String Substitution Systems
String Substitution Systems
Stephen Wolfram
(Unfinished draft as of March 28, 2006; with small updates October 2019)
(Unfinished draft as of March 28, 2006; with small updates October 2019)
Introduction
Introduction
Neighbor-Independent Rules
Neighbor-Independent Rules
Single-Rewrite Neighbor-Dependent Substitution Systems
Single-Rewrite Neighbor-Dependent Substitution Systems
Multiple Substitutions
Multiple Substitutions
Examples with Complex Behavior
Examples with Complex Behavior
Approaches to Analysis
Approaches to Analysis
Long Initial Conditions
Long Initial Conditions
Reversibility
Reversibility
Emulation
Emulation
Algebraic Representations (& Invariances)
Algebraic Representations (& Invariances)
Cyclic (Closed) Strings
Cyclic (Closed) Strings
(Unordered Strings)
(Unordered Strings)
Conditional Causal Invariance
Conditional Causal Invariance
Appendix: Implementation
Appendix: Implementation
Code Used
Code Used