The Cook Book
Recipe for the week of May 8 - 14
Larger than Life Batik
- For the past couple of years, in collaboration with Kellie Evans, I
have been studying a parameterized family of two-color CA rules known as
Larger than Life (LtL). In this straightforward generalization of
Conway's Game of Life, a 1 is born at site x if the number of 1's in
the neighborhood of x lies in the interval [b1,b2],
while a 1 survives at site x if the number of 1's in the
neighborhood lies in [d1,d2]. For simplicity, we take the
neighbor set to be a range-r box. Thus Conway's Game is the case
r=1, b1 = b2 = d1 = 3, and d2 = 4. LtL
has a remarkably rich phase space, with many qualitatively different
kinds of long-term, complex pattern formation. For an introductory
account with a couple of pictures, see the final section of my article
"Self-Organization of Random Cellular Automata: Four Snapshots" in
Probability and Phase Transition, ed. G. Grimmett, Kluwer, 1994.
- This week's soup depicts an LtL regime not mentioned in the above
paper. The parameters are r=13, b1=10, b2 = 100,
d1 = 100, and d2 = 320. I showed slides of this and other CA
images to an art class while visiting Dartmouth College last month. The
students were struck by a similarity between nucleating target patterns
and some of the mandala designs they had studied. This week's graphic
reminded them especially of batik. A larger 1024 by 768 swatch,
bigbatik.gif, conveys the analogy most
effectively.
- Beta release #2 of WinCA, available from the Kitchen Sink,
includes several Larger than Life demo experiments, e.g., bugmovie
and pretzels. However our understanding of the LtL phase portrait
remains sketchy. Happily, as of last week we have finally implemented these
dynamics on CAM8, enabling real-time visualization of long-range systems for
the first time. Look for some of our findings among this summer's
recipes...
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