Archive for the restricted patterns Category

Life Letters

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

And now introducing… Life Letters!

LifeAlphabet

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Life Digits (2)

Posted in restricted patterns on July 9, 2009 by DIVVS·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. 😉

Life Digits (1)

Posted in life digits, restricted patterns on June 25, 2009 by DIVVS·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!