Examples of cyclic tag systems. In each case the initial condition consists of a single black element. In case (c), alternate steps in the leftmost column (which in all cyclic tag systems determines the overall behavior) have the same nested form as the third neighbor-independent substitution system shown on page 83.

Fluctuations in the growth of sequences for cyclic tag systems (d) and (e) above. The fluctuations are shown with respect to growth at an average rate of half an element per step.