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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 8-combination 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 less-to-more approach (of the 8-combinations 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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