Chapter 5: Two Dimensions and Beyond

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]