1-Cell Thick Patterns (2)

Posted in 1-cell thick patterns on April 2, 2009 by DIVVS·IVLIVS

“What’s the smallest one cell high pattern to emit a glider?”

asks Macbi in a post at ConwayLife.com

I have modified my script in Perl for Golly, which explored all possible one-cell thick patterns, in order to provide a specific answer to the previous question.

It took five seconds to get the results…

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1-Cell Thick Patterns (1)

Posted in 1-cell thick patterns on June 10, 2008 by DIVVS·IVLIVS

Recently, I have programmed a script in Perl for Golly. It explores all possible patterns of height 1. The method is the exhaustive enumeration of sequences that don’t contain any isolated live cells or pairs of live cells.

This task has been done before by Paul Callahan in October 1998, when he did an exhaustive search to find the smallest undimensional example which exhibits infinite growth (that is, the population tends to infinity, or at least is unbounded). However, it seems that the only result he reported to a private mailing list of Life enthusiasts was the one that he was searching for: a 39×1 pattern that produces two block-laying switch engines.

I ignore how much time Callahan needed to generate such a discovery, but with today’s computers, we can accomplish this feat in less than two days. (Assume a well-designed script that also ignores patterns with only a mix of 3 and/or 4-cell groups; note that removing symmetrical patterns also helps to improve the overall speed.)

The purpose here is to comment on the patterns that my script found in terms of their increasing final population.

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Yet Another Rabbits Relative

Posted in methuselahs on June 10, 2008 by DIVVS·IVLIVS

Rabbits is a 9-cell methuselah (stabilizes at time 17331) found by Andrew Trevorrow (one of the developers of the almighty Golly simulator) in 1986.

The methuselahs section on Dean Hickerson’s Game of Life page is a good source for several rabbits relatives; however I did not find there the following 12-cell pattern, which fits inside a 5×4 square.

Someone probably found this pattern earlier, but I don’t think it has been mentioned before.  It runs for 17426 generations. As far as I know, only three other rabbits relatives last longer than that.

Yet another Rabbits relative

Pattern (RLE)
#CXRLE Pos=0,0
x = 5, y = 4, rule = B3/S23