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

From Stephen Wolfram: A New Kind of Science [citation]