Multiway Systems

rule set

1

2

3

4

5

6

steps

14

Multiway systems are substitution systems with a collection of possible states at every step. As in substitution systems, the rules give instructions on how to proceed if a certain pattern is matched. For example, two black cells should be replaced by one gray cell; if the state on which the rule is operating does not have any contiguous black cells, that part of the rule is not applied. Rules that have a positive pattern match for a particular step are called "applicable". At each step, each applicable rule is applied and each substitution leads to a new state.

Arrows go from each previous state to the states that are produced by the applicable rules. Rule icons are on the top left of the evolution. Initial conditions are shown as the first step of the evolution. This Demonstration samples six rule sets.