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Glider Dynamics in 3-Value Hexagonal Cellular Automata: The Beehive Rule
Andrew Wuensche

We present a 3-value cellular automaton which supports gliders, gliderguns and self-reproduction or self-destruction by glider collisions. The complex dynamics emerge spontaneously in both 2d and 3d according to the 6-neighbor, k-totalistic, “beehive” rule; the 2d dynamics on a hexagonal lattice is examined in detail. We show how analogous complex rules can be found, firstly by mutating a complex rule to produce a family of related complex rules, and secondly by classifying rule-space by inputentropy variance. A variety of complex rules opens up the possibility of finding a common thread to distinguish those few rules from the rest: an underlying principle of self-organization?

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