Explore Wolfram's substitution systems from "A New Kind of Science"
String rewriting systems that generate complex patterns through simple rules
Substitution systems, extensively studied by Stephen Wolfram in "A New Kind of Science," are computational systems that operate by repeatedly applying string rewriting rules. Starting from an initial string (axiom), each symbol is simultaneously replaced according to predefined rules, generating increasingly complex patterns.
These systems are closely related to L-systems (Lindenmayer systems) and demonstrate how simple rules can generate fractal patterns, biological growth models, and complex mathematical sequences like the Fibonacci sequence. Wolfram showed that even neighbor-independent substitution rules can produce sophisticated emergent behaviors.