Fractals Fractal Whats and Whys (In a Nutshell) - xbdev.net 2000 - 2024 (c) - Tutorials - Demos - Software, Game Development, Engineering, Data Mining, File Formats,Programming, Machine Learning

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  <title>Sierpinski Triangle</title>
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    function drawTriangle(x, y, size) {
      ctx.beginPath();
      ctx.moveTo(x, y);
      ctx.lineTo(x + size, y);
      ctx.lineTo(x + size / 2, y - Math.sqrt(3) * size / 2);
      ctx.closePath();
      ctx.stroke();
    }

    function drawSierpinski(x, y, size, depth) {
      if (depth === 0) {
        drawTriangle(x, y, size);
      } else {
        const halfSize = size / 2;
        drawSierpinski(x, y, halfSize, depth - 1);
        drawSierpinski(x + halfSize, y, halfSize, depth - 1);
        drawSierpinski(x + halfSize / 2, y - Math.sqrt(3) * halfSize / 2, halfSize, depth - 1);
      }
    }

    drawSierpinski(10, 390, 380, 5);
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Fractal Algorithms
   |
   ├── Generation Algorithms
   │     ├── Iterated Function Systems (IFS)
   │     │     ├── Barnsley's Fern
   │     │     └── Sierpinski Triangle
   │     │
   │     ├── Lindenmayer Systems (L-Systems)
   │     │     ├── Koch Snowflake
   │     │     └── Dragon Curve
   │     │
   │     ├── Chaos Game Representation
   │     │     ├── Sierpinski Triangle
   │     │     └── Barnsley's Fern
   │     │
   │     ├── Fractal Interpolation
   │     │     ├── Mandelbrot Set
   │     │     └── Julia Set
   │     │
   │     └── Random Fractal Generation
   │           ├── Fractional Brownian Motion (fBm)
   │           └── Perlin Noise
   │
   ├── Analysis and Visualization Techniques
   │     ├── Fractal Dimension Estimation
   │     │     ├── Box Counting
   │     │     ├── Hausdorff Dimension
   │     │     └── Information Dimension
   │     │
   │     └── Fractal Compression
   │           ├── Fractal Image Compression
   │           │     ├── Iterated Function Systems (IFS)
   │           │     └── Wavelet Fractal Compression
   │           │
   │           └── Fractal Audio Compression
   │                 ├── Fractal Coding
   │                 └── Fractal Interpolation
   │
   └── Applications and Uses
         ├── Fractal Image Generation and Art
         │     ├── Mandelbrot Set Visualizations
         │     ├── Julia Set Visualizations
         │     └── Flame Fractals
         │
         ├── Terrain Generation and Modeling
         │     ├── Diamond-Square Algorithm
         │     └── Midpoint Displacement Algorithm
         │
         ├── Data Compression and Encryption
         │     ├── Fractal Image Compression
         │     └── Chaos-Based Encryption
         │
         └── Chaos Theory and Dynamical Systems
               ├── Lorenz Attractor
               └── Hénon Map

Fractals > Fractal Whats and Whys (In a Nutshell)