Registered: Oct 2003
Reproducing pattern surrounds chaotic core of otherwise ordinary CA
Some essential background: My original interest in CA was sparked by a 1983 Scientific American column describing Ed Fredkin's trivial (XOR-based) solution to the previously holy grail of patterns which reproduce themselves. In that previous time of disruption due to flood damage along the Great Ocean Road, I was in Lorne for the weekend with a forgotten luggable with a small bitmapped screen and GW Basic to review for Australian Micro Computerworld, so implementing Fredkin's automata looked like an ideal test project. The next year I realised I could generalise it a bit using the early Mac's black and white graphics, and produced Pattern Breeder which was featured in turn in SciAm in September 1986, so I became more than familiar with Fredkin-style pattern replication. Exactly 25 years ago we were assembling Pattern Breeder packs ready to fly to San Francisco for Macworld Expo.
Fast forward. After two years accumulating masses of data on the very interesting Generations 345/3/6 rule, I found a quick method for generating rule trees for a slightly enlarged class of rules which I have called WMPVN for "weighted Moore plus Von Neumann" where the still, at least to my mind, totalistic count adds two for each directly adjacent cell (NSEW) and one for each diagonally adjacent, providing a count range of 0-12 rather than the 0-8 for Von Neumann used by Generations and other CA algorithms. WMPVN rules also borrow the dying cells notion from Generations, implementing what is really one fixed time count down state which ignores and is ignored by other cells as an increasing sequence of states. It turns out that it the small corner of the WMPVN rule space that I had identified as being likely to have comparators for Generations 345/3/6, that the most interesting have much longer dying times than in Generations, so I was steadily working through the 64 target families until derailed by a discovery in the early hours of Sunday morning that is the subject of this post.
Looking at my first candidate seeds for 45678c/459abc/12 I quickly saw that
was undergoing Fredkin-style replication, producing two copies of itself after 163 iterations. (Coincidentally that same shape was driving something else interesting under an unrelated rule I was monitoring on another computer at the same time.)
I'm now midway through test runs with my first 50 viable seeds. The take home message is that the slowly growing chaotic core is eventually surrounded by diagonally oriented fringes of replicators produced from one, two or three first movers. (I'm tempted to name the rule Othello because the first replicator to get a corner usually wins.) It is also important to note that the rate of growth of chaotic core inside this skin of replicators significantly exceeds the rate of growth of chaotic core exposed to empty grid, again illustrating the synergy between (deterministic) chaos and emergent order which has killed my long obsession with edge of chaos and given clarity to Wolfram's notion of Class 4 rules. To me, they are simply now rules which produce both chaos and order from different data patterns.
For those who have Golly 2.2 or are happy to get it from SourceForge. You just need to open the attached small zip file from Golly and run it. It is one of my early viable seeds. The first replicatior emerges on the SE flank around iteration 20,000, so you might want to hit Control>Faster (+) at some stage.
This has been downloaded 661 time(s).
Complex Systems Analyst
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