Dan Ellwein
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Ridgeland, MS
Registered: May 2004
Posts: 32 
1D CA Rules containing 1 Black Square...
There are 8 rules containing 1 Black square corresponding to the powers of 2...
Rules
1, 2, 4, 8, 16, 32, 64, 128
I wanted to see what the distribution of the 8 combinations (resulting from 3 adjacent cells) would be from running these CA's.
I ran these 8 Rules long enough for them to produce the pattern they were going to make.
Four of the Rules  8, 32, 64, 128 produced a single point.
Three Rules  2, 4, 16 produced a left diagnol, vertical line, and right diagonal respectively.
Rule 1 produced a horizontal line.
In all, it took a total of 10 iterations resulting in 42 combinations being produced.
Here is how the 8combination distribution looked:
BWB (5)  0
WBB (3)  1
BBW (6)  1
BBB (7)  3
WBW (2)  8
WWB (1)  9
BWW (4)  9
WWW (0)  11
All 8 combinations were produced except for combination  5.
This is understandable since this is the only one of the 8 combinations that has non adjacent black cells.
Using the above list I rearranged the order of the Rules based on a lesstomore approach (of the 8combinations produced) and got the following:
Rules
32, 8, 64, 128, 4, 2, 16, 1
I think this is a more useful way to look at the 256 Rules.
I have an excel file that graphically shows what I am (trying) to say.
I will email this to those who would like to look at it.
Dan Ellwein
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