The Cook Book

Recipe for the week of August 26 - September 1

Larger than Life Ladders

While the Kitchen stove was off for a summer vacation, Kellie Evans put the final touches on her PhD dissertation: Larger than Life: it's so nonlinear. To celebrate Kellie's finishing, this week's soup is the eighth and final snapshot in an LtL portfolio that we have featured this spring and summer. The rule has range 2 Box neighborhood, and birth and survival intervals [9,9] and [11,25], respectively. We started from a random initial state with density 13/23 of live sites, using the level-set representation of the dynamics which we have adopted throuhout the series.

As far as we know, this is the first non-nearest neighbor rule which produces ladders analogous to those found in the Life without Death (LwoD) recipes from February and April, 1995. Perhaps it will be possible to find similar periodic 'trails' for higher ranges in a suitable near-critical region of LtL phase space. We suspect that these ladders might typically coexist with dendritic snowflake-like growth dynamics, so there is at least the prospect of a better understanding of those intriguing nonlinear processes. Stay tuned.

Evans points out some distinctions between Life without Death and this week's soup, however. The only known LwoD ladders evolve in the horizontal and vertical directions, but her range 2 example admits diagonal ladders as well. Also, whereas the dendritic flow of LwoD seems to fill space with a positive density of occupied sites when started from certain finite initial seeds, the current dynamics can apparently only propagate by means of ladders. Thus our soup suggests that the infinite system should self-organize to a non-uniformly locally periodic final state with some remarkably large empty regions.

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