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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... and • Why I'm Using Wave Fun...
Cellular automata • Coding Adventure: Ant ...
Tiling spaces • The Infinite Pattern T...
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.
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