Self-reproduction by glider collisions: the beehive rule

We present a 3-value cellular automaton which supports self-reproduction 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 input-entropy variance. A variety of complex rules opens up the possibility of seeking a common thread to distinguish those few rules from the rest: an underlying principle of self-organization?