Rules with Abnormally Common High-Period Patterns

[drc]

p26 in B36/S125:

Code: Select all

x = 3, y = 4, rule = B36/S125
o$2o$b2o$2bo!

p16 in B3678/S34678:

Code: Select all

x = 2, y = 3, rule = B3678/S34678
2o$2o$bo!

[drc]

p32 in B3578S2478:

Code: Select all

x = 9, y = 4, rule = B3578/S2468
bo5bo$3o3b3o$3o3b3o$bo5bo!

[muzik]

Some well known ones:

tlife pre-loaf (p160)

Code: Select all

x = 4, y = 3, rule = tlife
3o$3o$3bo!

salad stairstep (p66)

Code: Select all

x = 3, y = 4, rule = salad
o$2o$b2o$2bo!

B2in3 S123a is absolutely brimming with high periods:

Code: Select all

x = 32, y = 11, rule = B2in3_S123a
15b2o$14bo12b3o$25bo5bo$13bob3o$o2bo7bo6bo$o2bo6bo2bo3bo8bo3bo$b2o7bo
2bo13b3o$13bobo12bo$2b2o10bo$bo2bo$bo2bo!

[Lewis]

B358/S23 has this p412 oscillator that's fairly common naturally as far as I can remember (maybe about as rare as the pulsar in Life, not sure if that counts for this thread):

Code: Select all

x = 14, y = 14, rule = B358/S23
2b3o4$10bo$10bobo$10bo2bo$12bo3$2o2b3o$2o$5bobo$6bo!

EDIT: also this P36 in Day & Night:

Code: Select all

x = 5, y = 5, rule = B3678/S34678
o$b2o$bob2o$2b3o$2b2o!

[muzik]

Rare-ish but still fairly common p14 in B3/S12 we all should know:

Code: Select all

x = 7, y = 3, rule = B3/S12
obo3bo$obo3bo$3bo!

[Apple Bottom]

Very small p40 oscillator:

Code: Select all

x = 3, y = 4, rule = B35678/S13
bo$3o$2bo$b2o!

Works in all rules from B356/S13 to B35678/S135678.

[drc]

(16,5)c/74 from B-Heptomino:

Code: Select all

x = 3, y = 4, rule = B3_S23-e4e
bo$2bo$2bo$3o!

[ygh]

What do I win? (p576 with 5-cell predecessor)

Code: Select all

x = 0, y = 0, rule = B3_S2-i3-a4cake
b2o$2o$bo!

[muzik]

What do I win?

Code: Select all

x = 0, y = 0, rule = B3_S2-i3-a4(cake)<--This
b2o$2o$bo!

here you go.

[ygh]

Are 3-cell guns good?

Code: Select all

x = 0, y = 0, rule = B2ce3ai_S2-i3-a5678
2bo$bo$o!

[wildmyron]

Are 3-cell guns good?

Code: Select all

x = 0, y = 0, rule = B2ce3ai_S2-i3-a5678
2bo$bo$o!

That 3 cell pattern is actually a predecessor of the gun - the lowest population phase of the gun is actually 20 bits (at 2 consecutive generations).

I would say that it is an extraordinary pattern: You have a volatile rule which doesn't hint at all at being explosive (in fact it stabilises quite quickly) with a 3 bit pattern that is a predecessor for a p163 statorless quad gun which fires 2c/13 diagonal gliders, where both the gun period and the ship period are prime and relatively high. That is fantastic! In fact, I'm sure I've run out of superlatives.

In addition, there's a tiny c/2 ship with two interesting head on collisions:

This one synthesizes the gun,

Code: Select all

x = 21, y = 3, rule = B2ce3ai_S2-i3-a5678
2o17b2o$2bo15bo$2o17b2o!

And in this collision one ships eats the other while passing through unscathed.

Code: Select all

x = 14, y = 13, rule = B2ce3ai_S2-i3-a5678
2o$2bo$2o8$2o8b2o$2bo7bo2bo$2o8b2o!

Edit:

Still a bit off-topic, but just wanted to add this push reaction for the gun. One of many I'm sure.

Code: Select all

x = 20, y = 20, rule = B2ce3ai_S2-i3-a5678
16bo$15bobo$14b5o$13bobobobo$14b5o$15bobo$16bo9$b3o$obobo$bob2o$b2obo$
3bo!

[Sphenocorona]

Since the above rule is closely related to the extremely oscillator-fertile B2ce3ai/S23 rule, I would not be surprised if it turns out to be omniperiodic as well. Here's a small sample of oscillators (or oscillator predecessors), most of them with extremely similar initial predecessors:

Code: Select all

x = 164, y = 192, rule = B2ce3ai_S2-i3-a5678
142b2o$142bo$139b2o2bob2o$140bo2b2obo$138bo9bo$87b2o49b2o2b3o2b2o$87bo
52b2obob2o$84b2o2bob2o50bobo$85bo2b2obo19b2o30bo$83bo9bo17bo$83b2o2b3o
2b2o14b2o2bob2o$85b2obob2o17bo2b2obo$107bo9bo$64b2o19b2o3b2o15b2o2b3o
2b2o$64bo20bo5bo17b2obob2o$61b2o2bob2o16b3ob3o19bobo$62bo2b2obo19bo23b
o$60bo9bo$60b2o2b3o2b2o$62b2obob2o$60b2o7b2o$60bo9bo$60b4o3b4o$64bobo
2$63bo3bo$63b2ob2o19bobo$65bo$87bobo53bo$87b3o52bobo$86b2ob2o49b2obob
2o$86bo3bo47b2o2b3o2b2o$86b2ob2o47bo9bo$60bo79bo2b2obo$58b2ob2o22b2obo
b2o47b2o2bob2o$58bo3bo20b2o2b3o2b2o18bo29bo$83bo9bo17bobo28b2o$59bobo
23bo2b2obo17b2obob2o$55b4o3b4o18b2o2bob2o15b2o2b3o2b2o$55bo9bo21bo19bo
9bo$55b2o7b2o21b2o20bo2b2obo$57b2obob2o44b2o2bob2o41b2o$55b2o2b3o2b2o
45bo45bo$55bo9bo45b2o41b2o2bob2o$57bo2b2obo69b2o20bo2b2obo$56b2o2bob2o
69bo19bo9bo$59bo70b2o2bob2o15b2o2b3o2b2o$59b2o70bo2b2obo17b2obob2o$
129bo9bo17bobo$129b2o2b3o2b2o18bo$131b2obob2o$133bobo$92b2o40bo$92bo
20b2o$89b2o2bob2o16bo$90bo2b2obo13b2o2bob2o$88bo9bo12bo2b2obo$88b2o2b
3o2b2o10bo9bo$90b2obob2o12b2o2b3o2b2o$92bobo16b2obob2o$93bo19bobo$114b
o8$74b2o$74bo59bo$71b2o2bob2o54bobo$72bo2b2obo14bo37b2obob2o$70bo9bo
11bobo34b2o2b3o2b2o$70b2o2b3o2b2o9b2obob2o17bo14bo9bo$69bo2b2obob2o2bo
6b2o2b3o2b2o14bobo15bo2b2obo20bo$74bobo11bo9bo12b2obob2o12b2o2bob2o19b
obo$75bo14bo2b2obo12b2o2b3o2b2o13bo21b2obob2o$89b2o2bob2o12bo9bo13b2o
18b2o2b3o2b2o$92bo18bo2b2obo35bo9bo$92b2o16b2o2bob2o37bo2b2obo$113bo
40b2o2bob2o$113b2o42bo$157b2o$58b2o75b2o$58bo16bo59bo$55b2o2bob2o11bob
o15b2o18b2o18b2o2bob2o$56bo2b2obo6bo2b2obob2o2bo10bo19bo20bo2b2obo$54b
o9bo5b2o2b3o2b2o8b2o2bob2o12b2o2bob2o14bo9bo$54b2o2b3o2b2o5bo9bo9bo2b
2obo13bo2b2obo14b2o2b3o2b2o$56b2obob2o9bo2b2obo9bo9bo9bo9bo14b2obob2o$
39b2o17bobo10b2o2bob2o9b2o2b3o2b2o9b2o2b3o2b2o16bobo$39bo19bo14bo15b2o
bob2o13b2obob2o19bo$5b2o29b2o2bob2o30b2o16bobo17bobo$5bo31bo2b2obo49bo
19bo$2b2o2bob2o25bo9bo$3bo2b2obo25b2o2b3o2b2o$bo9bo12b2o11b2obob2o$b2o
2b3o2b2o12bo14bobo17bo14b2o$3b2obob2o11b2o2bob2o10b3o16bobo13bo$22bo2b
2obo27b2obob2o8b2o2bob2o$20bo9bo4bo9bo8b2o2b3o2b2o7bo2b2obo$5b3o12b2o
2b3o2b2o23bo9bo5bo9bo$19bo2b2obob2o2bo7b3o14bo2b2obo7b2o2b3o2b2o$6bo
13bo9bo8bobo13b2o2bob2o9b2obob2o$20bo2b2ob2o2bo6b2obob2o14bo15bobo16bo
$6bo12bobo7bobo3b2o2b3o2b2o12b2o32bobo$20bo2b2ob2o2bo4bo9bo44b2obob2o$
20bo9bo6bo2b2obo25b2o9b2o6b2o2b3o2b2o14bo$19bo2b2obob2o2bo4b2o2bob2o
23bo2bo9bo2bo4bo9bo13bobo21bo$20b2o2b3o2b2o8bo27b2o13b2o6bo2b2obo13b2o
bob2o18bobo$20bo9bo8b2o48b2o2bob2o11b2o2b3o2b2o14b2obob2o$22bo2b2obo
63bo15bo9bo12b2o2b3o2b2o$21b2o2bob2o27b2o16bobo15b2o16bo2b2obo14bo9bo$
24bo31bo15b2obob2o30b2o2bob2o16bo2b2obo$24b2o27b2o2bob2o9b2o2b3o2b2o
31bo19b2o2bob2o$54bo2b2obo9bo9bo31b2o21bo$52bo9bo9bo2b2obo56b2o$52b2o
2b3o2b2o8b2o2bob2o$38b2o14b2obob2o13bo$38bo35b2o30b2o17b2o20b2o$22b2o
11b2o2bob2o13bobo29b2o16bo18bo21bo$22bo13bo2b2obo14bo14b2o14bo14b2o2bo
b2o11b2o2bob2o14b2o2bob2o$6bo12b2o2bob2o7bo9bo27bo12b2o2bob2o11bo2b2ob
o12bo2b2obo15bo2b2obo$2o9b2o7bo2b2obo7b2o2b3o2b2o9bo5bo8b2o2bob2o9bo2b
2obo9bo9bo8bo9bo11bo9bo$o2bo5bo2bo5bo9bo7b2obob2o11bo5bo9bo2b2obo7bo9b
o7b2o2b3o2b2o8b2o2b3o2b2o11b2o2b3o2b2o$b2o7b2o6b2o2b3o2b2o9bobo13bo5bo
7bo9bo5b2o2b3o2b2o9b2obob2o12b2obob2o15b2obob2o$bo9bo8b2obob2o12bo28b
2o2b3o2b2o7b2obob2o13bobo16bobo19bobo$3b2obob2o60b2obob2o11bobo16bo18b
o21bo$2bo2b3o2bo43bo5bo11bobo14bo$2b2o5b2o12bo30bo5bo12bo$4b2ob2o14bo
30bo5bo$4bo3bo30bo33bo$6bo31bobo16bo31bo$5b2o13b2obob2o9b2obob2o13bobo
$18b2o2b3o2b2o5b2o2b3o2b2o28bo15bo$18bo9bo5bo9bo9b2obob2o$20bo2b2obo9b
o2b2obo9b2o2b3o2b2o10bo$19b2o2bob2o8b2o2bob2o9bo9bo9bobo$22bo15bo15bo
2b2obo9b2obob2o12bo$22b2o14b2o13b2o2bob2o7b2o2b3o2b2o9bobo$56bo11bo9bo
7b2obob2o$56b2o12bo2b2obo7b2o2b3o2b2o$69b2o2bob2o7bo9bo12bo$72bo13bo2b
2obo13bobo17bo$50b2o20b2o11b2o2bob2o11b2obob2o14bobo$50bo37bo13b2o2b3o
2b2o10b2obob2o$47b2o2bob2o33b2o12bo9bo8b2o2b3o2b2o$48bo2b2obo49bo2b2ob
o10bo9bo$46bo9bo46b2o2bob2o12bo2b2obo18bo$46b2o2b3o2b2o49bo15b2o2bob2o
17bobo$48b2obob2o21b2o28b2o17bo19b2obob2o$50bobo23bo48b2o16b2o2b3o2b2o
$51bo21b2o2bob2o62bo9bo$74bo2b2obo64bo2b2obo$72bo9bo61b2o2bob2o$72b2o
2b3o2b2o64bo$74b2obob2o66b2o$76bobo$77bo17$51bo$50bobo$48b2obob2o$46b
2o2b3o2b2o$46bo9bo$48bo2b2obo$47b2o2bob2o$50bo26bo$50b2o24bobo$74b2obo
b2o$72b2o2b3o2b2o$72bo9bo$74bo2b2obo$73b2o2bob2o$76bo$76b2o!

The lack of blocks makes building hive conduits somewhat harder, but I have a feeling that something similar should still be possible.

[BlinkerSpawn]

The lack of blocks makes building hive conduits somewhat harder, but I have a feeling that something similar should still be possible.

Even if it isn't, though, the standard (2,1)c/3 signal should still function, correct?

[ygh]

p100 F-Pentomino

Code: Select all

x = 3, y = 3, rule = B2e3-a_S23
b2o$2o$bo!

[Rocknlol]

Quite a few B0 rules have naturally-occurring wicks and wickstretchers. I've found that when several of these wickstretchers collide, high-period oscillators tend to form. Here's a bunch of them, in ascending order of periodicity.


In B01346/S0123, the wickstretcher collisions form this p30 oscillator:

Code: Select all

x = 28, y = 28, rule = B01346/S0123
13bobo$13b3o$13b2o$13b2o$13b2o8$2o$b4o18b5o$5o18b4o$26b2o8$13b2o$13b2o
$13b2o$12b3o$12bobo!

In B013468/S23, they form this p64 oscillator:

Code: Select all

x = 32, y = 32, rule = B013468/S23
15bobo$15b3o$15b2o$15b2o$15b2o10$2o$b4o22b5o$5o22b4o$30b2o10$15b2o$15b
2o$15b2o$14b3o$14bobo!

In B013468/S0123, they form p50 and p104 oscillators:

Code: Select all

x = 22, y = 28, rule = B013468/S0123
10bobo$10b3o$10b2o$10b2o$10b2o8$2o$b4o12b5o$5o12b4o$20b2o8$10b2o$10b2o
$10b2o$9b3o$9bobo!

Code: Select all

x = 28, y = 28, rule = B013468/S0123
13bobo$13b3o$13b2o$13b2o$13b2o8$2o$b4o18b5o$5o18b4o$26b2o8$13b2o$13b2o
$13b2o$12b3o$12bobo!

In B01346/S23, they form p288 and p700 oscillators:

Code: Select all

x = 60, y = 60, rule = B01346/S23
29bobo$29b3o$29b2o$29b2o$29b2o24$2o$b4o50b5o$5o50b4o$58b2o24$29b2o$29b
2o$29b2o$28b3o$28bobo!

Code: Select all

x = 50, y = 50, rule = B01346/S23
24bobo$24b3o$24b2o$24b2o$24b2o19$2o$b5o38b6o$6o38b5o$48b2o19$24b2o$24b
2o$24b2o$23b3o$23bobo!

In B01346/S023, they form p620 and p1080 oscillators:

Code: Select all

x = 62, y = 62, rule = B01346/S023
30bobo$30b3o$30b2o$30b2o$30b2o25$2o$b5o50b6o$6o50b5o$60b2o25$30b2o$30b
2o$30b2o$29b3o$29bobo!

Code: Select all

x = 100, y = 100, rule = B01346/S023
49bobo$49b3o$49b2o$49b2o$49b2o44$2o$b4o90b5o$5o90b4o$98b2o44$49b2o$49b
2o$49b2o$48b3o$48bobo!

In B013468/S123, they form p328 and p1864 oscillators:

Code: Select all

x = 58, y = 58, rule = B013468/S123
28bobo$28b3o$28b2o$28b2o$28b2o2$26bo4bo4$28b2o2$26bo4bo$27bo2bo$28b2o
5$27bo2bo4$27bo2bo$26b6o$26b6o$6bo5bo11b10o11bo5bo$2o11bo5bo3b12o3bo5b
o$b4o5bo3bo9b10o9bo3bo5b5o$5o5bo3bo9b10o9bo3bo5b4o$13bo5bo3b12o3bo5bo
11b2o$6bo5bo11b10o11bo5bo$26b6o$26b6o$27bo2bo4$27bo2bo5$28b2o$27bo2bo$
26bo4bo2$28b2o4$26bo4bo2$28b2o$28b2o$28b2o$27b3o$27bobo!

Code: Select all

x = 58, y = 60, rule = B013468/S123
28bobo$28b3o$28b2o$28b2o$28b2o24$2o$b4o48b5o$5o48b4o$56b2o24$28b2o$28b
2o$28b2o$27b3o$27bobo!

You'll notice that I didn't show the wickstretchers colliding to form the p328 oscillator, and that's because it took about 100,000 generations for the whole mess to stabilize and the oscillator to actually appear. You might call it a methuselah if you didn't care much about the size of the bounding box.

Code: Select all

x = 210, y = 210, rule = B013468/S123
104bobo$104b3o$104b2o$104b2o$104b2o99$2o$b4o200b5o$5o200b4o$208b2o99$
104b2o$104b2o$104b2o$103b3o$103bobo!

In B01346/S123, they form p30 and p2212 oscillators (the p30 is identical to the one in B01346/S0123):

Code: Select all

x = 28, y = 28, rule = B01346/S123
13bobo$13b3o$13b2o$13b2o$13b2o8$2o$b4o18b5o$5o18b4o$26b2o8$13b2o$13b2o
$13b2o$12b3o$12bobo!

Code: Select all

x = 78, y = 76, rule = B01346/S123
38bobo$38b3o$38b2o$38b2o$38b2o32$2o$b4o68b5o$5o68b4o$76b2o32$38b2o$38b
2o$38b2o$37b3o$37bobo!

In B013468/S023, they form p82, p242, and p5852 oscillators:

Code: Select all

x = 32, y = 32, rule = B013468/S023
15bobo$15b3o$15b2o$15b2o$15b2o10$2o$b4o22b5o$5o22b4o$30b2o10$15b2o$15b
2o$15b2o$14b3o$14bobo!

Code: Select all

x = 40, y = 44, rule = B013468/S023
19bobo$19b3o$19b2o$19b2o$19b2o$19b2o15$2o$b5o28b6o$6o28b5o$38b2o15$19b
2o$19b2o$19b2o$19b2o$18b3o$18bobo!

Code: Select all

x = 142, y = 144, rule = B013468/S023
70bobo$70b3o$70b2o$70b2o$70b2o66$2o$b4o132b5o$5o132b4o$140b2o66$70b2o$
70b2o$70b2o$69b3o$69bobo!

Finally, while B01346/S2 doesn't have naturally-occurring wickstretchers, it does have this very common 6-cell p106 oscillator:

Code: Select all

x = 7, y = 2, rule = B01346/S2
o2bo2bo$o2bo2bo!

[_zM]

It's not as common, but there is this 4c/1292 forward rake in B37/S23-i4q5an.

Code: Select all

x = 4, y = 4, rule = B37/S23-i4q5an
obo$o2bo$o2bo$2bo!

[ygh]

It's not as common, but there is this 4c/1292 forward rake in B37/S23-i4q5an.

Code: Select all

x = 4, y = 4, rule = B37/S23-i4q5an
obo$o2bo$o2bo$2bo!

Two glider synthesis:

Code: Select all

x = 7, y = 4, rule = B37/S23-i4q5an
5b2o$bo2b2o$b2o3bo$obo!

[_zM]

Interesting flip reaction

Code: Select all

x = 8, y = 8, rule = B37/S23-i4q5an
2bo$b2o$2o4$6b2o$6b2o!

[shouldsee]

EDIT: actually p136

Code: Select all

x = 5, y = 3, rule = B01234678/S0346
2bo$o3bo$2obo!

PS: thank BlinkerSpawn for correction

p88

Code: Select all

x = 4, y = 5, rule = B0136/S0
obo$b2o$b3o$3o$b3o!

[BlinkerSpawn]

p252

Code: Select all

x = 5, y = 3, rule = B01234678/S0346
2bo$o3bo$2obo!

Actually p136.

[shouldsee]

p384

Code: Select all

x = 4, y = 4, rule = B01345/S1235
b2o$4o$4o$b2o!

p160

Code: Select all

x = 2, y = 2, rule = B0134/S0125
2o$2o!

[Bullet51]

p384

Code: Select all

x = 4, y = 4, rule = B01345/S1235
b2o$4o$4o$b2o!

Wow. Maybe a pretty smooth rule.

[shouldsee]

p384

Code: Select all

x = 4, y = 4, rule = B01345/S1235
b2o$4o$4o$b2o!

Wow. Maybe a pretty smooth rule.

LOL I have actually mostly abandoned the idea of smoothness.

The idea to introduce smoothness is to discriminate complex randomness from absolute randomness (white noise). But after days of search I am continuing improving my algorithm to detect complexity.

And the current idea is to detect covariance between proportion of different neighborhood through time. The idea is that, assume there is cooperative behavior, the number of cells under one neighborhood would co-vary with that in another neighborhood. This algorithim comes out to be the most useful one at the very moment.

This rule is one of its result.

[Bullet51]

And the current idea is to detect covariance between proportion of different neighborhood through time. The idea is that, assume there is cooperative behavior, the number of cells under one neighborhood would co-vary with that in another neighborhood. This algorithm comes out to be the most useful one at the very moment.

I'm not sure what does it mean. Does it mean counting the cells with B0..B8 and computing the covariance of those numbers?

[shouldsee]

And the current idea is to detect covariance between proportion of different neighborhood through time. The idea is that, assume there is cooperative behavior, the number of cells under one neighborhood would co-vary with that in another neighborhood. This algorithm comes out to be the most useful one at the very moment.

I'm not sure what does it mean. Does it mean counting the cells with B0..B8 and computing the covariance of those numbers?

Yes. When you are counting you have to take account into the current state of the central cell. This would attribute a neighborhood index to each cell. And by monitoring covariance between counts of different index values, we can identify the strength of tangling between neighorhoods.

At the moment I am trying to incorporate mutual information instead of covariance to detect such interaction.