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
Chaos Game
2023-05-15
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