#MCell 2.0
#GAME Cyclic CA
#RULE R1/T3/C4/NM
#BOARD 140x140
#SPEED 0
#WRAP 1
#D 
#D Self-Correcting Perfect Spirals
#D ===============================
#D 
#D      The Cyclic Cellular Automaton with range 1 box ("Moore")
#D neighborhood, threshold 3, and 4 colors is a particularly interesting
#D excitable system. From a uniform random configuration it quickly
#D self-organizes into a chaotic soup with large length scale similar in
#D structure to the equilibrium of turbulen.xpt. But later on, often after
#D more than one hundred updates, widely separated stable spiral cores
#D emerge and slowly take over the lattice.
#D 
#D      Spirals characteristic of this rule are particularly interesting for
#D three reasons. First, they are NOT stable periodic objects (spo's) in the
#D sense of Pritikin's monster (dan10.xpt) or the spiral cores of
#D prototypical GH and CCA rules. Rather, external patterns can destabilize
#D the boundary layer of the spiral. Secondly, the emergent spiral pattern
#D away from the boundary is perfect, i.e. without any 'glitches.' The
#D spirals of more aggressive excitable dynamics often work their way around
#D particularly stubborn obstacles, leaving residual anomalies. But based on
#D extensive experimentation it appears that the spirals of this rule
#D overrun any disordered environment without the slightest trace of the
#D displaced configuration. Thirdly, it would appear that spiral cores arise
#D either within the first several hundred updates or virtually never. Our
#D evidence for the last observation is the most impressionistic, but it
#D seems that the time to nucleation from uniform randomness has a very thin
#D tail. Perhaps the formation of a core is nearly impossible once the
#D surrounding soup acquires a sufficiently long correlation length.
#D 
#D David Griffeath
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