The Cook Book
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.
|
