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I nominate the patterns found by Nick Gotts in his Systematic survey of small patterns , including Bunnies 10a which broke a long-standing record for population 10 methuselahs. Thanks! I'm surprised (but of course, honoured) for this to be nominated, but I note: 1) That the systematic search of sma...

So it does - thanks.

The c/2 puffer growing from this: x = 3, y = 7, rule = B37/S23 b2o$2o$bo2$bo$2o$b2o! or even this: x = 3, y = 9, rule = B37/S23 bo$bo$2o2$2bo2$2o$bo$bo! emerged out of a large soup. I'd be surprised if it hasn't been reported before, but it doesn't appear in this thread. As with a lot of B37/S23 puf...

muzik wrote: Would exponential growth be possible with a linearly expanding neighbourhood? The most straightforward way to get exponential growth would be to work on a regular tiling of a hyperbolic surface (where the angles of a triangle sum to less than 180 degrees). For example, such a surface c...

This is more of a comment than a request, but I would personally be interested to see the results of running each starting 9 and 10 cell pattern for exactly 12 generations to check for oscillators and spaceships of periods that are a factor of 12. Thanks for your interest. I'd have to do something ...

The survey of single-cluster 10-cell patterns is complete, after 8 months. The total number of patterns generated and tested is 90465963 - right in line with my original estimate of just over 90 million. The only infinite growth patterns found are the one found by Paul Callahan in 1997, and the 5 tr...

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...

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$...

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...

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...

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...

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...

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 ...

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...

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...

OK, I can confirm that the two 10-cell patterns already reported are the only 17425-step methuselahs to turn up so far.

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...

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...

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:

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:

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...

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 ...

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...

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...

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