|With my four month old iMac running larger patterns non stop and shorter explorations running on my previous rev machine whenever I'm away from it for a few hours, new results continue to accumulate. But as has long been my habit, I'm often more focused on bigger picture implications than on the specifics, so I really do need to record something about recent directions.|
Whoa at 250,000 and even more so The Wild at 240,000 were starting to test the limits of even the new iMac so I decided to start using it to push other patterns to 200,000 from wherever I had paused them on the old iMac, though the first of those, the common enough bilaterally symmetric Wide-Block, has now in its second pause still only at 190,000 while I redirect priorities.
The first of those pauses was during an arguably overdue and somewhat interesting diversion into adjacent rules which also drew my attention back to two state b3/s345 (Conway's Life is b2/s23) which can be considered the base rule of Generations 345/3/6 (aka LOTE) and shares a few emergent properties including "sym" (space)ships. In the large, b3/s345 produces a rapidly growing circle of the kind of maze that commonly but temporarily stabilises within LOTE's relatively slowly growing chaotic core areas where it has a statistical upper size limit. In contrast any viable b3/s345 traps a large number and seeming variety of cyclic patterns as it grows which may be at the heart of the performance issues it ran into which prompted me to try to run it on the new iMac. Then when it was stalling not far beyond 48,000 with a live cell (two state) population less than half that reached with (six state) LOTE, our main electric switch failed and since that dark night I haven't got back to it because of something that has stayed more interesting.
From time to time I've run "look aheads" on various sub patterns relying on a now well confirmed but still statistical rule of thumb that no significant information travels faster than ship/engine speed of 1/2 cell per iteration. There are important local examples where this is not true, but given a well selected boundary which is regularly trimmed accordingly, such look aheads can be quite reliable longer term. I've long been interested in the S flank of Whoa because of an extraordinary series of interactions based on the p512t erosion of a wreckage-strewn tagalonged track that has a working paper title "Imagining Pythagorus" but which is a whole other story, though also the reason I pushed Whoa to 250,000 before seriously resuming The Wild.
This time around, I cropped an area with 40 million (live plus dying) cells (as shown in linked 2Mb image below) to use as a base for the look ahead run on the older iMac. This started to look like a good choice as the (retrimmed) pattern peaked close to 65 million in the 280,000s then, with that first growth peak being trimmed away more quickly, dropped close to 12 million in the 350,000s before rising again as the eventual tagalong overload on the Pythag track much further out became dominant. So when the look ahead reached 400,000 with a population over 57 million and certain to keep rising through 450,000 and Wide Block reached 190,000, both in the early hours of Thursday morning, it was time to switch the look ahead to the new machine and get the old machine back to some wider investigations.
It has become almost trite to recite new details that keep emerging, more so as my mind is ever drawn to "what it all means". Given certain disclaimers, especially the universal ones that apply to all cellular automata experiments, I'm more and more forming an impression that LOTE may be already deeper into the zone where deterministic chaos and emergent order can act synergistically (Wolfram's Class 4) than the microscale process which maintains the universe we find ourselves in might need to be. The really interesting thing about LOTE, and the reason for pushing one not quite randomly selected region quite so far, is the extraordinary balance through which none of a dozen plus distinct mechanisms for seeding remote growth centres comes to dominate. That in turn depends on a very specific balance between the frequency of the four relatively common forms of track/trail-laying engine and on none of their even rarer variant forms threatening to become dominant. It also depends on a very particular interaction profile between ships and debris whereby viable reignition is sufficiently rare.
After I've trimmed past the current growth burst in Whoa S (inside y=120000) and seen which subsequent growth centres are likely to become dominant further S, I'll try to follow up with a more illustrative summary.