# Notes

# Chapter 6: Starting from Randomness

## Section 1: The Emergence of Orderhttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-1--the-emergence-of-order

Properties of [initially random cellular automaton] patterns

## Section 2: Four Classes of Behaviorhttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-2--four-classes-of-behavior

Different runs [of initially random cellular automata]

States of matter [and cellular automaton classes]

Class 4 [cellular automaton] rules

Frequencies of [cellular automaton] classes

History [of cellular automaton classes]

Undecidability [of cellular automaton classes]

[Classes in] continuous cellular automata

Nearby cellular automaton rules

Game of Life [cellular automaton]

## Section 3: Sensitivity to Initial Conditionshttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-3--sensitivity-to-initial-conditions

## Section 4: Systems of Limited Size and Class 2 Behaviorhttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-4--systems-of-limited-size-and-class-2-behavior

Maximum periods [in cellular automata]

Additive cellular automata [in finite regions]

## Section 5: Randomness in Class 3 Systemshttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-5--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]

## Section 6: Special Initial Conditionshttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-6--special-initial-conditions

Repeating blocks [in cellular automata]

Localized structures [in cellular automata]

[Repetition in] 2D cellular automata

[Repetition in] systems based on numbers

Self-similarity of additive [cellular automaton] rules

Fractal dimensions [of additive cellular automata]

General associative [cellular automaton] rules

## Section 7: The Notion of Attractorshttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-7--the-notion-of-attractors

[Attractors in] discrete systems

Implementation [of cellular automaton state networks]

Generating functions [for regular languages]

[Cellular automaton state] network properties

Excluded blocks [in cellular automaton evolution]

Entropies and dimensions [in cellular automata]

2D generalizations [of entropies]

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

[State networks for] systems of limited size

Symmetries [and state networks]

[State networks for] shift rules

## Section 8: Structures in Class 4 Systemshttps://www.wolframscience.com/nks/chap-6--starting-from-randomness--notes#sect-6-8--structures-in-class-4-systems

Survival data [for initial conditions in code 20]

[Structures in] the Game of Life