Tony Smith
Meme Media
Melbourne, Australia
Registered: Oct 2003
Posts: 167 |
At the edges
I've done a lot of work with bounded Rule 22 automata which I call "Trapper" and which are mentioned a bit in another post Irreversibility precedes reversibility and links from there. The ends like yours are empty cells.
From random starting configurations, Trapper tends to converge to configurations where every 4th cell at every 4th generation follows Rule 90, but with slightly more interesting end conditions which are sensitive to trap width. It is often easier to think of adding a buffer cell beyond the active area so the rule is applied across w+2 input cells to give w output cells. Depending on trap width and the allignment of the Rule 90 cells with respect to the edge of the trap, the added edge cells can be either empty or a repeat (reflection) of the cell nearest the edge.
Some of those Rule 90 configurations form huge cycles (c.f. NKS pp. 951L, 963) which I developed a "milestone" technique to compute generations m*2^n for some convenient n via a short cut method involving reflection of a small number (d) of cells on one edge and reflection of the same number across an empty cell on the other edge to produce a starting configuration, the next milestone being given by xoring that configuration with itself displaced by 2d+1 cells.
Given all that and a few other results, I plan to generalise my finite CA engine so it works with a range of edge conditions.
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Tony Smith
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12-17-2003 12:20 AM
