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Recipe for the week of May 20 - 26

Larger than Life Fat Bugs with Stomachs

This week's soup displays a rich ecology of artificial life for a range 10 Box LtL rule from the first region of the parameter space that we investigated, about three years ago. Our initial idea was to explore the boundaries between phases under threshold-range scaling. Conway's range 1 Box [3,3], [3,4] rule is renowned for its complexity. Interpreting the parameters as proportions of the 9-cell neighborhood, approximate the birth and survival 'windows' of that CA as [(2.5)/9, (3.5)/9] and [(2.5)/9, (4.5)/9], respectively. Rescaling to the range 10, 441-cell neighbor set, we investigate rules with parameter values close to those shown here: [123,170] and [123,212]. Starting from a 50-50 mix of occupied and empty cells, and using a palette for occupied cells with temporal period 4, we witness a rich menagerie of fixed crystals, blinkers and bugs emerging from the 'seething gurp' of initial self-organization. Our soup contains three stationary periodic objects; can you find them? For range 2 or more, the prevalent bugs near this critical point have fat heads, thin tails, and stomachs. Our soup is crawling with them. Remarkably, these bugs are able to move in a preferred direction, usually horizontal, vertical or diagonal, despite Larger than Life's lattice symmetry. The same story holds for even larger range LtL rules with the same threshold/|neighborhood| proportions. For instance, the thumbnail image above shows a bug we captured from the range 20, [480,680], [480,850] rule. Such experiments raise the possibility that Conway's Life is a range 1 approximation to some critical point for the limiting Euclidean CA dynamics.

Our WinCA software, available from the Kitchen Sink, includes two fat bug demos. In bugmovie.xpt, one of the bugs is lopsided, gradually veering off the horizontal by a few degrees, while another moves in a diagonal direction. The animation shows their destructive collision, leading first to a swatch of seething gurp and then later to the emergence of a fixed crystal and new fat bug. Another demo, bosco.xpt, features a guy who moves in one direction for a stretch, destabilizes into gurp, re-organizes as an alter-ego moving in the exact opposite direction, destabilizes again, and reorganizes along the exact trajectory of the original, producing a periodic orbit of 166 updates!

By now you might be wondering what fat bugs have to do with Conway's gliders since their forms seems so different. One might simply attribute this discrepancy to the limited design possibilities of range 1 Box, but my student Kellie Evans has discovered another threshold-range scaling scheme, corresponding to another point in the phase diagram, that gives rise to more glider-like bugs we call skeeters. Moreover, to my great surprise, she has found compelling evidence for a connected component of phase space containing bugs with architectures which interpolate between the skeeters and the fat ones. We plan to feature Kellie's menagerie in a recipe this summer.

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