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Very nearly exploding rules

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Very nearly exploding rules

Postby Tropylium » November 4th, 2011, 2:54 pm

A rule I've found that seems to be sitting right on the edge is 237/34/3. Even small soups commonly last multiple kilogens and leave quite a bit of ash. Yet larger soups seem to eventually settle into just a few active areas which even more eventually wind down all the same.

A loaf is a common spark lasting 45 gens. The simplest pattern that could be called a methuselah I think is the stairstep hexomino, which lasts 1689 gens. At 7 cells, this pattern
x = 4, y = 4, rule = 237/34/3
2.A$.2A$A2.A$.2A!
(= gen 3 of the R-pentomino in Life) lasts 16928 gens…

There seem to be few objects. Five still lifes (block, boat, ship, longboat, beehive — I don't have a proof but I think no others exist) and a p9 "star" oscillator appear commonly. A c/4 spaceship, a p42 reaction between two loaves, and a p68 2-star reaction appear occasionally.
x = 33, y = 33, rule = 237/34/3
20.A5.2A$10.A4.2A2.A.A3.A.A$5.2A2.A.A2.A.A2.A.A2.A.A$5.2A2.2A3.2A4.A
3.2A6$.2A$4A$A3.B25.2A$.A27.A2.A$2.A2.B24.A.A$3.2A8.A17.A$12.A.A$11.A
.A.A$12.A.A9.A$13.A9.A.A$23.A2.A$24.2A10$9.A3.ABA$8.3A2.A2BA$9.A4.3A!
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Re: Very nearly exploding rules

Postby Tropylium » November 6th, 2011, 5:39 pm

Related to the previous: 238/3478/3 features pretty much the most spectacular "seed" explosion I've seen. A humble tub starts out as a failed 2D replicator that settles down after ~6800 generations and a bounding box of ~1200².

Overall this rule is more clearly stabilizing, tho.

Anyone aware of any other 2D replicators that eventually fail? 1D examples are abundant, but I only recall 2D near-replicator examples that grow outwards perfectly regularly while leaving chaotic exhaust towards the center (the same pattern in 238/3468/3 is an example of this sort), not any others that actually halt.

---

I've also changed the topic line to something of possibly more general interest, as I found another Generations rule of the kind: 2356/357/4. This requires humungous soups before it starts exploding. Anything less than 100×100 seems predisposed to stabilize. The general size of active areas seems to display sawtooth-ish behavior much akin to Life: one may with similar likelihood die down or take over half the pattern. Growth is secure only once there are 3-4 well-separated active areas.

This rule also spews 5c/12 bullet-heptomino-based spaceships all over the place, which are even easily reborn from collisions with still lifes; there's probably room for quite a bit of engineering if a gun could be constructed. Alas, no oscillators other than a delayed beacon seem to occur naturally.
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Re: Very nearly exploding rules

Postby EricG » November 7th, 2011, 11:43 am

2356/357/4 is a nice rule - thanks for posting it!

I haven't found a gun, but here's an oscillator that might be useful - maybe two or three of these can be arranged to make a gun:

x = 15, y = 12, rule = 2356/357/4
3.3A3.3A$2.C.AB3.BA.C$.B2.AB3.BA2.B$2ACB2A3.2ABC2A$.B.A2B3.2BA.B$2.4A
3.4A2$4.C5.C$4.2AC.C2A$3.3AB.B3A$3.4A.4A$5.A3.A!


Rakes and puffers are easier thanks to the ubiquitous sparky spaceship.

Here's a double backrake (it fires backward along the axis of its travel, so we can see what might be done with a gun):
x = 29, y = 15, rule = 2356/357/4
9.2A7.2A$9.2A7.2A$3.A21.A$2.ABA5.A7.A5.ABA$2.ACA3.4A5.4A3.ACA$C.3A.CB
ACACB3.BCACABC.3A.C$.B3.B.A2CA2C3.2CA2CA.B3.B$C2.A2.C.2B.2B3.2B.2B.C
2.A2.C$2.BAB19.BAB$2.BAB19.BAB$2.3A19.3A$10.A7.A$9.3A5.3A$9.BAB5.BAB$
9.3A5.3A!



Here's a a chaotic puffer/dirty rake :
x = 19, y = 14, rule = 2356/357/4
$13.A$12.ACA$5.3A4.A.A$4.CABAC3.ABA$3.B2.A2.B2.ACA$3.CAC.CAC2.ABA$3.B
2.A2.B3.A$4.C3AC$5.3A$6.A!



There are any number of those, by doubling them up, by shifting one component by one pixel, etc. This one seemed visually interesting because it made traffic lanes:
x = 44, y = 10, rule = 2356/357/4
10.A22.A$9.ACA20.ACA$2.3A4.A.A4.3A6.3A4.A.A4.3A$.CABAC3.ABA3.CABAC4.C
ABAC3.ABA3.CABAC$B2.A2.B2.ACA2.B2.A2.B2.B2.A2.B2.ACA2.B2.A2.B$CAC.CAC
2.ABA2.CAC.CAC2.CAC.CAC2.ABA2.CAC.CAC$B2.A2.B3.A3.B2.A2.B2.B2.A2.B3.A
3.B2.A2.B$.C3AC9.C3AC4.C3AC9.C3AC$2.3A11.3A6.3A11.3A$3.A13.A8.A13.A!


And finally, it can be cleaned up to make a clean triple-direction rake:
x = 368, y = 316, rule = 2356/357/4
165.A36.A$164.3A34.3A$164.CBC34.CBC$164.CAC34.CAC$165.B36.B$163.CA.AC
32.CA.AC$164.ABA34.ABA$163.2A.2A32.2A.2A$164.ACA34.ACA$165.A36.A7$
130.A11.A82.A11.A$7.2A120.ACA9.ACA80.ACA9.ACA120.2A$2A3.B3A119.2A.2A
7.2A.2A78.2A.2A7.2A.2A119.3AB3.2A$2ACBC.C2.A119.ABA9.ABA80.ABA9.ABA
119.A2.C.CBC2A$2A3.B3A119.CA.AC7.CA.AC78.CA.AC7.CA.AC119.3AB3.2A$7.2A
121.B4.A6.B82.B6.A4.B121.2A$129.CAC2.ACA4.CAC80.CAC4.ACA2.CAC$129.CBC
2.BCB4.CBC80.CBC4.BCB2.CBC$129.3A9.3A80.3A9.3A$130.A11.A82.A11.A7$
135.2A94.2A$135.2A94.2A7$118.ABA30.ABA60.ABA30.ABA$117.ACBCA28.ACBCA
58.ACBCA28.ACBCA$116.3A2BCBC24.CBC2B3A56.3A2BCBC24.CBC2B3A$117.A2.2AC
.A22.A.C2A2.A58.A2.2AC.A22.A.C2A2.A$120.AB5A18.5ABA64.AB5A18.5ABA$
120.2A4B.A16.A.4B2A64.2A4B.A16.A.4B2A$120.AB5A18.5ABA64.AB5A18.5ABA$
117.A2.2AC.A22.A.C2A2.A58.A2.2AC.A22.A.C2A2.A$116.3A2BCBC24.CBC2B3A
56.3A2BCBC24.CBC2B3A$117.ACBCA28.ACBCA58.ACBCA28.ACBCA$118.ABA30.ABA
60.ABA30.ABA2$42.2A280.2A$35.2A3.B3A280.3AB3.2A$35.2ACBC.C2.A278.A2.C
.CBC2A$35.2A3.B3A280.3AB3.2A$42.2A280.2A$135.2A94.2A$135.2A94.2A12$
165.A36.A$164.3A34.3A$164.CBC34.CBC$128.AB12.BA20.CAC34.CAC20.AB12.BA
$127.ACA2.2A4.2A2.ACA20.B36.B20.ACA2.2A4.2A2.ACA$127.A.2ACBCA2.ACBC2A
.A18.CA.AC32.CA.AC18.A.2ACBCA2.ACBC2A.A$124.2AC2AB2ACBA2.ABC2AB2AC2A
16.ABA34.ABA16.2AC2AB2ACBA2.ABC2AB2AC2A$124.2A.ABAC4A2.4ACABA.2A15.2A
.2A32.2A.2A15.2A.ABAC4A2.4ACABA.2A$125.B4.2A.A4.A.2A4.B17.ACA34.ACA
17.B4.2A.A4.A.2A4.B$124.AB2A.CA.A6.A.AC.2ABA17.A36.A17.AB2A.CA.A6.A.A
C.2ABA$124.4A2.BAC6.CAB2.4A72.4A2.BAC6.CAB2.4A$124.AB2A.CA.A6.A.AC.2A
BA72.AB2A.CA.A6.A.AC.2ABA$125.B4.2A.A4.A.2A4.B74.B4.2A.A4.A.2A4.B$
124.2A.ABAC4A2.4ACABA.2A72.2A.ABAC4A2.4ACABA.2A$124.2AC2AB2ACBA2.ABC
2AB2AC2A72.2AC2AB2ACBA2.ABC2AB2AC2A$127.A.2ACBCA2.ACBC2A.A78.A.2ACBCA
2.ACBC2A.A$127.ACA2.2A4.2A2.ACA78.ACA2.2A4.2A2.ACA$77.2A49.AB12.BA80.
AB12.BA49.2A$70.2A3.B3A210.3AB3.2A$70.2ACBC.C2.A208.A2.C.CBC2A$70.2A
3.B3A210.3AB3.2A$77.2A210.2A21$138.A90.A$137.ACA88.ACA$137.A.A88.A.A$
138.A90.A2$138.2A88.2A$138.2A88.2A$138.2A2.A82.A2.2A$138.C2.ACA80.ACA
2.C$137.A2C.2AC80.C2A.2CA$112.2A23.AB2ABABA78.ABAB2ABA23.2A$105.2A3.B
3A23.2A.C2AB4A72.4AB2AC.2A23.3AB3.2A$105.2ACBC.C2.A23.3C.B.C.2A72.2A.
C.B.3C23.A2.C.CBC2A$105.2A3.B3A18.3A3.B.2BCAC2.C72.C2.CAC2B.B3.3A18.
3AB3.2A$112.2A17.BA.BA3.ABA2C2BA74.A2B2CABA3.AB.AB17.2A$131.2CABA4.A
3.ABA74.ABA3.A4.ABA2C$131.2B2A.2A7.A76.A7.2A.2A2B$134.C.2CA90.A2C.C$
135.B2A.C2A84.2AC.2AB$136.2A3.AC82.CA3.2A$138.BAC86.CAB$134.C3.AC2AC.
C78.C.C2ACA3.C$135.5AB86.B5A$134.3A.3A86.3A.3A$135.2A.ACA86.ACA.2A$
139.B88.B3$165.A36.A$164.3A34.3A$164.CBC34.CBC$164.CAC34.CAC$165.B36.
B$163.CA.AC32.CA.AC$164.ABA34.ABA$163.2A.2A32.2A.2A$164.ACA34.ACA$
165.A36.A$150.3A62.3A$144.A5.3A62.3A5.A$143.B.B3.A3CA60.A3CA3.B.B$
143.C.C4.A.2A60.2A.A4.C.C$151.AC62.CA4$139.A10.2A64.2A10.A$138.A.A2.
2A4.A2B64.2BA4.2A2.A.A$139.A3.A5.C2A64.2AC5.A3.A$145.A.A.A68.A.A.A$
141.C.6ABCB64.BCB6A.C$141.B.A2B.A.C.B64.B.C.A.2BA.B$142.2A5.BA66.AB5.
2A$145.ABA.A68.A.ABA$145.ACAB70.BACA$146.3A70.3A4$152.A62.A$151.A.A
60.A.A$150.A.A62.A.A$151.A64.A15$150.C66.C$149.B2.ABA58.ABA2.B$150.C.
2AB58.B2A.C$152.A.B.BA52.AB.B.A$153.2BC.CA50.AC.C2B$153.3ABA52.AB3A$
150.B66.B$149.CBC64.CBC2$148.C3AC62.C3AC$149.3A64.3A$150.A66.A2$154.
2A56.2A$154.2A56.2A2$157.BCB48.BCB$152.A4.ACA48.ACA4.A$151.A.A4.A50.A
4.A.A$150.A.A62.A.A$151.A64.A$165.A36.A$164.3A34.3A$164.CBC34.CBC$
164.CAC34.CAC$165.B36.B$163.CA.AC32.CA.AC$164.ABA34.ABA$163.2A.2A32.
2A.2A$164.ACA34.ACA$165.A36.A14$156.2CB50.B2C$154.2A2C2A48.2A2C2A$
152.2A.3A.A48.A.3A.2A$151.3A3BA2.A46.A2.A3B3A$150.2ACA.2ACB3A44.3ABC
2A.AC2A$150.2A.A4.CBA46.ABC4.A.2A$151.3A3.C.2A46.2A.C3.3A$151.ACBC58.
CBCA$152.2AC.2A52.2A.C2A$153.AC4A50.4ACA$154.2A.C2A48.2AC.2A$152.BC2.
A.2A48.2A.A2.CB$153.C2A.2A50.2A.2AC$153.A.B.C52.C.B.A$154.ACB54.BCA7$
170.3A22.3A$170.AB24.BA$170.2A2.B18.B2.2A$171.2ACA18.AC2A$172.BC2A16.
2ACB$174.C2A14.2AC$173.A.CA14.AC.A$172.ACBA16.ABCA$172.3A18.3A$172.AB
A18.ABA$179.3A4.3A$179.ABA4.ABA$177.BC.A6.A.CB$176.2ACA.A4.A.AC2A$
177.BC.A6.A.CB$179.ABA4.ABA$179.3A4.3A3$161.A44.A$160.3A42.3A$160.CAC
42.CAC$160.ABA42.ABA$160.3A42.3A2$164.3A34.3A$162.2A.2A34.2A.2A$161.
3A.C.2A30.2A.C.3A$160.AC2A2C3A30.3A2C2ACA$159.A2C3.CAC5.2ACB14.BC2A5.
CAC3.2CA$159.A5.B.A.B.AB.A2C14.2CA.BA.B.A.B5.A$160.A2.BC2.AB2CABAB2A
14.2ABABA2CBA2.CB2.A$160.2A2C.CA2CA2.A.A.A14.A.A.A2.A2CAC.2C2A$161.2A
3.B2AC3.3A16.3A3.C2AB3.2A$167.A2.B26.B2.A$168.CB28.BC5$167.C9.C12.C9.
C$166.B11.B10.B11.B$166.2A9.2A10.2A9.2A$165.2A11.2A8.2A11.2A$163.3A2.
C7.C2.3A4.3A2.C7.C2.3A$163.2BC3A7.3AC2B4.2BC3A7.3AC2B$163.2B.3A7.3A.
2B4.2B.3A7.3A.2B$163.2A15.2A4.2A15.2A$165.BC11.CB8.BC11.CB2$171.3A20.
3A$164.3A3.CABAC3.3A6.3A3.CABAC3.3A$163.ABAB2AB2.A2.B2ABABA4.ABAB2AB
2.A2.B2ABABA$163.2B.2B.CAC.CAC.2B.2B4.2B.2B.CAC.CAC.2B.2B$163.2A.2A.B
2.A2.B.2A.2A4.2A.2A.B2.A2.B.2A.2A$164.C.C3.C3AC3.C.C6.C.C3.C3AC3.C.C$
171.3A20.3A$165.C6.A6.C8.C6.A6.C2$164.3A11.3A6.3A11.3A$164.3A11.3A6.
3A11.3A$165.A13.A8.A13.A!



I haven't been able to find a clean side rake -- if anyone does construct one, I'd love to see it!
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Re: Very nearly exploding rules

Postby 137ben » November 7th, 2011, 6:59 pm

A much nicer example is drylife, B37/S23. It supports many small 9c/28 spaceships/rakes/puffers, along with many complex structures similar to life. However, random soups tend to explode, but very, very slowly.
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Re: Very nearly exploding rules

Postby EricG » November 8th, 2011, 12:07 pm

Ben, I completely agree. When I first read the DryLife thread, my mouth dropped open in amazement (like some of the contributors). I'll link to that thread here for anyone new who isn't familiar with it:
viewtopic.php?f=11&t=490

But it is fun to see more "alien" rules too. And the topic of nearly exploding rules is a great one -- such rules recapture the feeling I had watching slow implementations of B3/S23 in the 1980s, before I found out that most soups die out fairly quickly in that rule.

Here's a small precursor to a clean side rake that shoots only to the left and right:
x = 29, y = 18, rule = 2356/357/4
9.A$2.A5.3A$.A.A4.BAB$2A.2A3.3A$2AC2A$2A.2A$.ACA$2.A3$19.A$18.3A5.A$
18.BAB4.A.A$18.3A3.2A.2A$24.2AC2A$24.2A.2A$25.ACA$26.A!


An asymmetrical side rake is surely possible by pairing up this rake side-by-side with a simple puffer, but I'd like to find a more compact example of one. ( Although it isn't the only reason I'm interested in CAs, I like staging shoot-em-ups like the one Platypus5 recently posted about, so I think of a rule as "fun" if it has both a gun, and a rake that either shoots forward or to just one side. :D )
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Re: Very nearly exploding rules

Postby Tropylium » November 8th, 2011, 1:49 pm

137ben wrote:A much nicer example is drylife, B37/S23. It supports many small 9c/28 spaceships/rakes/puffers, along with many complex structures similar to life. However, random soups tend to explode, but very, very slowly.


Yes, I suppose DryLife, and a number of other almost-Life rules, counts as nearly exploding (or rather, barely exploding) as well.

The explosion speed is not really what I'm getting at by "very nearly exploding", though; it's the threshold at how large does a soup have to be before it is "likely" to keep growing indefinitely. In DryLife, the smallest infinite growth pattern is the stairstep hexomino, and a 10×10 soup is easily sufficient. Also, once sufficiently large, barely any clouds of activity ever seem to completely die down, so it is at this point quite easy to tell if you have a chaotic infinite growth pattern on your hands. There are also natural regular infinite growth patterns like the twin-B puffer.

—From the 5c/12 rule, here's a simple clean block puffer:
x = 11, y = 4, rule = 2356/357/4
.A6.3A$3A5.3A$BAB6.A$3A!
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Re: Very nearly exploding rules

Postby EricG » November 8th, 2011, 3:19 pm

A small precursor to a clean rake that shoots to just one side:

x = 51, y = 104, rule = 2356/357/4
3.A$2.ABA$2.ACA$C.3A.C$.B3.B$C2.A2.C$2.BAB$2.BAB$2.3A78$29.3A$23.A5.A
BA$21.5A3.CAC$21.2B.2B3.3A$20.3A.3A3.A$21.2B.2B$21.2A.2A$23.A3$39.3A$
39.ABA5.A$39.CAC3.5A$39.3A3.2B.2B$40.A3.3A.3A$45.2B.2B$45.2A.2A$47.A!
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Re: Very nearly exploding rules

Postby Tropylium » November 8th, 2011, 5:51 pm

And here's an example of why I'm finding 237/34/3 amazing; a 40×40 seed that runs for just over 141000 generations before stabilizing. The final bounding box is around 1200 cells in both directions (excluding one escaping spaceship). If you were to watch it only up to the 50k mark (or even the 100k mark), you surely wouldn't consider this to be a finite-growth rule…
x = 40, y = 40, rule = 237/34/3
.AB.B3.4A.BA2.2B.A5.A.A2.B3.B2A.B$3B.B.A2.B.2A.2B2.A2B4.A.B.2A2.B2.A.
A$B.AB.2B.2B2.A2.2A.B.B2.A.B4.2BA.B$2.2B.2A2B.B2.BAB.B.BA.B3.BA3.2BA
3.2BA$2.4A2.2B.B.B.BA.B.B4AB.A2.AB4AB.2A$A2B.B3.A2.A3.A.A.2B.A2.B.A.
2B2A.A.BA$3.A.B4.A.A2.A3.AB2.2A3.A.A.2AB.B2A$2AB.BA3.B2.AB2.2B.2A.2B.
2A2.B2.B4A2.B$.B2.A2.2B.B2.A.AB2.AB2.B3.2B2AB.A.A.2AB$A2.2B.2B.B.2A.A
3.2B3.B2.A5.B2.A.B$.B3.A.4A2.BAB4.2AB.A.B2A.4BAB.3A$AB2.B2.2A2.AB2.B
2.BA2.2A.2A.B2ABA.2A2.B$2.B4.A3B2.A.A3BABABAB3.B.A.A.A.2B.B$A3.A2.B.B
.B.2A.2B.3BA.BA4.A2BA2.2B$2.A.2A4.AB3.A2B2.B.2A3.2AB2.2BA3.2A$A3B.AB
2A2.AB2AB.A3.A2.2B.2AB.2AB.2B.2B$B.B.B.BAB2.A3.2B4.A2.2B.2B.A.B.A.2A.
B$BA.2AB.B3.3A2.BA2.A.A.2B2.2B.B3.2AB.B$3.A3B.B.A.A.5AB3.A4BA2.A3.A2B
A$2A.2B.A2B2A2B2.2B.B.B2.2BABAB.BA.B3.A$.3A4.2A4.3AB3.2A3.A2.B6.ABAB$
.2AB3AB6.B.B.A4.2A3.2A.B2.B.A$A2B2.AB.B3.A.ABA5.B2AB.3A2B2.2B2.A$.2A
5.3B2AB2.2B.A9.B2.2B.A2BA$2BA.BA.A3BA2B4.B2.2A.A2.2B.B2.A.A.A$.2B.2A.
A3.BA.3B2.2A.BA.2A.A.2B3.ABAB$A2.2B3AB4A2.3BABA8.A3.AB2.A.A$.B.B.BA2.
A2.2A2.2BA.A3.BAB2.A.B.A.B$3.B2.2A.A.A.3A2.2B2ABA2B2A2BAB2.B.2B.A$B.B
3.2A.BAB.B2.AB.A.B2.A.B2.3AB.BA2.BA$3.AB3.B.A2.A3.B.B4.BABA3BA.B$2.A
3.A2.ABA4.B2.3B.B2.A.B3.2AB3.A$2B2A3.B.BA.B2.A2.B.BA.B2.2AB.B4.4B$.A
2.B3.ABA4.B.AB4A4.AB3.B.B3A.A$B2.BAB.AB2.2B3.B3.A2B3.B.3A.AB2AB.2A$.
2B.BA2.4B.BA.B2A2.A.2B2.ABABAB2.2B$A.B2.A.AB.2BABABA6.BA.3B.2BA3.A.2A
$B5.A.2A8.B.B.ABA3.AB3.A.4AB$A.2AB4.A2.2B2.A.A.B.ABA.A.A2.B3.B2.BA$2.
B2.2B3.2B.A2.A2.A.A.A3.BA2.A2.BA2.B!

I dare you to come up with something compareable in DryLife :)
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Re: Very nearly exploding rules

Postby Tropylium » March 26th, 2012, 3:20 pm

Been exploring some non-totalistic isotropic rules lately. Here's a ruletable for one very weakly exploding rule:
#Dustclouds03
n_states:2
neighborhood:Moore
symmetries:rotate4reflect

#B2 growth
0,1,0,1,0,0,0,0,0,1
0,0,1,0,1,0,0,0,0,1

#B3 except growth
0,1,1,0,1,0,0,0,0,1
0,1,1,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,0,1
0,1,1,0,0,0,0,1,0,1
0,1,0,1,0,1,0,0,0,1
0,1,0,1,0,0,1,0,0,1
0,1,0,0,1,0,1,0,0,1
0,0,1,0,1,0,1,0,0,1

#S0
1,0,0,0,0,0,0,0,0,1

#S3
1,1,1,1,0,0,0,0,0,1
1,1,1,0,1,0,0,0,0,1
1,1,1,0,0,1,0,0,0,1
1,1,1,0,0,0,1,0,0,1
1,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,0,1,1
1,1,0,1,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,1
1,1,0,0,1,0,1,0,0,1
1,0,1,0,1,0,1,0,0,1

#D1
1,1,0,0,0,0,0,0,0,0
1,0,1,0,0,0,0,0,0,0

#D2
1,1,1,0,0,0,0,0,0,0
1,1,0,1,0,0,0,0,0,0
1,1,0,0,1,0,0,0,0,0
1,1,0,0,0,1,0,0,0,0
1,0,1,0,1,0,0,0,0,0
1,0,1,0,0,0,1,0,0,0

#D4
1,1,1,1,1,0,0,0,0,0
1,1,1,1,0,1,0,0,0,0
1,1,1,1,0,0,1,0,0,0
1,1,1,0,1,1,0,0,0,0
1,1,1,0,1,0,1,0,0,0
1,1,1,0,1,0,0,1,0,0
1,1,1,0,1,0,0,0,1,0
1,1,1,0,0,1,1,0,0,0
1,1,1,0,0,1,0,1,0,0
1,1,1,0,0,1,0,0,1,0
1,1,1,0,0,0,1,1,0,0
1,1,0,1,0,1,0,1,0,0
1,0,1,0,1,0,1,0,1,0

#D5
1,0,0,0,1,1,1,1,1,0
1,0,0,1,0,1,1,1,1,0
1,0,0,1,1,0,1,1,1,0
1,0,0,1,1,1,0,1,1,0
1,0,0,1,1,1,1,0,1,0
1,0,0,1,1,1,1,1,0,0
1,0,1,0,1,0,1,1,1,0
1,0,1,0,1,1,0,1,1,0
1,0,1,1,0,1,0,1,1,0
1,1,0,1,0,1,0,1,1,0

#D6
1,0,0,1,1,1,1,1,1,0
1,0,1,0,1,1,1,1,1,0
1,0,1,1,0,1,1,1,1,0
1,0,1,1,1,0,1,1,1,0
1,1,0,1,0,1,1,1,1,0
1,1,0,1,1,1,0,1,1,0

#D7
1,0,1,1,1,1,1,1,1,0
1,1,0,1,1,1,1,1,1,0

#D8
1,1,1,1,1,1,1,1,1,0

To be specific, the rule is B3/S03, except with the two bounding-box extending birth environments replaced by their B2 counterparts:
...     ...
.*.  >  .*.
OOO     O.O

...     ...
.*O  >  .*O
.OO     .O.

(Also yes, the table could be written shorter with 8-fold rotation symmetry.)

I find it rather impressiv that there exists a 3-cell methuselah that takes ~14000 generations:
x = 4, y = 10, rule = Dustclouds03
o2$o7$3bo!

Objects-wise there's a fair-sized p2 oscillator grammar and a few larger oscs, including Life's clock (appearing much more regularly than I've seen in any Life-like CA) and an unbreakable frame. I rather like the "rotating" P6:
x = 49, y = 32, rule = Dustclouds03
33bo$26b2o3bo2bo$24b2o2b2o2bo$4b2o24bo$bo2b2o16b2o$43bo$20b2o3bo6bo8bo
bo$14bo11b2o2bob2o3b2o3b2o$bo3bo2bo3b2o4b2o4b2o5bo4bobo5b3o$2bo3b2o3bo
5bo8bo5bo3b2o6bo$45bo2$2bo$7b2obo$2ob2o$8bob2o$2bo32bo11bo$33bobo10bo$
34b2o3bo2bo3b3o$2bo33b10o$3bo8bo23bo8bo$4bo7b2o22bo2bo3bobo$o4bo6bo22b
2o3b3o2b2o$13bo22bo8bo$2bo9b2o22bo8bo$13bo21b2o8b2o$36bo8bo$36bo8bo$
36b10o$33b3o3bo2bo3b2o$35bo10bobo$34bo11bo!


It also seems that the rule grows much faster if there is bilateral symmetry, than if there isn't. Eg. this 3-cell seed reaches a population of 10k around 6 kgens:
x = 1, y = 6, rule = Dustclouds03
o2$o3$o!

Same seed, plus one dot to introduce asymmetry, only reaches a population of 10k after about 32+ kgens.
x = 2, y = 37, rule = Dustclouds03
bo31$o2$o3$o!

This kind of behavior may suggest the existence of an orthogonal spaceship or puffer engine…
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Location: Finland

Re: Very nearly exploding rules

Postby Tropylium » September 7th, 2012, 6:51 am

9 cell, 175773 generation methuselah from 237/34/3:
x = 3, y = 9, rule = 237/34/3
.2A$2AB$.A5$.A$.2A!
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Tropylium
 
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Location: Finland

Re: Very nearly exploding rules

Postby RKTES » August 6th, 2013, 11:02 am

How about B3/S1256? I was looking for chaotic rules with S1 (I decided on its neighbor B3/S126) and I found this VERY slowly exploding rule. Though there are plenty of patterns that settle down.
EDIT: 124567/345678/18 (a.k.a. the result of me trying to cram as many Bs and Ses into a Generations rule as possible) is also right on the edge, and, depending on your definition, may be classified as exploding or very chaotic.
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Re: Very nearly exploding rules

Postby towerator » September 25th, 2013, 5:59 am

I found a semistable, very small puffship reflector
x = 20, y = 37, rule = 2356/357/4
5$8.A$7.A.A$8.A.A$9.A6$3.3A$3.ABA$4.A$3.ACA$3.ABA$4.A4$4.C$4.C$3.ACA$
3.ABA$4.A!

The barge reappears, shifted and moved
This is game of life, this is game of life!
Loafin' ships eaten with a knife!
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Re: Very nearly exploding rules

Postby EricG » September 25th, 2013, 11:29 am

Towerator,

Yup, I love that rule. Earlier in this tread, Tropylium introduced 2356/357/4 and suggested it would be a good rule for engineering. I had so much fun thanks to that suggestion! Thanks Tropylium!

I spent a couple of weeks with 2356/357/4 and with some related rules which support the 5c/12 spaceship, and came up with various guns, rakes, breeders, etc. I really like the overall topic of this thread - "Nearly Exploding Rules" - and some of the other 5c/12 rules don't explode at all, so I'll start a new thread "5c/12 bullet rules". If you're interested in making spaceship guns, it is really fun to play with these rules.

I guess I should add some actual content. Here's one of the ways to make shuttles and loops which lead to guns:

x = 986, y = 473, rule = 2356/357/4
874.C2A.2AC$874.ABA.ABA$874.ACA.ACA$873.2A.B.B.2A61.A$872.C.A.C.C.A.C
58.A2BA$875.B3.B61.2BAC$622.C2A.2AC312.ABA.2A$622.ABA.ABA309.AC3ABABA
$622.ACA.ACA308.6AC.BA$621.2A.B.B.2A61.A246.AC2A.BA$620.C.A.C.C.A.C
58.A2BA$623.B3.B61.2BAC245.AC2A.BA$689.ABA.2A242.6AC.BA$686.AC3ABABA
221.2A20.AC3ABABA$685.6AC.BA187.A26.2A3.B3A23.ABA.2A$686.AC2A.BA188.A
BA25.2ACBC.C2.A22.2BAC$881.ACA25.2A3.B3A23.A2BA$686.AC2A.BA189.A33.2A
25.A$685.6AC.BA186.ABA$686.AC3ABABA186.3A51.3A$689.ABA.2A239.B3AB$
689.2BAC240.A2C.2CA$689.A2BA240.BAB.BAB$691.A241.A2CA2CA$934.B3AB$
936.A8$936.C3$882.A$881.ABA$881.ACA$839.3A3.3A34.C98.C$839.A2B3.2BA
34.C99.A$837.AC.A.A.A.A.CA131.4AC$836.AB2ABCB.BCB2ABA129.B2.CBA$837.
3B2A3.2A3B131.CB3A$837.AB4A.4ABA32.A$587.3A3.3A133.C110.3A.3A34.ABA
97.CB3A$587.A2B3.2BA134.A109.CAC.CAC7.ABA24.ACA96.B2.CBA$585.AC.A.A.A
.A.CA131.4AC106.3A.3A6.BCACB24.B98.4AC$584.AB2ABCB.BCB2ABA129.B2.CBA
107.A3.A6.2ACBCA23.ACA52.2A.2A6.2A17.2A.2A11.A$585.3B2A3.2A3B131.CB3A
118.2A2.3A7.C14.2ABA2.AB40.CB.BC3ACBCBA3.3CBA16.ABACBA9.C$585.AB4A.4A
BA254.2ACBCA24.2A.CA2C.2A.2A32.2CBC.CBCABA.2A6.2A17.2A.2A$588.3A.3A
134.CB3A119.BCACB24.AC3.AB3A.3A33.C3.C2.A$138.A449.CAC.CAC133.B2.CBA
120.ABA25.CB2C3.6A32.C.C3.C.C$136.2A.2A447.3A.3A134.4AC148.BC43.A7.A$
136.2B.2B448.A3.A90.2A.2A6.2A33.A195.ACA5.ACA$135.3A.3A493.AB40.CB.BC
3ACBCBA3.3CBA31.C152.BC42.BCB5.BCB$136.2B.2B490.C.CA2C.2A.2A32.2CBC.C
BCABA.2A6.2A185.CB2C3.6A33.2A3.2A$136.5A490.C3.AB3A.3A33.C3.C2.A198.C
3.AB3A.3A31.3A3.3A$138.A491.CB2C3.6A32.C.C3.C.C199.C.CA2C.2A.2A32.3A
3.3A$630.BC43.A7.A203.AB40.A3.A$674.ACA5.ACA242.3A3.3A$630.BC42.BCB5.
BCB242.3A3.3A$630.CB2C3.6A33.2A3.2A245.A5.A$631.C3.AB3A.3A31.3A3.3A$
631.C.CA2C.2A.2A32.3A3.3A$123.CB.BC9.C.C495.AB40.A3.A$121.2CBC.CB2C8.
B536.3A3.3A$123.C3.C547.3A3.3A164.A$121.C.C3.C.C546.A5.A163.2A.2A$
121.A7.A716.2A.2A$120.ACA5.ACA716.ACA$120.BCB5.BCB716.B.B$122.2A3.2A
719.C$121.3A3.3A718.B$121.3A3.3A718.C$123.A3.A719.3A$121.3A3.3A717.3A
119.3A$121.3A3.3A839.3A$122.A5.A841.C$970.B$970.C$95.3A.3A867.B.B$95.
3A.3A867.ACA$96.C3.C867.2A.2A$93.2A2.B.B2.2A864.2A.2A$93.2AC2A.2AC2A
866.A$93.2A.CA.AC.2A$95.2A3.2A3$884.A5.A$883.3A3.3A$883.3A3.3A$885.A
3.A40.BA$883.3A3.3A32.2A.2A.2CAC.C$883.3A3.3A31.3A.3ABA3.C$632.A5.A
245.2A3.2A33.6A3.2CBC$631.3A3.3A242.BCB5.BCB42.CB$631.3A3.3A242.ACA5.
ACA$633.A3.A40.BA203.A7.A43.CB$631.3A3.3A32.2A.2A.2CAC.C199.C.C3.C.C
32.6A3.2CBC25.ABA$631.3A3.3A31.3A.3ABA3.C198.A2.C3.C33.3A.3ABA3.CA24.
BCACB$632.2A3.2A33.6A3.2CBC163.2A.2A17.2A6.2A.ABACBC.CB2C32.2A.2A.2CA
C.2A24.ACBC2A$630.BCB5.BCB42.CB152.C9.ABCABA16.AB3C3.ABCBC3ACB.BC40.B
A2.AB2A14.C7.3A2.2A$630.ACA5.ACA195.A11.2A.2A17.2A6.2A.2A52.ACA23.ACB
C2A6.A3.A$631.A7.A43.CB148.C4A98.B24.BCACB6.3A.3A$631.C.C3.C.C32.6A3.
2CBC148.ABC2.B96.ACA24.ABA7.CAC.CAC$633.C3.C33.3A.3ABA3.C149.3ABC97.A
BA34.3A.3A$631.2CBC.CB2C32.2A.2A.2CAC.C252.A32.AB4A.4ABA$585.C47.CB.B
C40.BA153.3ABC131.3B2A3.2A3B$584.A136.A3.A107.ABC2.B129.AB2ABCB.BCB2A
BA$581.C4A134.3A.3A106.C4A131.AC.A.A.A.A.CA$581.ABC2.B133.CAC.CAC109.
A99.C34.A2B3.2BA$581.3ABC134.3A.3A110.C98.C34.3A3.3A$717.AB4A.4ABA
205.ACA$581.3ABC131.3B2A3.2A3B205.ABA$581.ABC2.B129.AB2ABCB.BCB2ABA
205.A$581.C4A131.AC.A.A.A.A.CA$584.A134.A2B3.2BA$97.A487.C133.3A3.3A
154.C$25.C2A.2AC63.2A.2A24.B$25.ABA.ABA63.2B.2B23.C.C$25.ACA.ACA62.3A
.3A$24.2A.B.B.2A62.2B.2B118.2A$23.C.A.C.C.A.C61.5A117.ACBA$26.B3.B66.
A120.2A$12.A3.A$11.3A.3A200.2A662.A$11.CAC.CAC85.C.C18.A92.ACBA659.B
3AB$11.3A.3A86.B17.5A69.2A20.2A659.A2CA2CA$8.AB4A.4ABA79.A2B2.3A14.2B
.2B62.2A3.B3A681.BAB.BAB$8.3B2A3.2A3B79.4A.ACBA12.3A.3A2.A58.2ACBC.C
2.A680.A2C.2CA$7.AB2ABCB.BCB2ABA74.C.C.A2B2.3A14.2B.2BA.A.A57.2A3.B3A
682.B3AB$8.AC.A.A.A.A.CA76.B6.B17.2A.2A.A.A65.2A683.3A51.3A$10.A2B3.
2BA14.A69.C.C18.A4.A100.3A702.ABA$10.3A3.3A13.ABA194.BCBC642.A25.2A
33.A$32.ACA106.2A.2A82.A2.3A.2CA636.A2BA23.3AB3.2A25.ACA$33.A80.A3.A
21.3A.3A81.6ACB3A635.CA2B22.A2.C.CBC2A25.ABA$32.ABA78.3A.3A20.A5.A82.
2A.2A.C3.A632.2A.ABA23.3AB3.2A26.A$32.3A78.A.A.A.A19.2CA3.A2C88.B2A
633.ABAB3ACA20.2A$114.A3.A20.BA5.AB724.AB.C6A$236.B2A384.A250.AB.2ACA
$229.2A.2A.C3.A382.A2BA$228.6ACB3A383.CA2B248.AB.2ACA$40.A187.A2.3A.
2CA382.2A.ABA246.AB.C6A$39.3A187.BCBC387.ABAB3ACA243.ABAB3ACA$37.AC.B
CA187.3A387.AB.C6A242.2A.ABA$36.2ABC.BA52.3A.3A520.AB.2ACA245.CA2B61.
B3.B$37.AC3A53.3A.3A772.A2BA58.C.A.C.C.A.C$96.C3.C521.AB.2ACA246.A61.
2A.B.B.2A$37.AC3A51.2A2.B.B2.2A516.AB.C6A308.ACA.ACA$36.2ABC.BA50.2AC
2A.2AC2A306.A3.A205.ABAB3ACA309.ABA.ABA$37.AC.BCA50.2A.CA.AC.2A304.4A
.4A203.2A.ABA312.C2A.2AC$39.3A53.2A3.2A306.3AB.B3A205.CA2B61.B3.B$40.
A368.2AC.C2A206.A2BA58.C.A.C.C.A.C$409.C5.C207.A61.2A.B.B.2A$202.CB5.
BC475.ACA.ACA$204.A3.A198.4A3.4A268.ABA.ABA$30.ABA.ABA166.3A.3A196.B.
A2B3.2BA.B267.C2A.2AC$30.3A.3A166.3A.3A195.2ACB2A3.2ABC2A$30.3A.3A
166.ABA.ABA196.B2.AB3.BA2.B$31.A3.A371.C.AB3.BA.C$29.CB5.BC370.3A3.3A
2$199.A$138.2A3.2A53.3A$136.2A.CA.AC.2A50.ACB.CA$136.2AC2A.2AC2A50.AB
.CB2A$136.2A2.B.B2.2A51.3ACA180.A3.A$139.C3.C238.3A.3A35.3A$138.3A.3A
53.3ACA178.AB2A.2ABA34.ABA$138.3A.3A52.AB.CB2A177.A7.A35.A$7.3A187.AC
B.CA165.ABA.ABA7.2AC.C2A35.ACA$7.CBCB187.3A167.3A.3A7.2A3.2A21.2A12.A
BA$2.A2C.3A2.A187.A168.3A.3A35.2A13.A$.3ABC6A357.A3.A$A3.C.2A.2A356.C
B5.BC35.A$.2AB350.A5.A49.ABA$92.BA5.AB20.A3.A227.3A3.3A48.ACA12.C$.2A
B88.2CA3.A2C19.A.A.A.A78.3A145.CAC3.CAC49.C13.C$A3.C.2A.2A82.A5.A20.
3A.3A78.ABA145.2ACB.BC2A49.C12.ACA$.3ABC6A81.3A.3A21.A3.A80.A146.ABCA
.ACBA62.ABA$2.A2C.3A2.A82.2A.2A106.ACA145.2ACA.AC2A63.A$7.CBCB194.ABA
13.3A3.3A123.2CBA.AB2C$7.3A100.A4.A18.C.C69.A14.A2B3.2BA123.BCA3.ACB
49.A$42.2A65.A.A.2A.2A17.B6.B76.AC.A.A.A.A.CA107.3A3.3A7.B3.B50.ABA$
42.3AB3.2A57.A.A.A2B.2B14.3A2.2BA.C.C74.AB2ABCB.BCB2ABA106.A2B3.2BA4.
C.C5.C.C47.ACA$41.A2.C.CBC2A58.A2.3A.3A12.ABCA.4A79.3B2A3.2A3B105.AC.
A.A.A.A.CA3.B7.B49.A$42.3AB3.2A62.2B.2B14.3A2.2BA79.AB4A.4ABA104.AB2A
BCB.BCB2ABA17.3A39.ABA$20.2A20.2A69.5A17.B86.3A.3A108.3B2A3.2A3B18.B
2A.2A36.3A$19.ABCA92.A18.C.C85.CAC.CAC98.A3.A5.AB4A.4ABA17.AC2AB2CA$
20.2A200.3A.3A97.A.A.A.A7.3A.3A20.BCA.3A$223.A3.A98.3A.3A7.CAC.CAC20.
C$20.2A120.A66.B3.B113.A3.A8.3A.3A23.C$19.ABCA117.5A61.C.A.C.C.A.C
124.A3.A23.C$20.2A118.2B.2B62.2A.B.B.2A$139.3A.3A62.ACA.ACA154.C.C$
114.C.C23.2B.2B63.ABA.ABA154.B.B$115.B24.2A.2A63.C2A.2AC155.A$142.A9$
497.A260.B65.B$327.3A56.A107.CA2BA258.A2CB62.A2CB$327.3A55.ABA107.2AB
C257.A.A2C61.A.A2C$328.C56.ACA107.A2BA256.2A.AC2A59.2A.AC2A$328.B57.C
367.2ACAC3A.2A55.2ACAC3A.2A$328.C15.A41.C108.A2BA256.BC2.2B2ABA56.BC
2.2B2ABA$327.B.B13.ABA74.BCB72.2ABC258.BCA2B.2A40.C.A15.BCA2B.2A$327.
ACA13.ACA73.C.A.C70.CA2BA302.A2C.4A$326.2A.2A10.C.3A.C70.2A.C.2A72.A
259.BCA2B.2A35.2ABAB.B.CA13.BCA2B.2A$326.2A.2A11.B3.B39.A30.4A.ABA
330.BC2.2B2ABA36.A2C.4A12.BC2.2B2ABA$328.A12.C2.A2.C37.ABA30.2A.C.2A
329.2ACAC3A.2A40.C.A12.2ACAC3A.2A$343.BAB39.ACA31.C.A.C331.2A.AC2A59.
2A.AC2A$343.BAB40.A33.BCB333.A.A2C61.A.A2C$343.3A39.ABA12.C.C.C.C350.
A2CB62.A2CB$306.ACA.ACA72.3A11.C7.C19.C2A.2AC324.B65.B$305.A3B.3BA41.
3A15.C.A25.A3.A21.ABA.ABA$306.BAB.BAB41.B3AB10.A2C.4A23.ABA.ABA20.ACA
.ACA$306.3A.3A40.A2C.2CA8.2ABAB.B.CA22.3A.3A19.2A.B.B.2A$306.C5.C40.B
AB.BAB9.A2C.4A48.C.A.C.C.A.C$353.A2CA2CA13.C.A52.B3.B55.2A$354.B3AB
128.AB2A$356.A105.2A22.CA.AC12.2A23.2A$325.ACA133.2A.A17.A2.B2.3A12.
3AB3.2A15.2A.A$138.2A3.2A179.5A133.2A17.AB2AC4A12.A2.C.CBC2A16.2A$
136.2A.CA.AC.2A177.AB.2A.A150.CBA2.AC15.3AB3.2A$136.2AC2A.2AC2A178.2A
.AC2AB129.2A17.2CA2C.2A14.2A23.2A$136.2A2.B.B2.2A179.C.2A2.ACB48.A3.A
73.2A.A16.BA4.A39.2A.A$139.C3.C183.BC.C.BC2A46.3A.3A73.2A18.AB.BAB40.
2A$138.3A.3A183.A.C2.CB46.AB2A.2ABA94.3C$138.3A.3A183.3A.B23.C24.A7.A
94.BAB$327.A2BC2A35.ABA.ABA7.2AC.C2A96.A$328.A2CB36.3A.3A7.2A3.2A77.A
65.A$111.A5.A250.3A.3A89.A2BA62.A2BA$110.3A3.3A250.A3.A90.2BAC62.2BAC
$110.3A3.3A248.CB5.BC88.ABA.2A60.ABA.2A$112.A3.A237.A5.A100.AC3ABABA
57.AC3ABABA$110.3A3.3A234.3A3.3A98.6AC.BA32.C.C21.6AC.BA$110.3A3.3A
234.CAC3.CAC99.AC2A.BA35.B23.AC2A.BA$111.2A3.2A235.2ACB.BC2A137.A2B2.
3A$109.BCB5.BCB233.ABCA.ACBA99.AC2A.BA31.4A.ACBA19.AC2A.BA$109.ACA5.A
CA233.2ACA.AC2A98.6AC.BA29.A2B2.3A19.6AC.BA$110.A7.A234.2CBA.AB2C99.A
C3ABABA33.B23.AC3ABABA$110.C.C3.C.C234.BCA3.ACB102.ABA.2A32.C.C25.ABA
.2A$112.C3.C222.3A3.3A7.B3.B104.2BAC62.2BAC$101.B8.2CBC.CB2C220.A2B3.
2BA4.C.C5.C.C101.A2BA62.A2BA$100.C.C9.CB.BC220.AC.A.A.A.A.CA3.B7.B
104.A65.A$336.AB2ABCB.BCB2ABA$337.3B2A3.2A3B118.C65.C$327.A3.A5.AB4A.
4ABA117.B2.BC3ACA16.ABA37.B2.BC3ACA$326.A.A.A.A7.3A.3A121.C.2CAB4A14.
BCACB37.C.2CAB4A$326.3A.3A7.CAC.CAC122.BAB4CA15.ACBC2A37.BAB4CA$327.A
3.A8.3A.3A124.3AB8.C7.3A2.2A39.3AB$101.A239.A3.A146.ACBC2A$99.5A367.
3AB17.BCACB40.3AB$99.2B.2B365.BAB4CA16.ABA39.BAB4CA$98.3A.3A363.C.2CA
B4A56.C.2CAB4A$99.2B.2B363.B2.BC3ACA56.B2.BC3ACA$99.2A.2A364.C65.C$
101.A4$478.C49.CBA13.C$478.B.3A12.A33.2CBA11.B.3A$479.3AB11.3A26.BC.C
2.4A12.3AB$480.3A11.CBC25.A4.C2.3A13.3A$494.CAC26.BC4.AB$480.3A12.B
33.ACA14.3A$479.3AB10.CA.AC31.ACA13.3AB$478.B.3A11.ABA33.A13.B.3A$
478.C14.2A.2A46.C$494.ACA$495.A4$483.2A64.2A$323.C157.2A.BA61.2A.BA$
322.A158.2A.3A60.2A.3A$319.C4A158.C.2A62.C.2A$319.ABC2.B173.2A.2A6.2A
$319.3ABC158.C.2A12.ABACBA3.3CBA36.C.2A$481.2A.3A11.2A.2A6.2A36.2A.3A
$319.3ABC157.2A.BA61.2A.BA$319.ABC2.B158.2A64.2A$319.C4A$266.2A.2A6.
2A43.A$266.ABACBA3.3CBA43.C$266.2A.2A6.2A34.3A$312.CABAC$311.B2.A2.B$
311.CAC.CAC$311.B2.A2.B$256.A55.C3AC$255.BAB55.3A182.C$254.A.C.C55.A
180.2A2.C$249.2A3.2AB2.A235.ABA$249.3AC.AB4A235.2A2.C$248.4A2.ABA2BA$
249.ABC243.2A2.C$274.2A6.2A.2A208.ABA63.A$249.ABC18.2A.AB3C3.ABCABA
208.2A2.C60.BAB$248.4A2.ABA2BA10.2A2.2A6.2A.2A211.C60.C.C.A$249.3AC.A
B4A298.A2.B2A3.2A$249.2A3.2AB2.A298.4ABA.C3A$254.A.C.C60.C211.2A.2A6.
2A2.2A10.A2BABA2.4A$255.BAB60.C2.2A208.ABACBA3.3CBA.2A18.CBA$256.A63.
ABA208.2A.2A6.2A$318.C2.2A243.CBA$558.A2BABA2.4A$318.C2.2A235.4ABA.C
3A$320.ABA235.A2.B2A3.2A$318.C2.2A180.A55.C.C.A$319.C182.3A55.BAB$
501.C3AC55.A$500.B2.A2.B$500.CAC.CAC$500.B2.A2.B$501.CABAC$502.3A34.
2A6.2A.2A$494.C43.AB3C3.ABCABA$495.A43.2A6.2A.2A$494.4AC$267.2A64.2A
158.B2.CBA$266.AB.2A61.AB.2A157.CB3A$265.3A.2A36.2A6.2A.2A11.3A.2A$
266.2A.C36.AB3C3.ABCABA12.2A.C158.CB3A$307.2A6.2A.2A173.B2.CBA$266.2A
.C62.2A.C158.4AC$265.3A.2A60.3A.2A158.A$266.AB.2A61.AB.2A157.C$267.2A
64.2A4$322.A$321.ACA$273.C46.2A.2A14.C$269.3A.B13.A33.ABA11.3A.B$269.
B3A13.ACA31.CA.AC10.B3A$269.3A14.ACA33.B12.3A$287.BA4.CB26.CAC$269.3A
13.3A2.C4.A25.CBC11.3A$269.B3A12.4A2.C.CB26.3A11.B3A$269.3A.B11.AB2C
33.A12.3A.B$273.C13.ABC49.C5$283.C65.C$275.AC3ACB2.B56.AC3ACB2.B$274.
4ABA2C.C56.4ABA2C.C$275.A4CBAB39.ABA16.A4CBAB$277.B3A40.BCACB17.B3A$
320.2ACBCA146.A3.A$277.B3A39.2A2.3A7.C8.B3A124.3A.3A8.A3.A$275.A4CBAB
37.2ACBCA15.A4CBAB122.CAC.CAC7.3A.3A$274.4ABA2C.C37.BCACB14.4ABA2C.C
121.3A.3A7.A.A.A.A$275.AC3ACB2.B37.ABA16.AC3ACB2.B117.AB4A.4ABA5.A3.A
$283.C65.C118.3B2A3.2A3B$467.AB2ABCB.BCB2ABA$285.A65.A104.B7.B3.AC.A.
A.A.A.CA$284.A2BA62.A2BA101.C.C5.C.C4.A2B3.2BA$284.CA2B62.CA2B104.B3.
B7.3A3.3A$282.2A.ABA25.C.C32.2A.ABA102.BCA3.ACB$282.ABAB3ACA23.B33.AB
AB3ACA99.2CBA.AB2C$282.AB.C6A19.3A2.2BA29.AB.C6A98.2ACA.AC2A$284.AB.
2ACA19.ABCA.4A31.AB.2ACA99.ABCA.ACBA$311.3A2.2BA137.2ACB.BC2A$284.AB.
2ACA23.B35.AB.2ACA99.CAC3.CAC$282.AB.C6A21.C.C32.AB.C6A98.3A3.3A$282.
ABAB3ACA57.ABAB3ACA100.A5.A$282.2A.ABA60.2A.ABA88.CB5.BC$284.CA2B62.C
A2B90.A3.A$284.A2BA62.A2BA89.3A.3A$285.A65.A77.2A3.2A7.3A.3A36.B2CA$
332.A96.2AC.C2A7.ABA.ABA35.2AC2BA$331.BAB94.A7.A24.C23.B.3A$331.3C94.
AB2A.2ABA46.BC2.C.A$288.2A40.BAB.BA18.2A73.3A.3A46.2ACB.C.CB$287.A.2A
39.A4.AB16.A.2A73.A3.A48.BCA2.2A.C$288.2A23.2A14.2A.2CA2C17.2A129.B2A
CA.2A$306.2A3.B3A15.CA2.ABC150.A.2A.BA$288.2A16.2ACBC.C2.A12.4AC2ABA
17.2A133.5A$287.A.2A15.2A3.B3A12.3A2.B2.A17.A.2A133.ACA$288.2A23.2A
12.CA.AC22.2A105.A$327.2ABA128.B3AB$328.2A55.B3.B52.A.C13.A2CA2CA$
382.C.A.C.C.A.C48.4A.2CA9.BAB.BAB40.C5.C$383.2A.B.B.2A19.3A.3A22.AC.B
.BAB2A8.A2C.2CA40.3A.3A$384.ACA.ACA20.ABA.ABA23.4A.2CA10.B3AB41.BAB.B
AB$384.ABA.ABA21.A3.A25.A.C15.3A41.A3B.3BA$384.C2A.2AC19.C7.C11.3A72.
ACA.ACA$411.C.C.C.C12.ABA39.3A$395.BCB33.A40.BAB$394.C.A.C31.ACA39.BA
B$393.2A.C.2A30.ABA37.C2.A2.C12.A$393.ABA.4A30.A39.B3.B11.2A.2A$320.A
72.2A.C.2A70.C.3A.C10.2A.2A$319.A2BAC70.C.A.C73.ACA13.ACA$319.CB2A72.
BCB74.ABA13.B.B$319.A2BA108.C41.A15.C$431.C57.B$319.A2BA107.ACA56.C$
319.CB2A107.ABA55.3A$319.A2BAC107.A56.3A$320.A10$447.A$446.B.B$446.C.
C2$448.C23.A3.A$447.C23.3A.3A8.A3.A$450.C20.CAC.CAC7.3A.3A$444.3A.ACB
20.3A.3A7.A.A.A.A$443.A2CB2ACA17.AB4A.4ABA5.A3.A$405.3A36.2A.2AB18.3B
2A3.2A3B$405.ABA39.3A17.AB2ABCB.BCB2ABA$406.A49.B7.B3.AC.A.A.A.A.CA$
405.ACA47.C.C5.C.C4.A2B3.2BA$405.ABA50.B3.B7.3A3.3A$406.A49.BCA3.ACB$
456.2CBA.AB2C$392.A63.2ACA.AC2A$391.ABA62.ABCA.ACBA$391.ACA12.C49.2AC
B.BC2A$392.C13.C49.CAC3.CAC$392.C12.ACA48.3A3.3A$405.ABA49.A5.A$406.A
35.CB5.BC$444.A3.A$392.A13.2A35.3A.3A$391.ABA12.2A21.2A3.2A7.3A.3A$
391.ACA35.2AC.C2A7.ABA.ABA$392.A35.A7.A$391.ABA34.AB2A.2ABA$391.3A35.
3A.3A$430.A3.A6$401.3A3.3A$400.C.AB3.BA.C$399.B2.AB3.BA2.B$398.2ACB2A
3.2ABC2A$399.B.A2B3.2BA.B$400.4A3.4A2$402.C5.C$402.2AC.C2A$401.3AB.B
3A$401.4A.4A$403.A3.A!
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Re: Very nearly exploding rules

Postby c0b0p0 » April 9th, 2014, 4:12 pm

RKTES wrote:How about B3/S1256? I was looking for chaotic rules with S1 (I decided on its neighbor B3/S126) and I found this VERY slowly exploding rule. Though there are plenty of patterns that settle down.


I was also searching for very nearly exploding rules with S1 (but without S2). I tried some rules with S13 and eventually found B3578/S0138 to be the best rule of this type. The Sidewinder works here, as well as more exotic ships. Looking at the fano.ics.uci.edu database, it appears that the slowest ship is this one.
x = 5, y = 5, rule = B3578/S0138
bobo$ob3o$3bo$obo$o!

Unfortunately, I cannot seem to find any smoking ships in this rule.
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Re: Very nearly exploding rules

Postby simsim314 » April 9th, 2014, 6:42 pm

For 2356/357/4 here is all it's needed for construction arm with 5 streams, that was build for Serizawa Linear Replicator:

x = 1029, y = 133, rule = 2356/357/4
61$77.C.C$75.2A2.C3.2ACA$75.A3B4.AB3A$75.2A2.C3.2ACA$77.C.C11$893.C.C
$886.AC2A3.C2.2A$471.C.C122.C.C257.2A27.3ABA4.3BA$464.AC2A3.C2.2A113.
AC2A3.C2.2A198.C.C54.2A28.AC2A3.C2.2A$463.3ABA4.3BA112.3ABA4.3BA191.A
C2A3.C2.2A89.C.C$110.A321.2A30.AC2A3.C2.2A113.AC2A3.C2.2A94.C.C93.3AB
A4.3BA$109.3A320.2A37.C.C122.C.C89.AC2A3.C2.2A92.AC2A3.C2.2A$109.CAC
175.2A6.2A.2A56.C.C328.3ABA4.3BA99.C.C$109.ABA174.AB3C3.ABCABA49.AC2A
3.C2.2A197.2A97.2A29.AC2A3.C2.2A$109.3A175.2A6.2A.2A48.3ABA4.3BA197.
2A97.2A36.C.C64.2A$349.AC2A3.C2.2A401.2A$356.C.C2$108.2C.2C118.C.C$
110.B113.AC2A3.C2.2A$108.C.B.C110.3ABA4.3BA$109.ABA112.AC2A3.C2.2A$
109.3A119.C.C3$194.2A$194.2A!


For this rule what is missing for universal constructor is synthesis of the p72 oscillator (or what could be much better is stable reflector and duplicator, which very probably exists in this rule).
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Re: Very nearly exploding rules

Postby Dets65 » July 5th, 2014, 4:40 pm

c0b0p0 wrote:
RKTES wrote:How about B3/S1256? I was looking for chaotic rules with S1 (I decided on its neighbor B3/S126) and I found this VERY slowly exploding rule. Though there are plenty of patterns that settle down.


I was also searching for very nearly exploding rules with S1 (but without S2). I tried some rules with S13 and eventually found B3578/S0138 to be the best rule of this type. The Sidewinder works here, as well as more exotic ships. Looking at the fano.ics.uci.edu database, it appears that the slowest ship is this one.
x = 5, y = 5, rule = B3578/S0138
bobo$ob3o$3bo$obo$o!

Unfortunately, I cannot seem to find any smoking ships in this rule.

Took a large area and filled it with random static and ran it for about 700,000 gens, still hasn't become stable. And over all of that time, only one spaceship has been created, but I noticed 4 oscillators.

Here's the patterns I found in case you want them.
#CXRLE Pos=25,30
x = 171, y = 6, rule = B3578/S0138
bo2bo46bo77bo36b2o$ob2obo43b2o116b3o$91b3o34b2o39bo$92bo35bo39b3o$92bo
$92bo!
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Re: Very nearly exploding rules

Postby Tropylium » November 28th, 2014, 4:42 pm

c0b0p0 wrote:I was also searching for very nearly exploding rules with S1 (but without S2). I tried some rules with S13 and eventually found B3578/S0138 to be the best rule of this type. The Sidewinder works here, as well as more exotic ships.

This is a pretty good case, yes. The rule seems to have a very clear "soup size effect" — random clouds of activity will die out fast if exposed to vacuum, but can linger on indefinitely inside an ash zone. Soups seem to need to be somewhere around 120×120 before chaotic growth cases start to turn up commonly!
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Re: Very nearly exploding rules

Postby Kiran » March 4th, 2015, 7:09 pm

x = 51, y = 16, rule = 237/34/3
50.A$49.2A11$2.A$.2A$2A$A!

This nine cell (51x16) pattern appears to explode, I tracked it in golly for 500000 generations but it still shows no sign of subsiding.
The census after 5*10^5 generations is 112362 cells, a 2305x2491 box (excluding two spaceships)
and profuse activity.
I do not know it's eventual fate.
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Re: Very nearly exploding rules

Postby Kiran » March 8th, 2015, 6:27 pm

UPDATE:
After 10^6 generations there are 243851 cells, a 3111x4008 box (excluding 4 spaceships) and still no sign of stability.
Kiran Linsuain
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Re: Very nearly exploding rules

Postby Kiran » March 9th, 2015, 3:54 pm

Is there any script for testing Methuselahs that stops by itself when the pattern stabilizes?
That way I could just keep it running overnight and check it in the morning.
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Re: Very nearly exploding rules

Postby wildmyron » March 10th, 2015, 2:50 am

Kiran wrote:Is there any script for testing Methuselahs that stops by itself when the pattern stabilizes?
That way I could just keep it running overnight and check it in the morning.

Well, you could just set the step to a high value at which golly is still running reasonably efficiently and let it run. For this case step=3 seems to be a good value initially but you may want to reduce to step=2 now that you're at 10^6 gen.

Unless you want to know when it stabilised. This is actually quite tricky because you want to balance efficiency and a reliable test for periodicity. You could use an adaptation of the stabilise3() function from apgsearch. You will want to set the period to be a multiple of the most common period objects in the rule (in this case the p9 oscillator seems like the main thing to consider); lengthen the time in will run for before giving up; remove the naivestab tests; and you will want to replace the "g.run(period)" statement with something like "for j in xlength(n): g.step()" with step already set to 2 or 3. But the main issues are that stabilise3() makes assumptions about the bounding box of the final stabilised area and hashing is a computationally expensive process.

If you can be certain of the period of all naturally occurring patterns then you could use the naivestab() function from apgsearch. Choose a period which is the lowest common multiple of all known periods. Something like this:

import golly as g

# Tests for population periodicity:
# Kludged to use stepsize of 2; period must be multiple of 4
def naivestab(period, security, length):

    depth = 0
    prevpop = 0
    for i in xrange(length):
        for j in xrange(period // 4):
            g.step()
        currpop = int(g.getpop())
        if (currpop == prevpop):
            depth += 1
        else:
            depth = 0
        prevpop = currpop
        if (depth == security):
            # Population is periodic.
            return True

    return False

lcm = 9
security = 20
length = 10**8 // lcm

g.setstep(2)

if(naivestab(4*9, security, length)):
    g.show("Population stabilised")
else:
    g.show("Stabilisation failed")

g.setstep(0)


This is not open ended but will run for a lot longer than apgsearch' default stabilisation routine. I expect you will quit the script before it reaches 100 million gen if the pattern continues to grow indefinitely. I adjusted parameters slightly for your purpose - using step size of 2 seems about right for this pattern in this rule, but you may want to adjust up or down. If some other oscillator or ship emerges with a period which does not divide 36 then the test for stabilisation will fail.
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Re: Very nearly exploding rules

Postby c0b0p0 » March 10th, 2015, 8:52 pm

12478/378/3 also seems to fit the definition. Although large soups are not explosive, there is a 7-cell 17361-generation methuselah, shown below.
x = 14, y = 4, rule = 12478/378/3
10.A$9.A$2A8.A$12.2A!

The rule does not seem to have any other objects of interest. I know of no gliders and only three oscillators (excluding trivial variations of the second one), shown below.
x = 57, y = 5, rule = 12478/378/3
.2A$B53.2A$2A18.2A31.A2.A$19.B2.A31.A.A$19.2A33.2A!
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Re: Very nearly exploding rules

Postby Kiran » March 10th, 2015, 10:19 pm

If some other oscillator or ship emerges with a period which does not divide 36 then the test for stabilisation will fail.

Alas, p42 and p68 oscillators exist, luckily they are rare so perhaps none would remain.
Also how to run that script, does it need Python?
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Re: Very nearly exploding rules

Postby wildmyron » March 10th, 2015, 11:24 pm

Kiran wrote:
If some other oscillator or ship emerges with a period which does not divide 36 then the test for stabilisation will fail.

Alas, p42 and p68 oscillators exist, luckily they are rare so perhaps none would remain.
Also how to run that script, does it need Python?

Yes, it does require Python. When you asked for a script I assumed that's what you meant. Golly only works with Python 2.X (not 3.X) and you need to match 32 / 64 bit versions.

It is certainly possible to use a standalone methuselah detection program but I don't know of any publicly available, especially for rules other than GoL.

You didn't mention whether you want to know when the pattern stabilised.

The high period oscillators make the method using the script above very awkward. To detect population periodicity in the presence of those oscillators you would need to use period = 1071, and to take advantage of step > 0 would require period = 2142 or 4284. It is of course possible to detect population periodicity in other ways which don't depend on knowledge of existing periods but that requires a quite different technique. See the oscar.py script for an example based on hash values - which could be applied to population values alone provided some additional checking is done.
wildmyron
 
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Joined: August 9th, 2013, 12:45 am

Re: Very nearly exploding rules

Postby c0b0p0 » March 11th, 2015, 7:24 pm

I found three new oscillators, shown below.
x = 50, y = 7, rule = 12478/378/3
.A25.2A18.2A$A.A.A20.A3.A16.B2.A$A.A.A20.A.2A17.4A$3.A$.2A22.A.2A18.
2A$25.A3.A$27.2A!
c0b0p0
 
Posts: 645
Joined: February 26th, 2014, 4:48 pm

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