Chaotic dynamics on Fractals

1. The address of points on fractals
2. Continuous transformations from code space to fractals 1. Our goal is to construct a continuous transformation from the code space associated with an IFS onto the attractor of the IFS. This will allow us to formalize our notion of addresses. In order to make this construction, we will need two lemmas.
   1. https://frag997.github.io/p5-plus-plus/1.Projects/01.fractal_tree/
   2. https://frag997.github.io/ChaosGame-CPBR12/code/05.ChaosGame_v01/
   3. https://frag997.github.io/ChaosGame-CPBR12/code/07.ChaosGame_v02/

// Part 1: https://youtu.be/7gNzMtYo9n4

// https://thecodingtrain.com/CodingChallenges/123.1-chaos-game

// Part 2: https://youtu.be/A0NHGTggoOQ

// https://thecodingtrain.com/CodingChallenges/123.2-chaos-game 3. Dynamical systems 4. How to compute orbits by looking at pictures 5. Equivalent Dynamical Systems 1. definition: two metric spaces (x1, d1) and (x2, d2) are said to be topologically equivalent if there is a homeomorphism f:x1→x2. two subsets s1Cx2 and s2Cx2 are topologically equivalent. S1 and s2 are metrically equivalent if the (s1,d1) and (s2,d2) are equivalent metric spaces. 2. Attractive and repulsive fixed points in a web diagram 3. 6. the shadow of deterministic dynamics 7.