Notes
Chapter 6: Starting from Randomness
![Continual injection of randomness [in cellular automata]](/nks/notes/notes-6-1--continual-injection-of-randomness-in-cellular-automata/thumb.png "Continual injection of randomness [in cellular automata]")
![History [of emergence of order]](/nks/notes/notes-6-1--history-of-emergence-of-order/thumb.png "History [of emergence of order]")
![Properties of [initially random cellular automaton] patterns](/nks/notes/notes-6-1--properties-of-initially-random-cellular-automaton-patterns/thumb.png "Properties of [initially random cellular automaton] patterns")
Continual injection of randomness [in cellular automata]
History [of emergence of order]
Properties of [initially random cellular automaton] patterns
![3D class 4 [cellular automaton] rules](/nks/notes/notes-6-2--3d-class-4-cellular-automaton-rules/thumb.png "3D class 4 [cellular automaton] rules")
![Class 4 [cellular automaton] rules](/nks/notes/notes-6-2--class-4-cellular-automaton-rules/thumb.png "Class 4 [cellular automaton] rules")
![[Classes in] continuous cellular automata](/nks/notes/notes-6-2--classes-in-continuous-cellular-automata/thumb.png "[Classes in] continuous cellular automata")
![Different runs [of initially random cellular automata]](/nks/notes/notes-6-2--different-runs-of-initially-random-cellular-automata/thumb.png "Different runs [of initially random cellular automata]")
![Frequencies of [cellular automaton] classes](/nks/notes/notes-6-2--frequencies-of-cellular-automaton-classes/thumb.png "Frequencies of [cellular automaton] classes")
![Game of Life [cellular automaton]](/nks/notes/notes-6-2--game-of-life-cellular-automaton/thumb.png "Game of Life [cellular automaton]")
![History [of cellular automaton classes]](/nks/notes/notes-6-2--history-of-cellular-automaton-classes/thumb.png "History [of cellular automaton classes]")
![States of matter [and cellular automaton classes]](/nks/notes/notes-6-2--states-of-matter-and-cellular-automaton-classes/thumb.png "States of matter [and cellular automaton classes]")
![[Subset of] elementary rules](/nks/notes/notes-6-2--subset-of-elementary-rules/thumb.png "[Subset of] elementary rules")
![Undecidability [of cellular automaton classes]](/nks/notes/notes-6-2--undecidability-of-cellular-automaton-classes/thumb.png "Undecidability [of cellular automaton classes]")
3D class 4 [cellular automaton] rules
Class 4 [cellular automaton] rules
[Classes in] continuous cellular automata
Different runs [of initially random cellular automata]
Frequencies of [cellular automaton] classes
Game of Life [cellular automaton]
History [of cellular automaton classes]
Nearby cellular automaton rules
Random initial conditions in other systems
![Difference patterns [in cellular automata]](/nks/notes/notes-6-3--difference-patterns-in-cellular-automata/thumb.png "Difference patterns [in cellular automata]")
![Properties [of difference patterns]](/nks/notes/notes-6-3--properties-of-difference-patterns/thumb.png "Properties [of difference patterns]")
![Additive cellular automata [in finite regions]](/nks/notes/notes-6-4--additive-cellular-automata-in-finite-regions/thumb.png "Additive cellular automata [in finite regions]")
![Comparison of [periods for cellular automaton] rules](/nks/notes/notes-6-4--comparison-of-periods-for-cellular-automaton-rules/thumb.png "Comparison of [periods for cellular automaton] rules")
![Implementing boundary conditions [in cellular automata]](/nks/notes/notes-6-4--implementing-boundary-conditions-in-cellular-automata/thumb.png "Implementing boundary conditions [in cellular automata]")
![Maximum periods [in cellular automata]](/nks/notes/notes-6-4--maximum-periods-in-cellular-automata/thumb.png "Maximum periods [in cellular automata]")
![[Periods in] rules 30 and 45](/nks/notes/notes-6-4--periods-in-rules-30-and-45/thumb.png "[Periods in] rules 30 and 45")
Additive cellular automata [in finite regions]
Comparison of [periods for cellular automaton] rules
Implementing boundary conditions [in cellular automata]
![Additive [cellular automaton] rules](/nks/notes/notes-6-5--additive-cellular-automaton-rules/thumb.png "Additive [cellular automaton] rules")
![Densities in other [cellular automaton] rules](/nks/notes/notes-6-5--densities-in-other-cellular-automaton-rules/thumb.png "Densities in other [cellular automaton] rules")
![Generalized additivity [in cellular automata]](/nks/notes/notes-6-5--generalized-additivity-in-cellular-automata/thumb.png "Generalized additivity [in cellular automata]")
![Probabilistic estimates [of cellular automaton properties]](/nks/notes/notes-6-5--probabilistic-estimates-of-cellular-automaton-properties/thumb.png "Probabilistic estimates [of cellular automaton properties]")
![Rule 218 [with simple initial conditions]](/nks/notes/notes-6-5--rule-218-with-simple-initial-conditions/thumb.png "Rule 218 [with simple initial conditions]")
![Rule 22 [with simple initial conditions]](/nks/notes/notes-6-5--rule-22-with-simple-initial-conditions/thumb.png "Rule 22 [with simple initial conditions]")
![Rule 225 [with simple initial conditions]](/nks/notes/notes-6-5--rule-225-with-simple-initial-conditions/thumb.png "Rule 225 [with simple initial conditions]")
![Rule 94 [with simple initial conditions]](/nks/notes/notes-6-5--rule-94-with-simple-initial-conditions/thumb.png "Rule 94 [with simple initial conditions]")
Additive [cellular automaton] rules
Densities in other [cellular automaton] rules
Density oscillations in rule 73
Generalized additivity [in cellular automata]
Probabilistic estimates [of cellular automaton properties]
Rule 218 [with simple initial conditions]
Rule 22 [with simple initial conditions]
![Fractal dimensions [of additive cellular automata]](/nks/notes/notes-6-6--fractal-dimensions-of-additive-cellular-automata/thumb.png "Fractal dimensions [of additive cellular automata]")
![General associative [cellular automaton] rules](/nks/notes/notes-6-6--general-associative-cellular-automaton-rules/thumb.png "General associative [cellular automaton] rules")
![Localized structures [in cellular automata]](/nks/notes/notes-6-6--localized-structures-in-cellular-automata/thumb.png "Localized structures [in cellular automata]")
![Nested initial conditions [in cellular automata]](/nks/notes/notes-6-6--nested-initial-conditions-in-cellular-automata/thumb.png "Nested initial conditions [in cellular automata]")
![Repeating blocks [in cellular automata]](/nks/notes/notes-6-6--repeating-blocks-in-cellular-automata/thumb.png "Repeating blocks [in cellular automata]")
![[Repetition in] 2D cellular automata](/nks/notes/notes-6-6--repetition-in-2d-cellular-automata/thumb.png "[Repetition in] 2D cellular automata")
![[Repetition in] systems based on numbers](/nks/notes/notes-6-6--repetition-in-systems-based-on-numbers/thumb.png "[Repetition in] systems based on numbers")
![Self-similarity of additive [cellular automaton] rules](/nks/notes/notes-6-6--self-similarity-of-additive-cellular-automaton-rules/thumb.png "Self-similarity of additive [cellular automaton] rules")
![Uniqueness of patterns [in cellular automata]](/nks/notes/notes-6-6--uniqueness-of-patterns-in-cellular-automata/thumb.png "Uniqueness of patterns [in cellular automata]")
Fractal dimensions [of additive cellular automata]
General associative [cellular automaton] rules
Localized structures [in cellular automata]
Nested initial conditions [in cellular automata]
Repeating blocks [in cellular automata]
[Repetition in] 2D cellular automata
[Repetition in] systems based on numbers
![2D generalizations [of entropies]](/nks/notes/notes-6-7--2d-generalizations-of-entropies/thumb.png "2D generalizations [of entropies]")
![[Attractors in] discrete systems](/nks/notes/notes-6-7--attractors-in-discrete-systems/thumb.png "[Attractors in] discrete systems")
![[Cellular automaton state] network properties](/nks/notes/notes-6-7--cellular-automaton-state-network-properties/thumb.png "[Cellular automaton state] network properties")
![Entropies and dimensions [in cellular automata]](/nks/notes/notes-6-7--entropies-and-dimensions-in-cellular-automata/thumb.png "Entropies and dimensions [in cellular automata]")
![Excluded blocks [in cellular automaton evolution]](/nks/notes/notes-6-7--excluded-blocks-in-cellular-automaton-evolution/thumb.png "Excluded blocks [in cellular automaton evolution]")
![Generating functions [for regular languages]](/nks/notes/notes-6-7--generating-functions-for-regular-languages/thumb.png "Generating functions [for regular languages]")
![History [of dynamical systems approaches]](/nks/notes/notes-6-7--history-of-dynamical-systems-approaches/thumb.png "History [of dynamical systems approaches]")
![History [of finite automata]](/nks/notes/notes-6-7--history-of-finite-automata/thumb.png "History [of finite automata]")
![Implementation [of cellular automaton state networks]](/nks/notes/notes-6-7--implementation-of-cellular-automaton-state-networks/thumb.png "Implementation [of cellular automaton state networks]")
![[Properties of] random networks](/nks/notes/notes-6-7--properties-of-random-networks/thumb.png "[Properties of] random networks")
![Spacetime patches [in cellular automata]](/nks/notes/notes-6-7--spacetime-patches-in-cellular-automata/thumb.png "Spacetime patches [in cellular automata]")
![[State networks for] additive rules](/nks/notes/notes-6-7--state-networks-for-additive-rules/thumb.png "[State networks for] additive rules")
![[State networks for] shift rules](/nks/notes/notes-6-7--state-networks-for-shift-rules/thumb.png "[State networks for] shift rules")
![[State networks for] systems of limited size](/nks/notes/notes-6-7--state-networks-for-systems-of-limited-size/thumb.png "[State networks for] systems of limited size")
![Surjectivity and injectivity [of cellular automaton maps]](/nks/notes/notes-6-7--surjectivity-and-injectivity-of-cellular-automaton-maps/thumb.png "Surjectivity and injectivity [of cellular automaton maps]")
![Symmetries [and state networks]](/nks/notes/notes-6-7--symmetries-and-state-networks/thumb.png "Symmetries [and state networks]")
![Temporal sequences [in cellular automata]](/nks/notes/notes-6-7--temporal-sequences-in-cellular-automata/thumb.png "Temporal sequences [in cellular automata]")
2D generalizations [of entropies]
[Attractors in] discrete systems
Attractors in systems based on numbers
[Cellular automaton state] network properties
Entropies and dimensions [in cellular automata]
Excluded blocks [in cellular automaton evolution]
Generating functions [for regular languages]
History [of dynamical systems approaches]
Implementation [of cellular automaton state networks]
Nested structure of attractors
[Properties of] random networks
Spacetime patches [in cellular automata]
[State networks for] additive rules
[State networks for] shift rules
[State networks for] systems of limited size
Surjectivity and injectivity [of cellular automaton maps]
![Background [in rule 110]](/nks/notes/notes-6-8--background-in-rule-110/thumb.png "Background [in rule 110]")
![Collisions [in rule 110]](/nks/notes/notes-6-8--collisions-in-rule-110/thumb.png "Collisions [in rule 110]")
![Glider gun [in rule 110]](/nks/notes/notes-6-8--glider-gun-in-rule-110/thumb.png "Glider gun [in rule 110]")
![[Structures in] other 2D cellular automata](/nks/notes/notes-6-8--structures-in-other-2d-cellular-automata/thumb.png "[Structures in] other 2D cellular automata")
![Structures [in rule 110]](/nks/notes/notes-6-8--structures-in-rule-110/thumb.png "Structures [in rule 110]")
![[Structures in] the Game of Life](/nks/notes/notes-6-8--structures-in-the-game-of-life/thumb.png "[Structures in] the Game of Life")
![Survival data [for initial conditions in code 20]](/nks/notes/notes-6-8--survival-data-for-initial-conditions-in-code-20/thumb.png "Survival data [for initial conditions in code 20]")