Chapter 5 Notes > Section 7

	Notes for 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 PAGE IMAGES RELATED LINKS Main text from section Downloadable programs for this section Downloadable images Search Forum for this section Post a comment NKS | Online FAQs

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