Notes
Chapter 7: Mechanisms in Programs and Nature
![History [of universality of behavior]](/nks/notes/notes-7-1--history-of-universality-of-behavior/thumb.png "History [of universality of behavior]")
![Definition [of randomness]](/nks/notes/notes-7-2--definition-of-randomness/thumb.png "Definition [of randomness]")
![History [of randomness]](/nks/notes/notes-7-2--history-of-randomness/thumb.png "History [of randomness]")
![Power spectra [of random processes]](/nks/notes/notes-7-3--power-spectra-of-random-processes/thumb.png "Power spectra [of random processes]")
![Instability [and chaos theory]](/nks/notes/notes-7-4--instability-and-chaos-theory/thumb.png "Instability [and chaos theory]")
![Simple case [of three-body problem]](/nks/notes/notes-7-4--simple-case-of-three-body-problem/thumb.png "Simple case [of three-body problem]")
![Spinning and tossing [as sources of randomness]](/nks/notes/notes-7-4--spinning-and-tossing-as-sources-of-randomness/thumb.png "Spinning and tossing [as sources of randomness]")
Information content of initial conditions
Instability [and chaos theory]
Randomness in the solar system
Simple case [of three-body problem]
![Cellular automata [as randomness generators]](/nks/notes/notes-7-5--cellular-automata-as-randomness-generators/thumb.png "Cellular automata [as randomness generators]")
![[Generating sequences with] unequal probabilities](/nks/notes/notes-7-5--generating-sequences-with-unequal-probabilities/thumb.png "[Generating sequences with] unequal probabilities")
![Probabilistic rules [for cellular automata]](/nks/notes/notes-7-5--probabilistic-rules-for-cellular-automata/thumb.png "Probabilistic rules [for cellular automata]")
Cellular automata [as randomness generators]
[Generating sequences with] unequal probabilities
![[Circularity in] code 746](/nks/notes/notes-7-6--circularity-in-code-746/thumb.png "[Circularity in] code 746")
![[Circularity in] other rules](/nks/notes/notes-7-6--circularity-in-other-rules/thumb.png "[Circularity in] other rules")
![Domains [in code 976]](/nks/notes/notes-7-6--domains-in-code-976/thumb.png "Domains [in code 976]")
![History [of Central Limit Theorem]](/nks/notes/notes-7-6--history-of-central-limit-theorem/thumb.png "History [of Central Limit Theorem]")
![Implementation [of basic aggregation model]](/nks/notes/notes-7-6--implementation-of-basic-aggregation-model/thumb.png "Implementation [of basic aggregation model]")
![Isotropy [in lattice systems]](/nks/notes/notes-7-6--isotropy-in-lattice-systems/thumb.png "Isotropy [in lattice systems]")
![Related results [to Central Limit Theorem]](/nks/notes/notes-7-6--related-results-to-central-limit-theorem/thumb.png "Related results [to Central Limit Theorem]")
![Self-avoiding [random] walks](/nks/notes/notes-7-6--self-avoiding-random-walks/thumb.png "Self-avoiding [random] walks")
Diffusion-limited aggregation (DLA)
Discreteness in computer programs
Generalized aggregation models
History [of Central Limit Theorem]
Implementation [of basic aggregation model]
![1D [discrete] transitions [in cellular automata]](/nks/notes/notes-7-7--1d-discrete-transitions-in-cellular-automata/thumb.png "1D [discrete] transitions [in cellular automata]")
![2D [discrete] transitions [in cellular automata]](/nks/notes/notes-7-7--2d-discrete-transitions-in-cellular-automata/thumb.png "2D [discrete] transitions [in cellular automata]")
1D [discrete] transitions [in cellular automata]
2D [discrete] transitions [in cellular automata]
![Biologically motivated schemes [for combinatorial optimization]](/nks/notes/notes-7-8--biologically-motivated-schemes-for-combinatorial-optimization/thumb.png "Biologically motivated schemes [for combinatorial optimization]")
![Distribution [of constraint satisfaction]](/nks/notes/notes-7-8--distribution-of-constraint-satisfaction/thumb.png "Distribution [of constraint satisfaction]")
![Gradient descent [in constraint satisfaction]](/nks/notes/notes-7-8--gradient-descent-in-constraint-satisfaction/thumb.png "Gradient descent [in constraint satisfaction]")
![History [of combinatorial optimization]](/nks/notes/notes-7-8--history-of-combinatorial-optimization/thumb.png "History [of combinatorial optimization]")
![Implementation [of constraint satisfaction]](/nks/notes/notes-7-8--implementation-of-constraint-satisfaction/thumb.png "Implementation [of constraint satisfaction]")
![[Invariance examples in] 2D cellular automata](/nks/notes/notes-7-8--invariance-examples-in-2d-cellular-automata/thumb.png "[Invariance examples in] 2D cellular automata")
![Iterative improvement [of constraint satisfaction]](/nks/notes/notes-7-8--iterative-improvement-of-constraint-satisfaction/thumb.png "Iterative improvement [of constraint satisfaction]")
![NP completeness [and constraint satisfaction]](/nks/notes/notes-7-8--np-completeness-and-constraint-satisfaction/thumb.png "NP completeness [and constraint satisfaction]")
![[Sphere packings in] higher dimensions](/nks/notes/notes-7-8--sphere-packings-in-higher-dimensions/thumb.png "[Sphere packings in] higher dimensions")
Biologically motivated schemes [for combinatorial optimization]
Distribution [of constraint satisfaction]
Gradient descent [in constraint satisfaction]
History [of combinatorial optimization]
Implementation [of constraint satisfaction]
[Invariance examples in] 2D cellular automata
Iterative improvement [of constraint satisfaction]
NP completeness [and constraint satisfaction]
![[Nesting in] phase transitions](/nks/notes/notes-7-9--nesting-in-phase-transitions/thumb.png "[Nesting in] phase transitions")
![[Nesting in] random walks](/nks/notes/notes-7-9--nesting-in-random-walks/thumb.png "[Nesting in] random walks")
![[Overall] structure of algorithms](/nks/notes/notes-7-9--overall-structure-of-algorithms/thumb.png "[Overall] structure of algorithms")
![Previous approaches [to complexity]](/nks/notes/notes-7-9--previous-approaches-to-complexity/thumb.png "Previous approaches [to complexity]")
[Nesting in] phase transitions
Origins of localized structures
[Overall] structure of algorithms
Previous approaches [to complexity]