Frederico Meinberg showed some explorations of cyclic multiway systems. A problem often encountered in unrestricted multiway systems - with the strings on which their replacement rules operate usually taken as "open" at both ends - is that they show unbounded and typically exponential growth in both string lengths and the space of strings reached by the system. This can make it quite hard to analyze general multiway systems.
Meinberg therefore looked instead at the special case of strings that are taken as cyclic, as with finite width CAs, so that the right end of any string is taken as the left hand neighbor of its starting character. If one then also restricts the transformation rules to those with an equal number of characters on each side, the length of the string is preserved throughout the evolution. These simpler systems are much easier to analyze.
Meinberg showed some preliminary investigations of their typical behavior for small widths and with the simplest transformation rules. He found relatively simple behaviors, and noted that this is expected in limited width, where the limited number of states forces cycling at some point.
Meinberg's code was general enough to take any number of "colors" or possible characters in the strings, any length, and any number of allowed transformation rules. He concluded by calling his cyclic multiway systems a potentially interesting and as yet "untamed" computational animal, for future investigation.
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