Rules with interesting dynamics

For discussion of other cellular automata.
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I6_I6
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Re: Rules with interesting dynamics

Post by I6_I6 »

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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
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NimbleRogue
Posts: 764
Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

Post by NimbleRogue »

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
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NimbleRogue
Posts: 764
Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

Post by NimbleRogue »

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,   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
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