js"></script>
</head>
<body>
<div class="container">
<!-- page content -->
<h1>Generative algorithms</h1>
<h2>Fractals - Mandelbrot</h2>
<p>The Mandelbrot fractal is a fascinating mathematical set that exhibits
intricate and infinitely complex patterns. It was discovered and popularized
by the mathematician Benoît Mandelbrot in the 1970s</p>
<p>The Mandelbrot set is defined in the complex plane, which consists of numbers
with real and imaginary parts. Each point in the complex plane represents a
different complex number. For a given complex number \(c\), the behavior of the sequence
\(z_{n+1}=z_n^{2}+c\) is studied.</p>
<p>The interesting and visually stunning aspect of the Mandelbrot set lies in the points
that are outside the set. The iterations can lead to chaotic behavior, generating intricate
patterns with intricate detail, no matter how closely you zoom in. These patterns exhibit
self-similarity, meaning that smaller and smaller portions of the set resemble the overall
shape of the set.</p>
<p>When graphically visualizing the Mandelbrot set, points inside the set are usually colored
black, while the colors of the points outside the set are determined based on the number
of iterations required to reach an escape condition or the magnitude of divergence.</p>
<!--button class="button" onclick="load">Play me</button-->
<br>
<canvas id="canvas_fractals" width="1000" height="400"></canvas>
<script>
const canvas = new FractalGL("canvas_fractals");
</script>
<h2>Random walk</h2>
<br>
<canvas id="random_walk" width="1000" height="400"></canvas>
<script>
const canvas2 = new RandomWalk("random_walk");
</script>
<h2>Unstable</h2>
<br>
<canvas id="unstable" width="1000" height="400"></canvas>
<script>
const canvas3 = new Unstable("unstable");
</script>
</div>
</body>
</html>