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Notes
Chapter 7
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Chapter 7:
Mechanisms in Programs and Nature
Section 1:
Universality of Behavior
History [of universality of behavior]
Section 2:
Three Mechanisms for Randomness
Definition [of randomness]
History [of randomness]
Applications of randomness
Sources of randomness
Section 3:
Randomness from the Environment
Stochastic models
Ocean surfaces
Random walks
Electronic noise
Power spectra [of random processes]
Spark chambers
Physical randomness generators
Mechanical randomness
Electronic randomness
Quantum randomness
Randomness in computer systems
Randomness in biology
Section 4:
Chaos Theory and Randomness from Initial Conditions
Spinning and tossing [as sources of randomness]
Billiards
Fluttering
History of chaos theory
Information content of initial conditions
Recognizing chaos
Instability [and chaos theory]
Three-body problem
Simple case [of three-body problem]
Randomness in the solar system
Section 5:
The Intrinsic Generation of Randomness
Autoplectic processes
Algorithmic randomness
Cellular automata [as randomness generators]
Card shuffling
Random number generators
[Generating sequences with] unequal probabilities
Sources of repeatable randomness
Probabilistic rules [for cellular automata]
Noisy cellular automata
Repeatably random experiments
Section 6:
The Phenomenon of Continuity
Discreteness in computer programs
Central Limit Theorem
History [of Central Limit Theorem]
Related results [to Central Limit Theorem]
Random walks
Self-avoiding [random] walks
Basic aggregation model
Implementation [of basic aggregation model]
Generalized aggregation models
Diffusion-limited aggregation (DLA)
[Circularity in] code 746
[Circularity in] other rules
Isotropy [in lattice systems]
Domains [in code 976]
Spinodal decomposition
Section 7:
Origins of Discreteness
1D [discrete] transitions [in cellular automata]
2D [discrete] transitions [in cellular automata]
Phase transitions
The Ising model
General features of phase transitions
Percolation
Rate equations
Discreteness in space
Section 8:
The Problem of Satisfying Constraints
Rules versus constraints
NP completeness [and constraint satisfaction]
Distribution [of constraint satisfaction]
Implementation [of constraint satisfaction]
Iterative improvement [of constraint satisfaction]
Gradient descent [in constraint satisfaction]
Combinatorial optimization
Biologically motivated schemes [for combinatorial optimization]
History [of combinatorial optimization]
[Invariance examples in] 2D cellular automata
Circle packings
Sphere packings
[Sphere packings in] higher dimensions
Discrete packings
Voronoi diagrams
Discrete Voronoi diagrams
Brillouin zones
Packing deformable objects
Protein folding
Section 9:
Origins of Simple Behavior
Previous approaches [to complexity]
Uniformity in frequency
Repetition in numbers
Repetition in continuous systems
Examples of nesting
Nesting in numbers
Nested lists
[Nesting in] phase transitions
Self-organized criticality
[Nesting in] random walks
[Overall] structure of algorithms
Origins of localized structures