Search found 86 matches

by NickGotts
November 25th, 2019, 11:46 am
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

The search of single-cluster 10-cell patterns is nearly done - I've generated and tested 85,844,356 patterns, and estimate the total is around 91,000,000. The search has turned up two more patterns that lead into a figure 8 to add to the one I noted in an earlier comment. I found another 5. but on c...
by NickGotts
November 8th, 2019, 5:15 pm
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

Another slight improvement (in terms of life-span) to bunnies10. Let's call this one bunnies10b: lasts 17431. x = 9, y = 6, rule = B3/S23 o$bo$2bo$3bo$2b2obo$6b3o! Bounding box 9*6, MCPS 11. Here's an alternative form - the two have the same immediate successor: x = 9, y = 6, rule = B3/S23 o$2bo$bo$...
by NickGotts
November 8th, 2019, 5:14 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Another slight improvement (in terms of number of life-span) to bunnies10. Let's call this one bunnies10b: lasts 17431. x = 9, y = 6, rule = B3/S23 o$bo$2bo$3bo$2b2obo$6b3o! Bounding box 9*6, MCPS 11. Here's an alternative form - the two have the same immediate successor: x = 9, y = 6, rule = B3/S23...
by NickGotts
November 8th, 2019, 6:19 am
Forum: Patterns
Topic: Soup search results
Replies: 2097
Views: 1216017

Re: Soup search results

However, it's definitely true that infinite-growth patterns haven't traditionally been included in the "methuselah" category. Otherwise there are all kinds of difficult cases that would have to be considered, especially from Nick Gotts' old "Patterns with Eventful Histories" blog , from back in the...
by NickGotts
September 19th, 2019, 10:10 am
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

Cross-posted from "Systematic Survey of Small Patterns". Here are two more variants of bunnies10a (10-cell single-cluster patterns that last 17425 steps). The one on the left has a bounding box 7*5, and an MCPS of 11, which according to the usual criteria for methuselahs makes it the preferred varia...
by NickGotts
September 19th, 2019, 10:09 am
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Here are two more variants of bunnies10a (10-cell single-cluster patterns that last 17425 steps). The one on the left has a bounding box 7*5, and an MCPS of 11, which according to the usual criteria for methuselahs makes it the preferred variant. x = 27, y = 5, rule = B3/S23 bo19bo$3o17b2obo$3bobo19...
by NickGotts
June 12th, 2019, 5:44 am
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Sarp wrote: Are you sure? Code: Select all / Show in Viewer x = 8, y = 6, rule = B3/S23 7bo$6b2o$2o$o$o$bo! You're right of course - and in an earlier post, I described the 8-cell patterns that produce a pentadecathlon plus debris as well as those which produce a pentadecathlon alone - but managed ...
by NickGotts
June 8th, 2019, 11:44 am
Forum: General Discussion
Topic: Is anyone studying the active part of soups?
Replies: 8
Views: 4496

Re: Is anyone studying the active part of soups?

Rhombic wrote : Currently analysing some large 3% density soups to understand what the initial steps in growth would be in an aperiodic, arbitrarily low-density infinite plane. I don't think looking at 3% soups will get you far in understanding the arbitrarily low-density infinite plane ("Sparse Li...
by NickGotts
June 8th, 2019, 5:00 am
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

This is not something that has yet turned up in my survey of single-cluster 10-cell patterns, but something I noticed should do so later. As far as oscillator periods are concerned, we know that 3 cells are required for period 2, 7 for period 3, and 8 for period 15. Turns out 10 are needed for perio...
by NickGotts
June 5th, 2019, 4:19 am
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

OK, I can confirm that the two 10-cell patterns already reported are the only 17425-step methuselahs to turn up so far.
by NickGotts
June 4th, 2019, 6:57 pm
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

A for Awesome wrote (on the Systematic survey of small patterns thread: Trivial variant with a smaller bounding box: Code: Select all / Show in Viewer x = 7, y = 5, rule = B3/S23 bo$3obo$5bo$o3b2o$6bo! With its smaller bounding box, this is clearly the preferred variant, and I suggest putting it in...
by NickGotts
June 4th, 2019, 6:50 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

A for Awesome wrote: Trivial variant with a smaller bounding box: Code: Select all / Show in Viewer x = 7, y = 5, rule = B3/S23 bo$3obo$5bo$o3b2o$6bo! Thanks! Now you point it out, I find* it had actually turned up in my search a little earlier, only I didn't notice it, i.e., I failed to check exact...
by NickGotts
June 4th, 2019, 5:43 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

I managed to miscopy bunnies10a, posting bunnies10 instead. Thanks to moosey for catching the error on the Long-lived methuselahs thread. Here's the real bunnies10a:

Code: Select all

x = 8, y = 5, rule = B3/S23
2bo$ob2obo$6bo$o4b2o$7bo!
by NickGotts
June 4th, 2019, 5:41 pm
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

Apologies, and thanks for pointing out the error - which was not a miscount, but a miscopy, posting bunnies10 rather than the true bunnies10a, which is:

Code: Select all

x = 8, y = 5, rule = B3/S23
2bo$ob2obo$6bo$o4b2o$7bo!
by NickGotts
June 4th, 2019, 5:37 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Just a note on why I estimate 90,000,000 10-cell single-cluster patterns. The numbers of single-cell patterns with successive numbers of cells are (using my algorithm for generating them) as follows, with ratios between the counts for successive numbers of cells, to three decimal places, added in pa...
by NickGotts
June 4th, 2019, 5:16 pm
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

Here's a 10-cell methuselah lasting 17,425 steps - thus beating bunnies10 by just 2 steps: x = 6, y = 6, rule = B3/S23 bo$2obo$4b2o$o2bo$o$o! Step 30 of the pattern is almost the same as step 28 of bunnies10, but lacks a glider which the latter has just thrown off. It thus ends with a population of ...
by NickGotts
June 4th, 2019, 5:13 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Having generated and run 21,186,740 10-cell single-cluster patterns (out of an estimated 90,000,000), I have the first interesting result to report: a methuselah lasting 17,425 steps - thus beating bunnies10 by just 2 steps: x = 6, y = 6, rule = B3/S23 bo$2obo$4b2o$o2bo$o$o! Step 30 of the pattern i...
by NickGotts
April 10th, 2019, 5:31 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

I believe I have now tested all the 9-cell patterns necessary to confirm that there are no infinite-growth patterns with less than 10 cells, reaffirming Paul Callahan's result of 1997. I will now continue on two lines of work in parallel: (1) Checking through all my reasoning and code and possibly s...
by NickGotts
January 21st, 2019, 7:43 am
Forum: Patterns
Topic: Pattern of the Year 2018 competition: Voting
Replies: 57
Views: 27916

Re: Pattern of the Year 2018 competition: Voting

#01 **
#07 ***
#09 **
#11 **
#14 *
#16 *
#19 **
#21 *
#23 *
by NickGotts
January 2nd, 2019, 1:54 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

Thanks for that correction, 77topaz. Progress report: I've now surveyed all the three-cluster 9-cell patterns (the 3-3-3s), and those two-cluster (6-3 and 5-4) patterns in which the larger initial cluster does not , when run by itself turn into a glider, or produce any gliders. Nothing of particular...
by NickGotts
January 1st, 2019, 1:35 pm
Forum: Patterns
Topic: Long-lived methuselahs
Replies: 76
Views: 81867

Re: Long-lived methuselahs

Cross-posted from "Systematic Survey of Small Patterns" http://www.conwaylife.com/forums/viewtopic.php?f=2&t=3604 Here are (what I believe to be) all the distinct 8-cell patterns that last more than 8192 steps. x = 220060, y = 65, rule = B3/S23 40002b2o60018b2o19978b2o30001b2o19995b2o$2o9998b2o9998b...
by NickGotts
December 17th, 2018, 7:15 am
Forum: Patterns
Topic: Soup search results
Replies: 2097
Views: 1216017

Re: Soup search results

dvgrn says: The exponential curve is painfully bumpy, not nice and smooth. If the number of methusalehs in successive bins approximates to a power law, then the curve is not exponential: power law distributions approach zero much more slowly. See https://en.wikipedia.org/wiki/Power_law . I think the...
by NickGotts
December 12th, 2018, 5:51 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

This post is about oscillators, and particularly, oscillator periods. For patterns up to six cells, the only oscillators that appear in the final static debris (I have not checked all intermediate steps) have period 2 (add period 1 if you want to regard still-lifes as period 1 oscillators!). Up to f...
by NickGotts
December 12th, 2018, 3:05 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

2718281828, I have to admit I don't quite understand your definition of a "methusaleh" - I'm not sure I could apply it to decide whether a given pattern is a "methusaleh", or which of two "methusalehs" is more methusalehish. Usually, they are described in terms of the number of steps to stability ra...
by NickGotts
December 12th, 2018, 2:59 pm
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31453

Re: Systematic survey of small patterns

This post is about 8-cell patterns that produce *WSSs. There are no patterns with fewer than eight cells that produce any form of spaceship other than a glider. With 8 cells, of course you can produce an LWSS (just remove the spark from the LWSS’s recurring 9-cell pattern). But it turns out both the...