Cyclic Tag Systems

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A cyclic tag system is a tag system where the rule alternates between two sets of blocks to be added at each step. Here the blocks are combinations of one to three blue and orange blocks. Note that a rule in a regular tag system always specifies the same blocks to be added at each step, depending on the color of the first block of the previous step.


Just as in a regular tag system, one block is removed from the front of the previous step's array of blocks (call that ) and the number of blocks specified by the rule is added to the end of , which then becomes the next step of the evolution.

A plot of the length of each step of the evolution is shown at the top left. The rule icons showing the full icon specifying the alternating sets of blocks to be added to and removed from the next step and a summary of the rule are shown at the top right. A shortened evolution that shows the alternation of rules is at the bottom right, and the full evolution is at the bottom left.

Note that when an orange cell is removed, nothing is ever added to the end; new cells are added only when a blue cell is removed.

There are a total of rules.


Contributed by: Abigail Nussey (March 2011)
Open content licensed under CC BY-NC-SA



Tag systems are described in S. Wolfram, A New Kind of Science, Champaign, IL: Wolfram Media Inc., 2002 pp. 95–96.

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