[Hints of emergent order with a half life] - A New Kind of Science: The NKS Forum
A New Kind of Science: The NKS Forum
Hints of emergent order with a half life(Click here to view the original thread with full colors/images)
Posted by: Tony Smith
For more than a year my studies on the WMPVN rule space have been increasingly drawn to rules of the form WMPVN-45678x_459_n, where the x indicates the presence or absence of c that signifies "survive 12" and n is the number of "colors" which is two more than the number of "dying" states. As the rate of growth of "chaotic core" increases with decreasing n, my results to date are for n>10.
Like all the rules I've been studying these past three and a half years, the critical feature is the ability of two close c/2 spaceships to interact to leave a puffer trail. In the cases I'm concerned about here, those trails can involve one or two "growth shoulders" which are almost equivalent to wick stretchers in other rules as a 3 in 2 sloping edge forms between the c/2 engine and the point of the shoulder which repeats period 2m at a displacement of (m-3, 2) where m is quite variable but of order 100.
As shown in the attached screen capture from WMPVN-45678c_459_17, "gutters" and "braids" can persist behind the sloping edge because they are immune to disturbance from the side and only erode into tail chaos at less than c/2. That image shows each shoulder eventually settling down to a p9576 cycle leaving a gutter plus a braid repeating on a 126 cell lateral cycle, but only after following its own distinct path into that attractor basin.
Before today it had seemed that growth shoulders all either terminate quite quickly, leaving an adorned c/2 engine that may or may not trail one or two gutters/braids or would settle into a large attractor basin characteristic of the particular rule, at least for some values of n.
Today that all changed. The first seed I tried with WMPVN-45678c_459_11 has bilateral symmetry and produced a (pair of) growth shoulder(s) which formed five trailing gutters separated by 16 cells laterally at p1008 before "climbing out" of that attractor basin, forming three more gutters at different separations and eventually terminating in the same persistent form as narrower engines.
On reflection, it took the strong visual clues inherent in gutters and braids to make obvious something I'd seen occasional clues of in very different rules. Cyclic behaviour (growth) can sometimes be subject to what looks like spontaneous termination, but only when the peak speed of chaotic disturbance matches the speed of growth. While the typical speed of spread of a perturbation within chaotic core in the rules I've been studying is significantly less than c/2, there are also processes which can move along suitable orderly substrates/tracks at c. (In fact such processes are fundamental to eroding out the gaps between the persistent gutters and braids discussed here, but that is a whole other story.)
What matters here is that IF "fundamental" particles are in reality persistent patterns in some underlying discrete firmament, there might now be one more clue to help explain how a tiny fraction have seriously long half lives.
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