Several demonstrations, as well as REC programs, involve Zhabotinsky-like automata. The classical Zhabotinsky reaction goes through a three step cycle, usually producing concentric rings of epidemiologically excitation; two different frequencies arise under slightly different circumstances.
The key to a continuing excitation, manifested by spiral waves, and discovered by Greenberg and Hastings, is a central nucleus consisting of a closed ring of successive states. That allows a neverending sequence of activation and recovery, which propagates outward from the nucleus.
Several nuclei will produce interacting spirals. Very short loops, often just a collection of three cells, form the most common nuclei.
The REC demonstration must be interrupted twice, by a keypress, in each case preferably after the waves have stabilized; it is called ``an interesting eater cycle'' in the menu. Sometimes a ``clean'' demonstration results, in a way resembling the peeling of an onion. On other occasions some wild evolution sets in, quickly overpowering the orderly regime that was intended for the demonstration.
But that, in itself, could be considered as a demonstration.