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 Sierpiński 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

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