Newsgroups: comp.theory.cell-automata 
From: hopk...@cs.cmu.edu (Don Hopkins) - Find messages by this author  
Date: 19 Nov 92 16:12:22 GMT 
Local: Thurs, Nov 19 1992 8:12 am  
Subject: Re: Symmetric Life rules 
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torb...@diku.dk (Torben AEgidius Mogensen) writes: 




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>   I have been doing some investigations of what I call "symmetric" Life 
>   rules. The idea is to have a set of rule for a variant of Conways Game 
>   of Life, which are symmetric in the sense that a pattern of empty 
>   cells in a field of set cells has exactly the same behaviour as the 
>   corresponding pattern of set cells on an empty field. [...] 

>   I have found such a set of rules and carried out some experiments with 
>   these. The rules are also interesting in that the central cell in the 
>   3x3 neighbourhood counts the same as the other cells. In short, given 
>   that N is the sum sum of all the cells in the 3x3 neighbourhood, a 
>   cell is generated for the next generation based on the following table 


>       N Cell 
>       0  . 
>       1  . 
>       2  . 
>       3  O 
>       4  . 
>       5  O 
>       6  . 
>       7  O 
>       8  O 
>       9  O 



Your rule is similar to the "anneal" rule, but more turbulent. 
Anneal is a voting rule (that counts the 9 neighbors like your rule), 
and votes with the majority -- unless it would be a close vote, then it 
it votes the other way, to shake things up.  The lookup table indexed 
neighbor count for anneal is { 0 0 0 0 1 0 1 1 1 1 }, and the lookup 
table for your rule is...... { 0 0 0 1 0 1 0 1 1 1 }.  The behavior of 
both rules when given random input is to anneal the 1's and 0's into 
bigger and bigger shivering blobs.  If a cell is surrounded by mostly 
the same color then it stays that way, but there is turbulance of 
cells changing back and forth along the edges, which eats away at 
sharp edges and smooths the blobs down, evaporating smaller blobs and 
connecting the larger ones until it looks something like black and 
white spotted cow hide. 

Rudy Rucker's "eco" rule uses "anneal" in one plane, in combination 
with either "life" or "brian's brain" in parallel planes.  Think of 
"anneal" as undulating land and water masses.  If the "anneal" plane 
is land, it computes "life" in the parallel plane at that cell, so you 
have all these critters running around on the land.  Otherwise it 
computes "brian's brain" (a *very* active rule), so there are many 
schools of fishes swimming around in the water.  It's even more 
interesting if you use "anti-life" (the bit reverse of "life", aka 
"pro-choice") instead, since the interactions between "anti-life" and 
"brian's brain" are much more exciting, as the background of 
"anti-life" is stimulus to "brian's brain", and vice-verse.   


        -Don