Rules with interesting dynamics - Page 49 - ConwayLife.com

Rules with interesting dynamics

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I6_I6: Posts: 1120; Joined: July 26th, 2025, 8:44 pm; Location: Here, there, somewhere, anywhere, everywhere.; Contact:
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Re: Rules with interesting dynamics

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Post by I6_I6 » September 17th, 2026, 3:34 pm

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#C [[ RANDOMIZE ]]
#R B36-in/S125678
!

At first, this looks like a boring chaotic exploding rule, but very rarely, amidst the chaos, expanding white blobs will start to appear. The blobs grow at the same speed as the chaos, so it never actually ends up engulfing everything. It would be really cool to see a rule like this where the blobs can catch up to the chaos and stop all the growth eventually.

Still lifes and basic small oscillators in this rule are like those from LowLife. The c/8d from 2x2 is also supported, and arises naturally occasionally:

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x = 4, y = 5, rule = B36-in/S125678
bo2$bobo$o2bo$3bo!

On a torus, blobs will eventually take over everything.

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#C [[ THEME Golly ]]
x = 27, y = 15, rule = LifeHistory
8.A$A6.A.A$3A4.BA2B.B2D$3.A4.2B.2B2DB$2.2A2.3B.6B2.3B$2.20B$4.19B$4.2B
C10BD4B$4.2B2C10BD4B$4.B2C11B2D3B$4.13B2D4B$5.12BD3B.B2A$6.13B3.BA.A$
6.3B.B3.B10.A$25.2A!

RuleEdit: A .rule file editing tool

NimbleRogue: Posts: 772; Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

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Post by NimbleRogue » September 18th, 2026, 10:52 pm

I found some incredibly interesting 6c/7 ships using an incredibly clean backend. Here are just a few

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x = 18, y = 7, rule = B2-kn3acnqy4-intz5-acqy6-in7c8/S1c2-ac3cin4cknqy5-kq6-n7e8
3bob3o2b3obo$6bob2obo$2b2ob2ob2ob2ob2o$b2ob2obo2bob2ob2o$18o2$o16bo!

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x = 20, y = 7, rule = B2-k3anqy4-iknrt5-cjky6-n78/S1c2ekn3knq4-eirwy5-cqy67e8
4bob3o2b3obo$3bo2bobo2bobo2bo$2bob4ob2ob4obo$bobo2bobo2bobo2bobo$20o2$
o18bo!

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x = 20, y = 5, rule = B2-k3acekn4acertwz5-ckny6-ei78/S2ik3aikny4aejnw5-ciy6aek7c8
4b3ob4ob3o$6b8o$3b2obobo2bobob2o$b2ob2ob2o2b2ob2ob2o$20o!

In fact, minus the corners the backend is just a flat line of cells.
The backend also works at other speeds, even faster ones, it just requires the right input from the front. This will hopefully make searching for faster speeds like 10c/11+ much easier

Here is a 6c/7 with a backend that's 2 cells longer than the previous ones

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x = 22, y = 7, rule = B2-k3-ijkr4-iknz5-ekqy6-n7/S1c2eik3-ciy4cejknwy5ajqr6-n78
5b3ob4ob3o$3b5obo2bob5o$2b2o2b2ob4ob2o2b2o$b4ob3ob2ob3ob4o$22o2$o20bo!

Edit 1:
5c/6 in the same form

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x = 20, y = 6, rule = B2-k3-eijn4-ijntw5aceiy6-ei8/S2-ek3ij4-cikr5-ikn6akn78
2bob3obo2bob3obo$8b4o$3b2ob8ob2o$2b16o$b18o$o18bo!

This one has a completely empty 6th row

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x = 18, y = 7, rule = B2-in3ejkny4aceiktw5-ijry6-c78/S1c2ci3-einr4kz5-ciy6-i7e
4b3o4b3o$bobo3b4o3bobo$2ob3ob4ob3ob2o$2b2ob2ob2ob2ob2o$18o2$o16bo!

Edit 2:
This one's pretty stripey

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x = 18, y = 7, rule = B2-kn3cejny4-cenw5aejr6-ac7e8/S1c2ac3cky4ikqrtw5-knq6-a8
2b3obo4bob3o$4bob6obo$b6ob2ob6o2$18o2$o16bo!

This is the cleanest backend reaction I have seen so far

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x = 20, y = 6, rule = B2-ik3-eijn4-eirty5acjqr6aek7e8/S01e2-kn3acik4-aiqry5-eijq6-ik78
2b3ob3o2b3ob3o$bob3ob2o2b2ob3obo$4bobob4obobo$2bob3ob4ob3obo$b18o$o18b
o!

This 6c/7 has a clean p2 backend reaction

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x = 20, y = 7, rule = B2-in3-ijn4acejrw5ikq678/S1c2e3aikq4-aeirz5-acik6aik7e8
4b3ob4ob3o$3bobo2bo2bo2bobo$b7ob2ob7o$2bobobo2b2o2bobobo$20o2$bo16bo!

Edit 3:
D2_+1 6c/7

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x = 27, y = 7, rule = B23aeqy4acjtwz5aiknq6-ik7e8/S2cik3-ikqy4aknqtwz5aejqr678
4bo2b3obo3bob3o2bo$2b3o4bob5obo4b3o$b5o4b7o4b5o$3b5ob4ob4ob5o$2b9ob3ob
9o$b25o$o25bo!

There you are

NimbleRogue: Posts: 772; Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

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Post by NimbleRogue » September 21st, 2026, 7:24 pm

A (3,1)c/4 with the same backend as the orthogonal ones

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x = 11, y = 7, rule = B2-kn3aer4-aekr5cekqr6-n/S1e2e3aeikn4aeijkq5aceny6-i7e8
bobob3ob2o$2ob3o2bo$2b3o2bo2bo$b2ob2obo2$2b8o$bo8bo!

I also realized that we could use the backend of May13's OT (2,1)c/3s to find some fast obliques

Here is a (3,1)c/4

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x = 12, y = 11, rule = B2-i3eknq4aciqwz5-qy6-c78/S1e2ckn3-aijr4ceikqrt5cjnqr6-i78
b3o2bob2o$2b2ob2o$5obobo2bo$b5o2b3o$2b7obo$3b3obobo$4b3o2bo$5b5obo$6b
3o$7b3o$8bo!

a (4,1)c/5

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x = 11, y = 11, rule = B2-in3ejnry4-eijry5-cik678/S1c2ck3qry4ajrtwyz5cikny6-i78
b2obo$2b2obo$6o$b8o$2b4obobo$3b5ob2o$4b3ob2o$5b4o$6b5o$7b3o$8bo!

and some (5,1)c/6s

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x = 11, y = 11, rule = B2aci3cjkn4-qrw5-ciq6acn78/S01e2cn3-iknq4aeqrtyz5-aqry678
b2obob2o$2b4o2bo$7obo$b6obo$2b5o$3b5o2bo$4b5o$5b4o$6b3o$7b3o$8bo!

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x = 14, y = 14, rule = B2acn3cejn4-acijr5-cnq6-e78/S1e2in3cjy4eirwz5-ak6-k78
b3ob6o$2bo4b3ob2o$5o2b2obo$b4o2b3obo$2b5obob2o$3b5ob2ob2o$4b6ob2o$5b7o
$6b6o$7b5o$8b5o$9b3obo$10b3o$11bo!

Some of them have very clean right edges

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x = 17, y = 18, rule = B2-ek3jknqr4cejknwz5-cqy6aci8/S01e2ek3aknry4-eitw5-aekq6-i78
b3ob5o$2b4o2bo2b2obo$5ob3ob2obob2o$b13obo$2b8ob2ob2o$3b3ob3o2b4o$4b8o
2b2o$5b8ob3o$6b10o$7b5ob3o$8b7o$9b6o$10b5o$11b4o$12b3o$13b2o$14bo$15bo
!

As of yet I have not been able to force the bottom right edge without the LLS searches returning UNSAT for speeds (6,1)c/7 and above. But I am running some (7,1)c/8 frontend searches that are just forcing the the back edge to work and I am getting the best results we have seen yet

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x = 53, y = 19, rule = B2-i3ej4-acrtw5-cey6-kn78/S1e2ekn3ceqry4-ikntz5-aikq6-ik78
45bobo$39b3obo2b2o2b2o$22b3ob4o7b2ob2ob2ob3obo$16b2obobo2bo2b3o9bob3ob
o3b2o$15bo2bob2o2b3o2b2o3bo2bo3b7ob4o$14b6obob4o2b2o2bob6ob10o$13b3o3b
o3b2ob2ob5ob6ob9o$15b5ob3ob17ob7o$14bo3b2o2bo2b24o$12b4ob8ob16ob5o$16b
ob29o$12b4o3b27o$13b2ob29o$11b4ob28o$13b30o$7b2o3b3ob26o$7b2obo2bo2b
25o$3bob2ob3obobob24o$2obob5obobob5o6b13o!

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x = 26, y = 16, rule = B2ace3kry4aeinryz5-ciq6ae78/S02-ak3jqy4aejkry5-ace6-e78
15bo2b2obo$12b2o4b2obob2o$11bob5obobo$11bob8ob2o$12b8ob5o$9bob14o$6b2o
2b14o$5bo3bob12o$4bo2b2obob10o$7b14o$2bob4ob11o$b3o2b13o$2bob14o$obob
13o$b15o$2b13o!

This one is wild

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x = 36, y = 37, rule = B2ace3kry4aeinryz5-ciq6ae78/S02-ak3jqy4aejkry5-ace6-e78
25b4obobo$22b2o2bobobob3o$21bob6o2bo$22b8o2b2o$19bo2b8o3b3o$21b5o2b7o$
16b2obob13o$15bo5bob10o$15bo5b11o$13bo2b2ob12o$12bo2b15o$11bo4b13o$11b
17o$11b2ob13o$11bo2b12o$9b2o2b12o$10b3ob2ob7o$11b12o$11b11o$9b2ob9o$8b
12o$8bob9o$10b8o$5b2o4b6o$5bo2bo2b5o$5b3o2b5o9b3o$9b5o4b2obobo2bo2b2o$
3bo4b5o4bob2obob2obo$9b3obo4b8ob3o$3b3o2b6ob2ob7o3b4o$4bob8o3b10ob3o$
4b8o3b15o$3b26o$b2ob24o$5o3b19o$2bo5b18o$b2obo3b17o!

I am expecting that (7,1)c/8 and (8,1)c/9 are just around the corner

Deepest partial yet

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x = 43, y = 34, rule = B23cejy4-aertw5aijkn6-ei78/S1e2ek3eqry4-eintz5jnry678
35bobo$29b3obo2b2o2b2o$27b2ob2ob2ob3obo$28bo3b4obob2o$27b5ob5ob4o$28b
2ob11o$24bo2b14o$23bo2b14o$23b16o$22bob14o$22bo2b12o$22b14o$22bob11o$
22b12o$17b3o3b10o$19bobo2b8o$18b2obob8o$15bob5ob7o$15b6ob7o$16b12o$14b
2ob10o$17b9o$15b10o$8bo2bob2ob8o$8bob2o4b7o$6b7o3b6o$5b2o4b2ob7o$6bob
4o2b6o$6bo3b2ob6o$7b6ob4o$5b12o$2bob2ob9o$6o2b7o$3o4b7o!

Even better

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x = 77, y = 71, rule = B2-n3ejy4-art5-cqry6aik78/S1e2ek3eqr4aejrtwy5jnry678
64b4obobob3o$61b2obob2obobo2bo$60bobo2b3o2b5o$61b16o$59bob11ob3o$59bob
14o$60b14o$60b13o$56bo3b12o$54bobo2b12o$54bo3b12o$54b2ob12o$55b13o$52b
2ob12o$52bob12o$54b11o$51bob11o$50bob11o$52b10o$50b11o$45b2o3b10o$44bo
bo2b10o$44b4o2b8o$43b14o$42b2ob3ob7o$42bo2b3ob6o$42bo2b9o$39b2ob2ob8o$
39b2o2bo2b6o$39b4o2b6o$37b13o$37bo4b7o$41b7o$36b11o$37bobob5o$33b2ob9o
$29bo4b2ob7o$26b2obob4ob7o$25bob2ob12o$27bob12o$24b16o$23b2o2b12o$23b
15o$24b13o$26b10o$21b2o2b10o$18b4o3b9o$19b4ob9o$18bob2ob9o$17bobob10o$
16b2ob11o$19b10o$16b12o$15bob10o$13b13o$14b11o$14bob8o$15b8o$13bo3b5o$
10bo2bob6o$10b10o$10b9o$13b5o$7bo2bob5o$3b2o2b3o2b4o$2bob2o4b5o$3bo6b
4o$3b3o2b5o$o8b3obobo$2b3o2bobobo4bo$bob3o2bobo5bobo!

Edit 1:
Finally found a (6,1)c/7

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x = 12, y = 12, rule = B2aci3cjny4ijknrtw5-eikn6-n7e8/S13r4-enwyz5-ajkr678
2bob2obob2o$2bo2bo2bo2bo$2b3ob2ob2o$4obobob2o$b11o$2b3o2b3o$3b7o$4b6o$
5b5o$6b3obo$7b3o$8bo!

Edit 2:

Some more (6,1)c/7 results. All of the results I have found have the same backend even though I wasn't constraining the backend in the search, which might mean this is the only one that works

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x = 12, y = 12, rule = B2-ek3-aeir4-acz5-ijny6-n7e8/S13cr4-cinwy5-ajkr678
2bob2obob2o$2bo2bo2bo2bo$2b3obobo$6o2b3o$b3o3b5o$2b8o$3b7o$4b6o$5b5o$
6b3obo$7b3o$8bo!

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x = 12, y = 12, rule = B2-ek3cjknq4-acqz5aekqr6-n7e/S12n3cr4akrtz5-ajy6-e78
2bob2obob2o$2bo2bo2bo2bo$2b3o2b2o$4ob6o$b5o2b4o$2b4o2b2o$3b7o$4b6o$5b
5o$6b3obo$7b3o$8bo!

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x = 12, y = 12, rule = B2-ek3jknqy4-ajz5-ijny6-n7e/S13qr4-jntw5-ajr6-e78
2bob2obob2o$2bo2bo2bo2bo$2b6o2bo$3o3bob3o$b11o$2b8o$3b7o$4b6o$5b5o$6b
3obo$7b3o$8bo!

All of these were found with this LLS search ./lls -r pB2a345678/S012345678 in6.csv -p '>0'

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0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
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0,   0,   0,   0,   0,   0,   1,   1,   1,a609,a610,a611,a612,a613,a930,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0    0
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0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
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0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
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0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
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0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
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0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,a153,a154,a155,a156,a157,a158,a159,a160,a161,a162,a163,a936,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,a103,a104,a105,a106,a107,a108,a109,a110,a111,a112,a113,a935,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,a203,a204,a205,a206,a207,a208,a209,a210,a211,a212,a213,a934,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   1,   1,   1,a306,a307,a308,a309,a310,a311,a312,a313,a933,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   1,   1,   1,a407,a408,a409,a410,a411,a412,a413,a932,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   1,   1,   1,a508,a509,a510,a511,a512,a513,a931,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   1,   1,   1,a609,a610,a611,a612,a613,a930,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0    0
0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   1,a710,a711,a712,a713,a929,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   1,a811,a812,a813,a924,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   1,a912,a913,a925,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   1,   1,   1,a915,a926,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,a918,a919,a920,a927,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,a921,a922,a923,a928,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0

B1e has a speed limit of (5,1)c/6 oblique, but there are no known examples.
The same backend works In B1e and I wonder if it could work for (5,1)c/6

I have found some (2,1)c/3s

Code: Select all

x = 12, y = 12, rule = B1e2cen3eikny4-aejtz5acery6akn78/S012e3jnqy4-aijkq5ijknr6-e78
3b4ob2o$ob2o3bo3bo$obo2bo3bobo$b2obo5bo$b5ob4o$2b5o2b2o$3b4obobo$4b6o$
5b5o$6b4o$7b4o$9b2o!

And some (3,1)c/4s

Code: Select all

x = 11, y = 11, rule = B1e2cen3-ajy4ajqtz5-ejkr6ace7/S1c2akn3nqy4ejknqrt5ceinq6-i78
b4ob2o$obob2o4bo$4obo3b2o$b4obobo$2b6o$3b4o2bo$4b5o$5b4o$6b3obo$7b4o$
8b2o!

Edit 3:

Here is a B1e (4,1)c/5

Code: Select all

x = 11, y = 12, rule = B1e2ce3eiknq4-inqr5-nq6aci78/S1c2eik3-aejq4ceikqyz5ijknq678
3b4o$bo2bo4bo$ob2obob4o$7o2b2o$b6o$2b3o$3b4o2bo$4b5o$5b3ob2o$6b3obo$7b
3o$8b2o!

I realized that requiring 2-3 rows of the backend to be on may have been restricting the space too much

Here is another B1e (4,1)c/5 where only two rows are required to be on. It has an interesting backend

Code: Select all

x = 11, y = 11, rule = B1e2ce3ijn4eiknrtz5-eiqr6-i78/S02-in3-ijry4-anwyz5-aejr6-ai7
2bob3o$b5o2bobo$obo2b2o3bo$2obobo2b2o$b5ob2o$2b2obob2obo$3b3ob2obo$4b
3obo$5b3obo$6b4o$7b2o!

I did some searches for some (6,1)c/7s with a 2 cell thick backend with B2a and I found some interesting results

Code: Select all

x = 11, y = 13, rule = B2ace3cenr4-iqrw5-ikry6-e7c8/S012i3aejky4-cktwy5jnqry678
2b4ob3o$2bo6bo$2b4o2b2o$7o3bo$b5o3bo$2b3ob3o$3b3ob2obo$4b5o$5b3obo$6b
3o$7b3o$8b3o$9bo!

Code: Select all

x = 12, y = 12, rule = B2aci3ejny4aijntwz5acijk6-k78/S12c3ajnry4-eiqtw5cjnqy6-e78
2b4ob3o$b2ob2o$2b2obobo$4o2bo$b3ob2o$2b7o$3b4obobo$4b5o2bo$5b5o$6b2obo
bo$7b2obo$8bo!

This checkerboard (5,1)c/6 is incredibly clean

Code: Select all

x = 11, y = 12, rule = B2-en3-aiky4-cinqy5-jk6-ai7c8/S012ek3aeq4aejkqrz5-ejn6-en
2b2obob2o$b3ob3o$2bob7o$2obob2ob3o$b2ob5obo$2b2obob2obo$3b2obobobo$4b
2obo$5b2ob2o$6b2ob2o$7b3o$8bo!

Only requiring one row in the back to be on allows even more (6,1)c/7 variations. This one has the thinnest frontend I have found. In fact, the max height is smaller than the (6,1)c/7 in the 5s database

Code: Select all

x = 11, y = 9, rule = B2-ek3jkqry4-jknz5-aik6-i7/S01e2i3ejky4eijkryz5-aen6ckn78
3b3obo$2ob5ob2o$b2ob2o2b2o$2bobo3bo$3bob4obo$4bob2o$5bobo$6bobo$7bo!

There you are

LaundryPizza03: Posts: 2643; Joined: December 15th, 2017, 12:05 am; Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: Rules with interesting dynamics

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Post by LaundryPizza03 » October 8th, 2026, 2:58 am

This rule seems to be stable with c and c/2d objects. Dynamically, it resembles the stable B1e rules.

Code: Select all

x = 0, y = 0, rule = B01c2akn3ein4nt5ar6i/S1e2-cn3ackq4q5ek6a
b!
#C [[ RANDOMIZE RANDWIDTH 128 RANDHEIGHT 128 ]]

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!

LaundryPizza03 at Wikipedia

NNlk05: Posts: 796; Joined: January 14th, 2026, 8:42 pm; Location: Exploring in the Jungle of the INT Rulespace; Contact:
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Re: Rules with interesting dynamics

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Post by NNlk05 » October 10th, 2026, 3:53 pm

Stange rule (look to the left)

Code: Select all

x = 10, y = 10, rule = B2a/S1e3a5i
6o2b2o$6o2b2o$4b6o$4b6o$6o2b2o$6o2b2o$2o2b2o2b2o$2o2b2o2b2o$2b6o$2b6o
!

Feci quod potui, faciant meliora potentes.

Code: Select all

x = 10, y = 3, rule = B34twz/S23
b2o4b2o$obo4bobo$2bo4bo!
[[ AUTOSTART AUTOHIDEGUI TRACK 0 -47/270 ZOOM 4 GPS 45 STEP 3 THEME BOOK ]]

https://nnlk05.github.io

=3

NimbleRogue: Posts: 772; Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

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Post by NimbleRogue » October 11th, 2026, 12:14 pm

Another (9,1)c/10

Code: Select all

x = 112, y = 113, rule = B2aci3eqr4ainqtwy5ajnry6aei78/S01e2-ai3nq4-cenw5-ajy6-ei78
6bob2obobobob2obo$6bo4b5o2b2obob2o$2b2ob8obo2b4o3b2o$3obo2b9ob3ob2obo
$b20o3b3o$2b22ob2o$3b12ob11o$4b21o3b2o$5b21ob2o2bobo$6b23o4bo$7b21ob2o
bob2o$8b27o$9b25obo$10b25o$11b20ob2o$12b18ob3o$13b20o2b2o$14b22o$15b21o
3bo$16b19o2b3o$17b20o$18b19o$19b19o$20b10ob8o$21b8ob9o2bo$22b21o2b3o$
23b22obobo$24b20o2b4o$25b14o4b6o3b2o$26b14obo2b5ob2o2bo$27b14o4b4o2bo
2bo$28b14o2b5o3b2o$29b14ob5o2b3o2bo$30b9ob15obo$31b7o3b15o$32b24obo$33b
24o$34b22obo$35b24o$36b24obo$37b23o$38b21o$39b20obo$40b21o$41b19o2b2o
$42b19o2bo$43b17o2b2o$44b16ob4o$45b21ob2o$46b16ob3ob2o$47b17ob2o$48b16o
4b2o$49b22o$50b18ob3o$51b18ob2o$52b19o$53b19o$54b19o$55b17o$56b15ob2o
2b2o$57b17o3b2o$58b16obob3o$59b17o2b2o$60b13o3bo$61b12o4b2o$62b10o3b4o
$63b10ob8obobo$64b18obobo$65b16ob4o$66b18ob2o$67b19o$68b17o$69b17o$70b
16o$71b16o2bo$72b16o2bo$73b16o2bo$74b19o$75b12ob2o$76b10o4bo$77b11ob2o
$78b12o$79b12o$80b12obo$81b11o3b2o$82b15o$83b4o3b7o$84b12o$85b10ob2o$
86b11obo$87b12obo$88b11obo$89b10ob2o2b2o$90b7obo4b3o$91b9obo3bo$92b10o
bo2b2o$93b7obo2b3obo$94b8ob2o2b2o$95b14o$96b13o$97b11o$98b12o$99b13o$
100b11o$101b9o$102b9o$103b9o$104b6o$105b5o$106b5o$107b3o$108bo$109bo!

Edit 1:
Another 9c/10

Code: Select all

x = 19, y = 13, rule = B2acn3anqr4acqrz5cknr6-e/S12i3aej4cjnqz5-acej6-ci7
2b2obobobobobob2o$3o2bo7bo2b3o$bob4o2bo2b4obo$2bob11obo$o4bobo3bobo4b
o$3bo5bo5bo$2bo4bo3bo4bo$3bo11bo$9bo2$7bo3bo$6bobobobo$3bobo7bobo!

There you are

OogaBooga_: Posts: 74; Joined: February 7th, 2026, 8:34 pm; Location: Quantum Superposition

Re: Rules with interesting dynamics

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Post by OogaBooga_ » October 19th, 2026, 2:53 am

NimbleRogue wrote: September 10th, 2023, 9:12 pm
Saka wrote: June 3rd, 2020, 4:37 am This is from "Rules with interesting dynamics" but I love it so much, I'll post it here as well!
A 3c/1597d in an amoeba rule!
Code: Select all
x = 25, y = 25, rule = B2c3-i4inr5-n678/S4t5678
21b3o$17bo3b4o$15b3ob6o$13b12o$13b10o$11b12o$5bobo3b11o$bob3obob15o$2b
21o$b22o$2b20o$22o$b19o$b19o$2b16o$18o$2b15o$2b17o$4b13o$4b15o$5b13o$
7b11o$7b10o$9bob3obobo$9bo3bo!
Based on that rule I'm doing a search
Of intrest is this rule with a p3624
Code: Select all
x = 27, y = 27, rule = B2ck3-i4inrwy5-knqy6ace78/S2ein3jny4iknrtz5acijn6-k78
24bobo$23b3o$22b5o$22b4o$13bo7b4o$13bobo3b4o$7bo3b5ob5o$3bob3ob13o$4b
17o$b20o$3b17o$b21o$b20o$23o$b20o$b20o$3b17o$3b17o$4b15o$4b17o$5b15o$
3b17o$5bob12o$5bo3b9obo$11b5obo$11b5obo$13bo!
Why is this rule intresting? Its intresting because of its amoebae they somehow are very choatic but also look to stay a simmilar shape for long periods of time despite that, and replicate
Code: Select all
x = 141, y = 102, rule = B2ck3-i4inrwy5-knqy6ace78/S2ein3jny4iknrtz5acijn6-k78
 ![[ RANDOMIZE ]]
This kind of amoebae can be found in many of the other rules too.
Also this rulespace is great with things like this 3c/6491d ship
Code: Select all
x = 25, y = 25, rule = B2c3-eiy4inr5aijr6aei78/S2cei3c4int5acijn6-i78
20b3obo$18b6o$14bob9o$14bob9o$12b13o$10b14o$2bo7b14o$2bobo3b15o$5ob17o
$ob19o$23o$b20o$b20o$3b17o$b19o$3b15o$3b15o$4b13o$2b15o$4b12o$4b14o$6b
ob9o$6bo3bob7o$10bob3obo$14b3o!
Also thanks Ampere for bringing this rulespace back up into view from discord
From a search based on an old Silversmith rule
Code: Select all
x = 5, y = 4, rule = B2ce3ej4ejqrw5-aeqr6cn7e8/S2-ck3ejnqr4eijnqr5ackry6cek
2bo$2bobo$2obo$o!
MatchPatt has turned up tons of intresting things The search is attached
Lastly I have done more smaller searches around my crazy 5s rule that are really cool and will update it sometime soon

A trio of spaceships in the checkerboard space; one of which is oblique and a new 5S speed!
(technically it's a previously unobserved period multiple of an already known speed)

Code: Select all

x = 165, y = 7, rule = B2-a3ej4ejqrw5-aeqr6cn78/S2-ck3ejnqr4eijnr5ckry6cek
4o94bobobo59bobo$bob2o91bobobobobo56bobo$obo94bobobobo58b2o$2bo93bobo
bobobo55b2o$97bobobobo58bo$96b9o54bo$160bo!

EDIT:

A failed-oscillator puffer

Code: Select all

x = 5, y = 4, rule = B2ce3ej4ejqrwtz5-aeqr6cn7e/S2-ck3ejnqrk4eijnq5ackry6ek
2bo$2bobo$2obo$o!

EDIT:

A 16c/354 in an interesting amoeboid rule

Code: Select all

x = 5, y = 4, rule = B2ceik3ejk4ejqrwt5-aeqrjk6acekn7/S2-cki3ejnqr4eijnqz5iackryqn6cekina78
2bo$2bobo$2obo$o!

Quintuplets!!

Code: Select all

x = 151, y = 21, rule = B2cei3ejr4ejqrw5-aeqr6cn78/S2-ci3ejnqr4eijnqr5ackry6e
87bobobobobo$87bobobobobo$83bo2bobobobobobo2bo$81bobobobobobobobobobo
bo$79b2obobobobobobobobobobob2o$77bobobobobobobobobobobobobobobo$75b2o
bobobobobobobobobobobobobobob2o$73bobobobobobobobobobobobobobobobobob
obo$69bob2obobobobobobobobobobobobobobobobobobob2obo22bobo$67bobobobo
bobobobobobobobobobobobobobobobobobobobobo19bobobo$66bobobobobobobobo
bobobobobobobobobobobobobobobobobobo13bobobobobobobobo$65bobobobobobo
bobobobobobobobobobobobobobobobobobobobobo10b2obobobobobobobob2o$65b2o
bobobobobobobobobobobobobobobobobobobobobobobobob2o8bobobobobobobobob
obobobo$65b3obobobobobobobobobobobobobobobobobobobobobobobob3o7bobobo
bobobobobobobobobobo$21bo7bo16bobo3bobo12b2obobobobobobobobobobobobob
obobobobobobobobobob2o8bobobobobobobobobobobobobobo$25bo18b2obobobobo
b2o11b2obobobobobobobobobobobobobobobobobobobobobob2o9b2obobobobobobo
bobobobobob2o$17bobobobobobobobobo8bobobobobobobobobo10b2obobobobobob
obobobobobobobobobobobobobobob2o10b3obobobobobobobobobobob3o$15b2obob
obobobobobobob2o6b2obobobobobobob2o11b2obobobobobobobobobobobobobobob
obobobobob2o13b2obobobobobobobobobob2o$3o14bobobobobobobobobo8b3obobo
bobobob3o12b2obobobobobobobobobobobobobobobobobobob2o14b7obobobobob7o
$bobo10bobobobobobobobobobobobo7b2obobobobob2o15b2obobobobobobobobobo
bobobobobobobobob2o21b2obobobob2o$obo12b21o8b13o15b39o21b11o!

From left to right:

(21,7)c/112 ((3,1)c/16)

4c/16 (c/4)

2c/6 (c/3)

20c/48 (5c/12)

6c/14 (3c/7)

Side-note: the ship on the far left is not the only one supporting that speed, nor is it necessarily the smallest, it's just the one I found first.

Code: Select all

x = 37, y = 10, rule = B3-knq4-aiwy5e6eik7c/S2aek3-aey4iq5a6ack
bo33bo$2o33b2o$bo33bo6$7b3o17b3o$8bo19bo!

feel free to look at my miscellaneous creations at viewtopic.php?f=12&t=7212

LuveelVoom: Posts: 876; Joined: April 27th, 2022, 7:59 pm; Location: The 102 dimensional INT hypercube

Re: Rules with interesting dynamics

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Post by LuveelVoom » October 22nd, 2026, 8:04 pm

Watch this, then interrupt the symmetry:

Code: Select all

x = 3, y = 3, rule = B2ce3aqy4ejqtw5cjkqr6aen7c8/S12in3aijqr4cjq5cjkry6-ac8
b2o$o$o!

OCA primer (WIP): User:LuveelVoom/A_Primer_On_OCA
My rules: https://conwaylife.com/forums/viewtopic.php?f=11&t=6843
Free compute: https://conwaylife.com/forums/viewtopic ... 77#p234677
Discord user: LuveelVoom

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