# Symmetric Substitution Systems

Symmetric Substitution Systems

Symmetric sequential substitution systems can produce highly complex behavior from simple deterministic rules, much like cellular automata. However, symmetric sequential substitution systems can produce a wider variety of behavior because the string length can change very quickly.

This Demonstration lets you explore the fascinating space of these systems by observing space-time plots of their dynamics, where each successive row (reading down) represents the string produced upon the next time step. Each individual system is described by seven rewrite rules (shown at the top) that show which strings (above) should be replaced by which other strings (below). Unlike classic substitution systems, at each time step the string is updated by scanning it from left to right and applying the rules whenever possible in a nonoverlapping way.