• Chaos Game

  • Cover
  • How to read this book?
  • 1 Hello, fractals!
    • 1.1 Wacław Sierpinski
    • 1.2 Hello, fractals!
      • 1.2.1 Cantor dust
      • 1.2.2 Sierpinski triangle
    • 1.3 But why does it work?
      • 1.3.1 Topological dimension
      • 1.3.2 Minkowski dimension, or fractal box-counting dimension
      • 1.3.3 Sierpinski carpet
    • 1.4 Examples in Python
      • 1.4.1 Cantor dust
      • 1.4.2 Sierpinski triangle
      • 1.4.3 Sierpinski carpet
    • 1.5 Examples in R
      • 1.5.1 Cantor dust
      • 1.5.2 Sierpinski triangle
      • 1.5.3 Sierpinski carpet
    • 1.6 Examples in Julia
      • 1.6.1 Cantor dust
      • 1.6.2 Sierpinski triangle
      • 1.6.3 Sierpinski carpet
  • 2 Fractal, that is fixed point
    • 2.1 Stefan Banach
    • 2.2 Fractal, that is fixed point
      • 2.2.1 Dragons and ferns
      • 2.2.2 Sierpinski pentagon
      • 2.2.3 Pythagoras tree
      • 2.2.4 Heighway Dragon
      • 2.2.5 Barnsley fern
    • 2.3 But why does it work?
      • 2.3.1 Metric space
      • 2.3.2 Hausdorff distance
      • 2.3.3 Cauchy sequence
      • 2.3.4 Complete space
      • 2.3.5 Contraction
      • 2.3.6 Affine transformation
      • 2.3.7 Hutchinson’s theorem
      • 2.3.8 Banach’s fixed point theorem
    • 2.4 Examples in Python
      • 2.4.1 Sierpinski triangle
      • 2.4.2 Sierpinski pentagon
      • 2.4.3 Heighway’s Dragon
      • 2.4.4 Symmetric binary tree / Pythagoras’ tree
    • 2.5 Examples in R
      • 2.5.1 Sierpiński triangle
      • 2.5.2 Sierpiński pentagon
      • 2.5.3 Heighway’s Dragon
      • 2.5.4 Symmetric binary tree / Pythagoras’ tree
    • 2.6 Examples in Julia
      • 2.6.1 Sierpinski triangle
      • 2.6.2 Sierpinski pentagon
      • 2.6.3 Heighway’s Dragon
      • 2.6.4 Symmetric binary tree / Pythagoras’ tree
  • 3 Chaos Game
    • 3.1 Hugo Steinhaus
    • 3.2 Chaos Game
      • 3.2.1 Chaos game and triangles
      • 3.2.2 What’s going on here?
      • 3.2.3 Chaos game and fractals
      • 3.2.4 Affine transformations
      • 3.2.5 Ferns and chaos
      • 3.2.6 More formally
    • 3.3 Applications
      • 3.3.1 Chaos game and genetics
      • 3.3.2 Chaos game and music
      • 3.3.3 The fractal dimension of the brain
    • 3.4 Examples in Python
      • 3.4.1 The Sierpinski triangle once again
      • 3.4.2 Barnsley fern
      • 3.4.3 Maple leaf
      • 3.4.4 Spiral
    • 3.5 Examples in R
      • 3.5.1 The Sierpinski triangle once again
      • 3.5.2 Barnsley fern
      • 3.5.3 Maple leaf
      • 3.5.4 Spiral
    • 3.6 Examples in Julia
      • 3.6.1 The Sierpinski triangle once again
      • 3.6.2 Barnsley fern
      • 3.6.3 Maple leaf
      • 3.6.4 Spiral
  • 4 Pocket atlas of fractals
    • 4.1 Barnsley fern
    • 4.2 Maple leaf
    • 4.3 McWorter’s pentigree
    • 4.4 Trees
    • 4.5 Spiral
    • 4.6 Sierpinski polygons
    • 4.7 Dragons
    • 4.8 Sky is the limit
  • Bibliography
  • Other books in the Beta and Bit series

Chaos Game