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Adding a dimension to "growing spaceship"/puffer

PostPosted: February 19th, 2011, 6:06 am
by ynotds
This has to be seen to be believed:
Open from Golly 2.2
(1.11 KiB) Downloaded 293 times
Just when I was congratulating myself on finally putting to bed the last renderings of my two years work work with Generations 345/3/6, aka LOTE, a pattern appeared which is already wallpaper. Still in the relatively early stages of exploring my LOTE-like corner of the previously mentioned WMPVN rule space, the coin fell on revisiting a family I had earlier left half done. Five weeks back I had run both the only viable (orthogonal) ship-ship collision seed in WMPVN-45678_459_18 and one of three viable in WMPVN-45678_459_16 to 100,000 iterations, but had not looked at the other two, nor at WMPVN-45678_459_17 which turned out to have two viable, the smaller of which produced this monster just before 50,000. Beyond the coexistence of three very distinct periodic processes, the main significance might be the complicated but ultimately wick stretcher-like expansion of an active moving edge by (70, 4) every 152 iterations, a problem I don't recall having seen even an engineered solution to. The alternation of 9 wide stable structure and 15 wide long period channels behind the edge is just a bonus. And yes, it is in some ways reminiscent of Star Wars, but in a corner of rule space with much lower natural growth.

18 months on

PostPosted: August 25th, 2012, 12:14 am
by ynotds
I and several computers are increasingly preoccupied surveying similar "growth shoulder" mechanisms found across some but far from all rules of the form WMPVN-45678x/459/n, where x indicates the presence or absence of c (12).

It is still too early to try to report anything comprehensive, but the rule which scores highest in the intersection of productivity and interest is 45678c/459/11 where I've been running viable seeds to 70,000 iterations, beyond which they become impractically slow, and using full screen capture at 24" iMac resolution to record mostly still growing structures which are uploaded to:
The currently 50 PNGs cover 46 developing structures, the three biggest as left-right pairs and one ancillary flotilla, with more on the way.

Having proclaimed in a conference paper in February that attractor basins are it, this rule has since shown that escape from chaos into some periodic process is not everywhere guaranteed. While there is one relatively very short period attractor and at least one very long period one in these examples and others suggest aperiodic shoulder growth can remain at risk of termination, more than a few show no obvious indicator of a likely end state. Further reflection and some less productive recent work with /7 suggest uncertainty at the edge of chaos is something that should have still been admitted, but had become obscured in February by a long run of emergent orderly forms under other rules in the family.