Over the last couple of months, Nathaniel Johnston's Online Soup Search for Conway's Life has been hunting for 20x20 random "methuselah" patterns, using a modest-sized distributed network -- a good fraction of the spare CPU cycles of perhaps a dozen computers. As of the end of August, the conwaylife.com server has tallied the final stabilizations of over 111 million random 20x20 Conway's Life "soups", totaling over three billion Life objects (still-life, oscillator, or spaceship). This is slowly approaching the scale of Achim Flammenkamp's earlier random-ash census project from a decade and a half ago -- which represented an impressive amount of dedicated CPU time for 1994.
Methuselah survival times appear to fit a simple inverse exponential sequence. Lifespans between 1000(N-1) and 1000N are about twice as frequent as lifespans between 1000N and 1000(N+1) -- for a wide range of N. Version 1.03 of the script continuously updates an on-screen table of these frequencies, starting at N=5. It is an open question how far this relationship continues, or whether a larger sample will yield a more precise approximation of the curve.
My ongoing project of going through collisions of a Glider with 16 and 17 bit stable
objects looking for those that might be useful in object construction has found
something else interesting. For the first time, I've come across a methuselah pattern that generates
a natural, non-trivial Clock. The starting pattern is a Glider colliding with a 17-bit object. The Clock appears at generation 864, while the pattern finally settles down at 1507 generations
In the past, some of my large random pattern surveys turned up the occasional Clock, but whenever I looked closely at them, all that were examined showed that the Clock formed in the first generation or two and then somehow managed to survive all the turmoil of the next few thousand generations. I don't remember ever seeing one that appeared midway or late in a pattern's evolution.
Jason Summers took one of the predecessor generations and was able to produce a six-Glider construction which cleanly builds a Clock in 52 generations.
Clocks can be constructed with as few as four Gliders, and a few constructions from other objects are also known.
Andrzej Okrasinski has found a new methuselah record holder, a 15 bit intial pattern with a final population of 1623 after 29053 generations. David Bell quickly found a 13 cell predecessor, bringing the record to 29055.
Some of the more unusual objects which make an appearance but which aren't in the final
census include
a Lightweight Spaceship [9P4H2V0.1],
a Fishook Eater [7.3],
a Long Barge [8.9],
a Big S [14.492],
a Bi-Pond [16.2630]
and an unnamed 13 bit object
[13.182].
| Size | Discoverer | Gens | Final Pop. | Final Pattern, Census |
|---|---|---|---|---|
| 13 |
[David Bell] |
29055 | 1623 |
102(4.1), 2(4.2), 15(5.1), 6(6.2), 57(6.4), 1(7.2), 18(7.4), 5(8.7), 2(12.41), 135(3P2.1), 1(6P2.1), 1(6P2.2), 28(5P4H1V1.1) |
| 15 |
[Andrzej Okrasinski] |
29053 |
Note: Not all of the paths of escaped gliders are shown.
Tomas Rokicki has announced some of the results of a survey for methuselahs. The table below shows the record holding patterns for given bit sizes. More information can be found at his webpage. Other information about methuselahs, can be found at Dean Hickerson's website. Andrzej Okrasinski also announced his finding of the current record holding pattern.
| Size | Name | Gens | Final Pop. | Final Pattern, Census & Discoverer |
|---|---|---|---|---|
|
r Pentomino |
1103 | 128 |
8(4.1), 1(5.1), 1(6.2), 4(6.4), 1(7.4), 4(3P2.1), 6(5P4H1V1.1) |
|
| 5 |
|
1105 | ||
| 6 |
|
1108 | ||
| 7 |
Acorn [Charles Corderman] |
5206 | 633 |
34(4.1), 8(5.1), 3(6.2), 30(6.4), 2(6.5), 5(7.4), 2(8.7), 1(8.8), 41(3P2.1), 13(5P4H1V1.1) |
| 8 |
[Tomas Rokicki] |
7467 | 952 |
51(4.1), 2(4.2), 11(5.1), 4(6.2), 35(6.4), 16(7.4), 2(8.7), 1(14.475), 61(3P2.1), 1(6P2.1), 24(5P4H1V1.1) |
|
Rabbits [Andrew Trevorrow] |
17331 | 1749 |
109(4.1), 4(4.2), 18(5.1), 7(6.2), 65(6.4), 18(7.4), 3(8.7), 136(3P2.1), 2(6P2.1), 40(5P4H1V1.1) |
|
| 9 |
[Paul Callahan] |
17410 | ||
| 10 |
[Tomas Rokicki] |
17423 | ||
| 11 |
[Tomas Rokicki] |
17465 | ||
| 12-18 |
[Tomas Rokicki] |
23334 | 2898 |
207(4.1), 7(4.2), 23(5.1), 12(6.2), 115(6.4), 2(7.2), 32(7.4), 4(8.7), 171(3P2.1), 1(6P2.1), 2(6P2.2), 70(5P4H1V1.1), 1(9P4H2V0.1) |
| 19 |
[Andrzej Okrasinski] |
28786 | 3091 |
196(4.1), 6(4.2), 31(5.1), 9(6.2), 143(6.4), 3(6.5), 34(7.4), 6(8.7), 2(12.41), 1(14.475), 213(3P2.1), 47(5P4H1V1.1) |
Note: Not all of the paths of escaped gliders are shown.