Archive for the n-cell thick patterns Category

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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