Archive for the 1-cell thick patterns Category

1-Cell Thick Patterns (3)

Posted in 1-cell thick patterns on July 23, 2009 by DIVVS·IVLIVS

These are the smallest (in terms of bits) one cell thick patterns to emit a glider, lightweight (LWSS), middleweight (MWSS) and heavyweight (HWSS) spaceship.

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n-Cell Thick Patterns (3)

Posted in 1-cell thick patterns, n-cell thick patterns on June 23, 2009 by DIVVS·IVLIVS

It is time for a list of the patterns that have maximum final noninfinite population for each minimal bounding box.

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n-Cell Thick Patterns (2)

Posted in 1-cell thick patterns, n-cell thick patterns on June 21, 2009 by DIVVS·IVLIVS

In this post, I resume the study of the minimum length of an n-cell thick pattern that exhibits infinite growth.

Details on 4-cell thick patterns were pending.  Find out about them here.

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n-Cell Thick Patterns (1)

Posted in 1-cell thick patterns, n-cell thick patterns on June 5, 2009 by DIVVS·IVLIVS

Couldn’t hold my curiosity any longer: “What is the minimum length of an n-cell thick pattern that exhibits infinite growth?”

From November 1997 to October 1998 Paul Callahan found several compact patterns that exhibit infinite growth. Two of these patterns give useful upper and a lower bounds, respectively.

1-cell thick

Minimum-length pattern that exhibits infinite growth:  1 x 39

39b

5-cell thick

Minimum-length 5-cell thick pattern that exhibits infinite growth: 5 x 5

5by5

What’s in between 1-cell thick and 5-cell thick patterns? How about 2-cell thick, 3-cell thick, and 4-cell thick patterns? I have modified my script in Perl for Golly to explore this question.

See details below for 2-cell thick and 3-cell thick patterns…

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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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