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Notes
Chapter 5
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Chapter 5:
Two Dimensions and Beyond
Section 1:
Introduction
Other lattices
1D phenomena
Section 2:
Cellular Automata
Implementation [of 2D cellular automata]
General rules [for multidimensional cellular automata]
Numbers of possible [2D cellular automaton] rules
Symmetric 5-neighbor [2D cellular automaton] rules
Growth [2D cellular automaton] rules
Code 942 slices
History [of 2D cellular automata]
Ulam systems
Limiting shapes [in 2D cellular automata]
Additive rules
Cellular automaton art
Code 175850
Code 746
Code 174826
Projections from 3D [cellular automata]
Other geometries [for cellular automata]
Networks [as basis for cellular automata]
Section 3:
Turing Machines
Implementation [of 2D Turing machines]
History [of 2D Turing machines]
Visualization [of 2D Turing machines]
Rules [for 2D Turing machines] based on turning
2D mobile automata
Section 4:
Substitution Systems and Fractals
Implementation [of 2D substitution systems]
Connection [of 2D substitution systems] with digit sequences
Sierpinski pattern
[2D substitution systems with] non-white backgrounds
Higher-dimensional generalizations [of substitution systems]
[Substitution systems based on] other shapes
Penrose tilings
Dragon curve
Implementation [of geometric substitution systems]
Connection [of geometric substitution systems] with digit sequences
Visualization [of geometric substitution systems]
Parameter space sets
Affine transformations
Complex maps
Fractal dimensions
History of fractals
The Mandelbrot set
Neighbor-dependent [2D] substitution systems
Space-filling curves
Section 5:
Network Systems
Implementation [of network systems]
Rule structure [for network systems]
[Systems based on] undirected networks
Computer science [and network systems]
Properties [of network systems]
Sequential network systems
Dimensionality of networks
Cellular automata on networks
Implementation [of network cellular automata]
Boolean networks
Section 6:
Multiway Systems
Implementation [of multiway systems]
General properties [of multiway systems]
Properties [of multiway system example]
Frequency of behavior [in multiway systems]
History [of multiway systems]
Semigroups and groups [and multiway systems]
Formal languages [and multiway systems]
Multidimensional multiway systems
Limited size versions [of multiway systems]
Multiway tag systems
Multiway systems based on numbers
Non-deterministic systems
Fundamental physics
Game systems
Section 7:
Systems Based on Constraints
The notion of equations [versus constraints]
Linear and nonlinear systems
Explanations based on constraints
1D [systems based on] constraints
1D cellular automata
[Excluded blocks in] dynamical systems theory
2D [systems based on] constraints
Numbering scheme [for 2D constraints]
Identifying the 171 patterns [that satisfy 2D constraints]
Checking [tilings with] constraints
Representing repetitive [2D] patterns
Searching for patterns [that satisfy constraints]
Undecidability [for 2D constraints]
NP completeness [for 2D constraints]
Enumerating patterns
Non-periodic pattern [forced by 2D constraint]
Other types of [2D] constraints
Forcing nested [2D] patterns
Relation to 2D cellular automata
Relation to 1D cellular automata
Non-computable [2D] patterns
Tiling [problems]
Polyominoes
Ground states of spin systems
Correspondence systems [as constraints]
Sequence equations
Pattern-avoiding sequences
Formal languages [and constraints]
Diophantine equations
Matrices satisfying constraints
Finite groups and semigroups
Constraints on formulas