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Introduction To Symbolic Dynamics

This video was made for 3 Blue 1 Brown's Summer of Math Exposition 2 competition. This is a brief summary of some of the more central elements in the field of Symbolic Dynamics. Some applications of symbolic dynamics for anyone interested (all 4 are worth watching): Wave function collapse    • Superpositions, Sudoku, the Wave Func...   and    • Why I'm Using Wave Function Collapse ...   Cellular automata    • Coding Adventure: Ant and Slime Simul...   Tiling spaces    • The Infinite Pattern That Never Repeats   0:00 - Introduction 0:31 - Dynamical Systems 1:10 - Baker’s Map 2:28 - Binary Fractions 3:08 - Baker’s Map on Binary Fractions 4:28 - Symbolic Dynamics Introduction 6:08 - Simple Example 6:34 - Subshifts 7:58 - Golden Mean Shift 9:09 - Even Shift 9:40 - Shift Invariant Rules 10:18 - Adjacency Rules 11:22 - Local Rules 12:03 - Shifts of Finite Type 13:05 - Simple Machines 14:51 - Sliding Block Codes 15:55 - Conjugacy 17:28 - Closing Errors: At 2:29 it should be b1,b2,b3,... not all b1. Also, natural numbers start at 1, not 0 as shown in much of the video. #some2