Strings That Are Derivable in a Certain Number of Steps by a Multiway System

As multiway systems evolve, they generate states with particular compositions. This Demonstration shows an abbreviated sample evolution of a multiway system on the left with its rule, and up to the first 15 steps tracking which states appear at which steps.
The characters "A" and "B" are represented by white and black cells, respectively.
One can answer the question "How many steps does it take to start at B and arrive at BAA?" For example, in the Thumbnail one sees right away that it takes five steps to get from B to BAA using those particular rules.

SNAPSHOTS

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DETAILS

See Stephen Wolfram's A New Kind of Science, pp. 796–799.
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