Registered: Oct 2003
This is basically about where NKS has led me almost nine years on, and where I've found it more productive to follow my nose.
Within the last 24 hours I have finished off my rendering of images of the 500+ worlds I have been able to explore the early moments of under the finely balanced physics emergent from the Generations 345/3/6, aka LOTE, rule across the past couple of years, and I have found something even more powerful in my chosen LOTE-like corner of the WMPVN metaverse. (To see the latter open and run the attached tiny zip in Golly 2.2.)
I should first say something about Generations type rules including WMPVN and numbering schemes. While traditional application of the notion of states/colours deems otherwise, these rules are morally three state rules: live, empty and dying, where the dying state differs from the others both in that it is ignored by and ignores them and because instead each dying cell carries a counter which simply decrements each step from first dying to empty. One important consequence is that while it takes exponential time to create rule trees for general multistate rules, I have provided a script which almost instantly generates every rule tree for any individual WMPVN rule up to Golly's maximum of 254 step dying.
My initial concern with NKS was that it appeared to represent a retreat from the to me then supreme notions of edge of chaos/Class 4 and I briefly developed a plan to tackle that question through a larger rule space, an idea that was finally buried when Apple dropped Altivec. Then along came Golly 2.0 and I learnt through LOTE that there is actually creative synergy between (deterministic) chaos (strictly defined as extreme sensitivity to initial conditions) and emergent order. They are not opposite sides of some border but rather their coexistence defines Class 4. My one more problem was that it was increasingly difficult to write about what I was finding under LOTE without better comparators, so the need for a larger rule space returned.
Here I must also say something about the wider CA community's persistent way of numbering rules and totalistic rules in particular. After moving on from the arbitrary neighbourhoods I long ago introduced in Pattern Breeder for other reasons, I have only really been captured by rules which avoided preferencing directions. The wider community has persisted with referring to Conway's Game of Life rule as b(orn)3/s(urvive)23 and similarly naming all outer totalistic von Neumann (8 neighbour) rules. Even within that rule space, there are things that can be seen from similar numbering that are missed by Wolfram's more orthogonal approach, e.g. adding an 8 to b or s often makes very little difference as cells rarely come into or stay in positions with 8 live neighbours under most rules. Generations rule numbering reverses the order to s/b (and without the letters) and adds a third number which is basically dying+2, or the number of states under naive interpretations.
I've never been entirely happy with the notion that diagonally adjacent should count the same as immediately adjacent (Moore neighbourhood) and I've long been comfortable with influence dropping as the inverse square of distance, so when a need to get into rule trees coincided with a need to start exploring an expanded rule space, creating "weighted Moore plus von Neumann" (WMPVN) became obvious. By counting adjacent cells as 2 and diagonal neighbours as 1, we finish up with a range of 0-12 possible neighbours in contrast to 0-8 for Generations. Each extra number is one bit in rule space, so WMPVN is already 2^8 times bigger than Generations. The numbering schemes also showed me that my only real comparator targets in Generations must be of the form 345x/3xxx/n where each x is an optional number decreasing from the maximum, and that the most important emergent behaviour I have become all too familiar with would be similarly found in WMPVN 45678xx/45xxxx/n. (WMPVN uses a-c for 10-12.) This initially looked to only be a four fold increase in space, but that was before the very different applicable ranges of n were investigated and found to have further expanded the target space several times over, with all that implies for fine grained navigation.
It is the couple of months starting to explore my target corner of WMPVN that has produced riches. When I started with LOTE I initially worked from just one seed (chosen by fortuitous mistake) then when that started to take too much capacity, I started looking at what were effectively new worlds sharing the same physics but differing in often spectacular ways through the orderly structures that unpredictably emerge. Under WMPVN it is very different as I try to get a map of the metaverse while individual universes (or closely related clusters) keep demanding more comprehensive attention. To date, I've only conceded to starting a couple of significant surveys of multiple viable seeds under the same rule: one for 45678c/459abc/12 in which a period 163 Fredkin XOR/Pattern Breeder-style replicator emerges and forms a growing skin around chaotic core, containing but accelerating the core growth, with which I've been running 50 seeds to 80,000; and 45678bc/459ab/24 whose first viable seed produced a very complicated expanding, rake-producing puffer ("delta") which had me quickly making up to a starting set of 20 viable seeds, all of which have now been run to 100,000 with that first seed still running on towards 200,000.
One early inescapable meta discovery about my target corner of the WMPVN metaverse is that all 45678bx/459xxx/>15 rules readily produce a 13/58 speed diagonal spaceship which provides an eight point compass-like background to patterns evolving under those rules as a contrast to the four point star that similarly serves LOTE and the rest of my corner of WMPVN. (Interactions between diagonally and orthogonally moving rakes also make deltas more spectacular.) That was but the first of several meta discoveries of regions of the metaverse where particular mechanisms conspicuously flavour generated patterns. But just as important are specific mechanisms which arise and play a dominant role in just one rule (or sometime 2 or 4 closely related rules) and you only get to discover those one at a time. In the particular case of the discovery in the attached zip (for some meaning of "in"), five weeks ago I had run seeds from the /16 and /18 rules to 100,000 but hadn't looked at /17 until today. And if you really can't run Golly to see it emerge from nowhere special, I've already made wallpaper out of it run to 20,000.
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Complex Systems Analyst
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