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Notes
Chapter 6
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Chapter 6:
Starting from Randomness
Section 1:
The Emergence of Order
Properties of [initially random cellular automaton] patterns
Continual injection of randomness [in cellular automata]
History [of emergence of order]
Section 2:
Four Classes of Behavior
Different runs [of initially random cellular automata]
[Subset of] elementary rules
States of matter [and cellular automaton classes]
Class 4 [cellular automaton] rules
Frequencies of [cellular automaton] classes
History [of cellular automaton classes]
Subclasses within class 4
Undecidability [of cellular automaton classes]
[Classes in] continuous cellular automata
Nearby cellular automaton rules
2D class 4 cellular automata
Game of Life [cellular automaton]
3D class 4 [cellular automaton] rules
Random initial conditions in other systems
Section 3:
Sensitivity to Initial Conditions
Properties [of difference patterns]
Difference patterns [in cellular automata]
Lyapunov exponents
Section 4:
Systems of Limited Size and Class 2 Behavior
Cyclic addition
Cyclic multiplication
Maximum periods [in cellular automata]
Additive cellular automata [in finite regions]
[Periods in] rules 30 and 45
Comparison of [periods for cellular automaton] rules
Implementing boundary conditions [in cellular automata]
Section 5:
Randomness in Class 3 Systems
Rule 22 [with simple initial conditions]
Rule 225 [with simple initial conditions]
Rule 94 [with simple initial conditions]
Rule 218 [with simple initial conditions]
Additive [cellular automaton] rules
Generalized additivity [in cellular automata]
Probabilistic estimates [of cellular automaton properties]
Density in rule 90
Densities in other [cellular automaton] rules
Density oscillations in rule 73
Section 6:
Special Initial Conditions
Repeating blocks [in cellular automata]
Localized structures [in cellular automata]
[Repetition in] 2D cellular automata
[Repetition in] systems based on numbers
Sarkovskii's theorem
Rule emulations
Renormalization group
Self-similarity of additive [cellular automaton] rules
Fractal dimensions [of additive cellular automata]
General associative [cellular automaton] rules
Nesting in rule 45
Uniqueness of patterns [in cellular automata]
Square root of rule 30
Nested initial conditions [in cellular automata]
Section 7:
The Notion of Attractors
[Attractors in] discrete systems
Implementation [of cellular automaton state networks]
Finite automata
Regular languages
Regular expressions
Generating functions [for regular languages]
History [of finite automata]
[Cellular automaton state] network properties
Excluded blocks [in cellular automaton evolution]
Entropies and dimensions [in cellular automata]
Cycles and zeta functions
2D generalizations [of entropies]
Probability-based entropies
Entropy estimates
Nested structure of attractors
Surjectivity and injectivity [of cellular automaton maps]
Temporal sequences [in cellular automata]
Spacetime patches [in cellular automata]
History [of dynamical systems approaches]
Attractors in systems based on numbers
Iterated maps
Attractors in Turing machines
[State networks for] systems of limited size
Symmetries [and state networks]
[State networks for] shift rules
[State networks for] additive rules
[Properties of] random networks
Section 8:
Structures in Class 4 Systems
Survival data [for initial conditions in code 20]
Background [in rule 110]
Structures [in rule 110]
Glider gun [in rule 110]
Collisions [in rule 110]
[Structures in] the Game of Life
[Structures in] other 2D cellular automata
Structures in Turing machines