1-Cell Thick Patterns (3)

Posted in 1-cell thick patterns on July 23, 2009 by DIVVS路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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Life Letters

Posted in restricted patterns on July 15, 2009 by DIVVS路IVLIVS

And now introducing… Life Letters!

LifeAlphabet

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Life Digits (2)

Posted in restricted patterns on July 9, 2009 by DIVVS路IVLIVS

Using the standard ‘life digits‘ these are the smallest numbers that can produce infinite growth for each base from 2 to 10:

Base 02: 16-digits: 0011001000100011
Base 03: 11-digits: 21011121122
Base 04: 10-digits: 0023321310
Base 05: 08-digits: 40101123
Base 06: 07-digits: 0253033
Base 07: 07-digits: 0051165
Base 08: 07-digits: 140732
Base 09: 07-digits: 140732
Base 10: 06-digits: 140732

Surprise! Dean Hickerson thought that the smallest number that produces infinite population growth was 154299. 馃槈

Life Digits (1)

Posted in life digits, restricted patterns on June 25, 2009 by DIVVS路IVLIVS

“Using the standard ‘life digits‘ what is the smallest number base that can produce infinite growth?”

asks knightlife in a post at ConwayLife.com.

As always, a quick modification of my script in Perl for Golly, wait 7 minutes and… profit.

The string in question is 0011001000100011 and has 16 bits.

Pattern (RLE)
#CXRLE Pos=0,0
x = 51, y = 5, rule = B3/S23
3ob3obobob3ob3obob3ob3ob3obob3ob3ob3obobo$obobobobobobobobobobobobobob
obobobobobobobobobobobo$obobobobobobobobobobobobobobobobobobobobobobob
obobo$obobobobobobobobobobobobobobobobobobobobobobobobobo$3ob3obobob3o
b3obob3ob3ob3obob3ob3ob3obobo!

It produces two block-laying switch engines, and achieves stability at generation 1507:

0011001000100011

And also, happy birthday to me!

n-Cell Thick Patterns (3)

Posted in 1-cell thick patterns, n-cell thick patterns on June 23, 2009 by DIVVS路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路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.聽 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路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:聽 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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