Life Digits (2)

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)

“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:

And also, happy birthday to me!

n-Cell Thick Patterns (3)

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

n-Cell Thick Patterns (2)

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.

n-Cell Thick Patterns (1)

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

5-cell thick

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

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…

1-Cell Thick Patterns (2)

“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…

1-Cell Thick Patterns (1)

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.

Yet Another Rabbits Relative

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.

Pattern (RLE)

#CXRLE Pos=0,0
x = 5, y = 4, rule = B3/S23
5o$2bobo$obobo$2o!