A tag system consists of a sequence of elements each represented by a color (here there are two colors). Each step of the evolution is determined by applying a rule that drops a particular number of elements from the front of the array generated on the previous step and appends a certain number of elements determined by the composition of the dropped elements.
Two systems are explored here: one that drops one element and appends up to three new elements (for a total of rules) and a second that drops two elements and appends up to four new elements (for a total of rules).
This Demonstration displays a chart that tracks the total length of each step for twice the number of steps as the visual evolution, the rule icons for the system, and the visual evolution itself.
In the controls, "dropped" means the number dropped from the previous array in order to determine the next step in the evolution. The value "1" means the first set of rules as described above and value "2" means the second set of rules; "zoom" changes the number of pixels per block.
Tag systems are described in S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media Inc., 2002 pp. 93–94.