Sequential substitution systems evolve by replacing the first sequence in a set of rules found in the current row of the evolution with a new sequence determined by the rules. In that sense the system is sequential, since if the first pattern in the rule set is not found, the system searches for the next, and then the next, until the pattern is found. The visual representation of sequential substitution systems keeps track of where the sequence was matched for each row (using black dots).
This Demonstration displays nine interesting rules for up to 500 steps. The evolution can be broken up into one to eight columns. The rule icon is shown at the top-left corner.