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Recipe for the week of August 28 - September 3

CCA Fossils (revisited)

Way back during the week of Nov. 28 last year, we discussed a Cyclic Cellular Automaton near the phase boundary between turbulent equilibrium and fixation. We noted the tendency of the rule to etch large 'fossilized' regions over time, but confessed to having no idea how the dynamics would behave on large arrays that were beyond the scope of the CAM6 technology available at that time.

This summer we have made considerable strides with the next generation mixmaster, CAM8. So we have returned to the same region of CCA phase space to put the new box through its paces. This week's soup depicts the even closer to critical range 2 Box, threshold 10, 4-color CCA on a 512 by 512 array, after 660,498 updates starting from a uniform random distribution of the colors.

We see that two horizontal bands of fossils have wrapped around the entire array, with extremely uniform triangular waves running between them. The smaller triangles at the top are moving in one direction, the larger ones at the bottom in the other. Can you figure out which direction is which?

The simulation from which our soup was prepared has now been running for almost a week. After more than 6 million updates the fossils and bands of triangles are still there, in nearly identical proportions, though much of the fine structure has changed of course. What have we learned? Mainly that our array isn't large enough, and that some quite interesting self-organization should occur if the dynamics have more room to move. We'll carry out the same CAM8 experiment on a larger array, say 2K by 2K, and report back later with our findings...

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