Rules with interesting dynamics

For discussion of other cellular automata.
User avatar
I6_I6
Posts: 1175
Joined: July 26th, 2025, 8:44 pm
Location: Here, there, somewhere, anywhere, everywhere.
Contact:

Re: Rules with interesting dynamics

Post by I6_I6 »

Code: Select all

#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:

Code: Select all

x = 4, y = 5, rule = B36-in/S125678
bo2$bobo$o2bo$3bo!
On a torus, blobs will eventually take over everything.

Code: Select all

#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
User avatar
NimbleRogue
Posts: 775
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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

x = 20, y = 7, rule = B2-in3-ijn4acejrw5ikq678/S1c2e3aikq4-aeirz5-acik6aik7e8
4b3ob4ob3o$3bobo2bo2bo2bobo$b7ob2ob7o$2bobobo2b2o2bobobo$20o2$bo16bo!
Edit 3:
D2_+1 6c/7

Code: Select all

x = 27, y = 7, rule = B23aeqy4acjtwz5aiknq6-ik7e8/S2cik3-ikqy4aknqtwz5aejqr678
4bo2b3obo3bob3o2bo$2b3o4bob5obo4b3o$b5o4b7o4b5o$3b5ob4ob4ob5o$2b9ob3ob
9o$b25o$o25bo!
There you are
User avatar
NimbleRogue
Posts: 775
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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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!

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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

Code: Select all

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!

Code: Select all

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!

Code: Select all

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'

Code: Select all

0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   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,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,   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,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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,   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
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0,   0
0,   0,   0,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   *,   0,   0,   0,   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
User avatar
LaundryPizza03
Posts: 2652
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: Rules with interesting dynamics

Post by LaundryPizza03 »

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
User avatar
NNlk05
Posts: 850
Joined: January 14th, 2026, 8:42 pm
Location: Exploring in the Jungle of the INT Rulespace
Contact:

Re: Rules with interesting dynamics

Post by NNlk05 »

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
The world is my country, science my religion.
User avatar
NimbleRogue
Posts: 775
Joined: January 11th, 2021, 11:48 pm

Re: Rules with interesting dynamics

Post by NimbleRogue »

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: 87
Joined: February 7th, 2026, 8:34 pm
Location: Quantum Superposition

Re: Rules with interesting dynamics

Post by OogaBooga_ »

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 right is not the only one supporting that speed, nor is it necessarily the smallest, it's just the one I found first.

Edit: corrected side-note
Last edited by OogaBooga_ on November 9th, 2026, 6:39 pm, edited 1 time in total.

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
User avatar
LuveelVoom
Posts: 998
Joined: April 27th, 2022, 7:59 pm
Location: The 102 dimensional INT hypercube

Re: Rules with interesting dynamics

Post by LuveelVoom »

Watch this, then interrupt the symmetry:

Code: Select all

x = 3, y = 3, rule = B2ce3aqy4ejqtw5cjkqr6aen7c8/S12in3aijqr4cjq5cjkry6-ac8
b2o$o$o!
User avatar
NNlk05
Posts: 850
Joined: January 14th, 2026, 8:42 pm
Location: Exploring in the Jungle of the INT Rulespace
Contact:

Re: Rules with interesting dynamics

Post by NNlk05 »

Interesting dynamics from an unlikely duo:

Code: Select all

x = 64, y = 64, rule = B2a/S23|B3/S23
3o4bo3bo2b3obo2bob2o3b2o2b2obo4bo3bobob2o5bo2b3o2bo$2o2bo7bobo3bo6b2o
4b4ob2o2bobo4b4o2bo2b3o4bo$ob3o9b2o3bob6ob3ob2ob3obo2bo2bo2bob4o4bobo
2bo$o2b2ob3o4b5o2bo2b3o2b4ob4o2bo2b2ob2obo2bob2o2b3o3bo$o2bobo6b4o2bo
2b3o11b3o3bo8bob2o2b3o2bobo$4obob3o2b3o2bo2bo2bobo3bob4o4b2o2bo3b4o2b
2obo3bob2o$2b3o5bobobobo3bobo4b4ob2o3b3ob3o3b4o2b2obobo2b2o$3ob2obob2o
bob5ob2obob5o2bo3b3o2bobo2b7o2b2ob3o$bob2ob2obo2bo2b2obo2bo3bo3b2o2b4o
bob2o3bo5b3o5bo3bo$bo2bobo2b2ob4obo2bo4bo3bo3b2o2bo2bob2o2bob7o2bo5bo
$o4bo4b6ob4ob2o4b4ob2obobob2o3bo2b3ob3obob4o$6obo2bo5bo6bob3obob2o5bo
b2obo2b4obo3bob7o$2o2b2ob2o3b6o4bo2bobob3o2b4ob2o2bob2obo5bob3o2bo$b2o
2bo2bob2obobo2b4o2bo2bo2bobobo3bobob3o4b2o2bob2o2bo2b2o$2ob7o3bob2o2b
4obob3obo2b6obobo5bobobob6o2bo$b2ob4o3bob3o2b5o3bo2b2obo2b2ob3o5b4o4b
o6bobo$obob2obob5obo6b2o2b2obobo4b2o2bo3b2o6b2o6bobo$2o2bobo6b3ob2obo
5b2o7b4ob3ob4ob2o3b2ob3o2bo$6o5b2o8bo2bobobobobobobo2bobob2obobobob2o
bobobobobo$2obo3bo4b3obob2ob2o2b4o2b2ob5ob2obob2obo4b2o4bo3bo$2o2bob4o
9bobobobobo5b2o3b2o5bo3b2obobob2obo3bo$3bo2b2o2b2o2b2o7b3o4bo4bo8b2o3b
2obo2b3o2bo2bo$o2bo4bob3ob3ob3obob2obo2b4obo2b3obo2bob2obob3obobo2bo$
ob2o2bo2b2ob5ob2ob4obob6obo2bob5obo2bo2b2ob2ob6o$4ob2o2b6ob2o2b5o2bob
o3b2o3bob3o2b3o2bobob5o3bo$b3o5b2obobobobobo2bob9o3bob4o2bo3b4o3b3o2b
o$bo3b8ob3ob2obo2b3o5b3ob2o2bobob2o3bo3b3o2bo$ob4o2b5o5b4o3b2o2bo2bo6b
3obobobo2bo2b2o5bobo$2b5o3b2obo3b2o3bo2bob3o3bobob3ob2ob2o2bo9b2obo$2o
b2o7b2obo8bo3b3obo3b5o2b2obo2bo3bo4b2o$2bo4b2o2bobo4b6o3bobob3o3bob4o
b4obob2o2bob7o$4b2ob3o3bo2bo2b3o2b2obo4b3ob3o2bo3b2obob3obo2b3ob2o$ob
5o4b2ob2o2b3obo2bobob5obob2o2bobo2bob2obobobob2obo2bo$3o2bob2o2bobob15o
bobobobob3ob3obo3bo2b3o3b2obo$obo4b2obo2bobo2b2ob2ob2obo2bo4b2ob11o2b
o3bob3o2b2o$bo2b2o4b5o3bob2obob2o4bob2o2bobob2o3bobo2b2o3b2obo2b2o$3b
o2b6ob3ob4ob2ob2ob8ob2o2bo2bob2ob2ob3obobo$2b3o2b3ob2o2bob2obobo7bo2b
ob4o5b8obo4b3ob2o$3b2ob2o2b3o3bo3b3o2b2obobobob3obo5b2obobo3b2o2bo3b3o
$ob2obo2b3obo2b4obo3b3obobo2bo2bo2bob5obo4bob2ob2o2b3o$o2b2ob2ob2o5b3o
b4o4bob4ob6obob7obo4bob2o2bo$o3bob4o4b6obo6b4o2bo2b5o2b4ob3o3b3ob2o2b
o$4b3o2bo2bobobobob3ob3obo2b3o4b3o2bo4b2obobob2obob4o$2b2o2bobobo3b2o
10bo2bo2b8obob2o2b2o2b2o4b3obobo$5ob2ob4o2bo3b2obo4b2ob4obo5b3obob4o3b
2o2b2o$b2o2bo3bo2bo4bo2b4obo2bobo8bob2o5b5o2b5o2b2o$b7o2b3o5bo3bob5o2b
obobo2bob2ob2o2b2ob2o2b2obob4o$o2b2ob2o2b7o3b3o2bob2o2b2obo2bobo2b4ob
2ob2ob3o2bo$2o2bobobob3o3b6o3b2ob2obo2bo2b2o4bo3bob6o4bo2bo$4obob2obo
3b3o2b6obo2bo2bob5ob3o2b2ob3o3bo2bob3obo$obo2bobob2o3b2obo6b3obobob2o
b2ob2o4b2o3bo5b2ob2obobo$o2b2o2b2ob3o2bo4b2ob2ob2obo3b4obo3b2ob4obo2b
8obo$o3b6ob3ob5obobo2bobo2b6o3b2obob2ob4ob3ob2o2b3o$o5b3o2bo5b4o3b2o2b
o2bo2b3ob3obo3b2ob7ob3o$7obo2b5ob6o2b3ob3ob3obo2bobo2bo4b4o3b3obo$ob2o
bob2ob4o3b4ob2ob2o4bob2o5bobobo3bob2o7b2obo$o3b2ob2ob2o2b3ob3o5b8obo3b
5o6b2obob4ob3o$2b2o2bo6bo2bob6obob4ob2obo2bo3bob2ob2ob2o2bo5bo$2o2b2o
2bob6o3bobobo2b3o2bo4b2obo2bo3b2ob2ob2ob2o2bobo$bob4o2bob2obobobob2ob
2obo2bo3bobo4b2o5b3ob2obobo2bo2b2o$7b2o4b2o2b5o2bobob2ob6obobo2bobo3b
3o2b2ob3obobo$2obo2bo5bobo5b2o2b2o3b2ob2ob7o3b5o3bobob2o$o2b3obo3bobo
b2ob3o2b4ob4o3b3o2b2obo2bobo4b2obob4o$bo9bo2b4o2b2o2bo6b2o3bo4b2obo3b
o4b2o4b3obo!
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
The world is my country, science my religion.
g0t0
Posts: 115
Joined: August 3rd, 2026, 7:05 am

Re: Rules with interesting dynamics

Post by g0t0 »

rutabaga wrote: September 7th, 2024, 4:43 pm

Code: Select all

x = 3, y = 3, rule = 2-a358/2-ak34crz78/3
.A$A.A$.A!
beautiful firecloud from just 4 cells lasts for 72000 generations, leaving only p68 in its wake

Code: Select all

x = 3, y = 3, rule = 2-a34q57c8/2-ak34j78/3
.A$A.A$.A
edit: this firecloud is a failed replicator that lasts for 150000+ generations
A symmetrical explosion but no explosion
Replicating or dying, that is a question.
1and0nlycordershippr
Posts: 423
Joined: December 20th, 2025, 8:34 pm
Location: Vietnam
Contact:

Re: Rules with interesting dynamics

Post by 1and0nlycordershippr »

Lines that are kind of weird

Code: Select all

x = 64, y = 64, rule = B1e4a/S1e2i3r4ar
b3o3b2o2b2o2bobob2o2bobo2b2o2bo2bobobo3bo4bob3o3bob2obo$3o7bo7bob3o5b
5o2bob3o2b2o3bobo3b4obo2bobo$2obo3b2obob2obo2bo3bob5o3b2o2b2obob4o2bo
b2ob3o2bob2ob2o$4ob2o4b2ob6obo3bob2ob2o2b4o2bo3bob4o4bo3b2ob3o$5o5bo3b
2o2b3o2bobobo4b5o2bobobob2obobob6o2b2obo$2o2b2o8bo7bob3ob2obob2obo2b2o
6b2obo2b2ob2obo$2o4b2o2bo2bo3bo2bo2bobobobob3o2b2obobo2bo6bobob3obo$o
bo2bobo3bob3o3b2o2b3o2b3obob3o2bo10b3ob3obob4o$bo2b2o2bo4b3ob3obobobo
bob2o2bobobo2b3obob2o2bo4bobo2bo2bo$bo2bo5bo3b5o2bo2bo3b2ob2ob2o2b3ob
ob2obob2obob3o2bobo$b3o2bo6bob2o7b3obo2b3o2b6ob2obob5obob2o3bobo$4b2o
2bob5ob3ob2o2bobob4obobo2bobo2b4obo3bob2ob2o4bo$2o3b2ob2ob3o4b2obobo2b
o3b2o3b2obob3ob10obobob2o$2b2o2bo2bo2bo2b4o3bobo2b3o4bo2bob4obobob2o3b
4obob2obo$5b3obo3bobo3bobo2bobob3o3b2o2b4obo4b2o3b3ob3obobo$bob4o2b3o
bo3b3o2bob5ob3o2bob3ob2o2b4o3b4obobobobo$bo2b3o2b3ob6ob3o4b2obo2b5o3b
2ob2o2bo3b2ob2ob2o3bo$obobobob2ob3o2b10obobob3o5b2o2bobob4o3b2obobobo
bo$o3b4ob2ob2o3b2o2bob2ob5o2b3ob4obo4b3ob2o3b4obo$ob3ob2obob2o4b4o2b2o
2bobo2bob4obo3bo3b3o2bo2bob5obo$o2bo5bo4b3obob3o2b2obobobobo4b2o2b2ob
obob2o3b3o5bo$b4o2b2o3bo2bo8b3o2bo2bo4bo3b7o2bobo2bo4b3o$2ob3o3bob5ob
o3b2obobo2bo10b4obob2ob2ob4obobo$3bo5bobob3obo3bo2bo2b3o2bo3bo2b2ob2o
3b3o3bob2obo2bobo$2obo7bo2bobo2b2o4b3o2bo4bo4bob2obo2bobobo2b3ob2obo$
3ob2o2b3ob2ob3o2b6o2b2obo3bo3bo2bo3b2o5b2obo2b5o$6b3o2bobob2o6bobobo2b
4o2b2o4bobobo6b2o2bob2o2bo$2bo3b3o2bo3bobo2bo2b6o2b6obobo6bo2b2obobo3b
4o$2bob2o5bobob4ob2obob7o3b2ob3o2bo2bobob2o2bo2b7o$2o3bob2ob2ob10ob3o
b4o2b5o3b2o2b3o2b10obo$bob3o2bo3bobo2b3obo4bo2bo2bobo3b2obobo2bob2o2b
6o4b2o$3b5obobobo6bob2ob3o6b2o2bobo2bo3b2ob3o3b3o$bobobo2bo4b2ob2ob2o
bob2o3bobobob2ob2o5b2ob4obo2bo4b2o$2ob3o2bo3bob2obob5o2bo4bobo2b2ob2o
bo2b8o2b4o2bobo$3o3bo3b2o4bo2b4obobo3bo2b2obob5o2b2o3b2o3b2obobobo$o2b
2o3bobo5bo2bo2bo3bo2bobobob2obob2o2bo4b2o2b5obobobo$4b2ob2ob7o3b2obob
ob3ob2o2bob3obobobobo3b2obobo2bo2bo$2b2o2b2o2b3o2b2o2bobo2b2obo3bo4b2o
bo6b4o3b2ob2ob5o$bobo3bob3ob5ob5ob2ob4o2bo6b5o2b3o3b3o2bob3o$2o5bobob
obo2bo2bo4bob4obobo2b9o2b2obob3o2bob5o$bo3b2ob3ob2ob2o2b2o2b2ob2obob3o
b2obo3bo5b3ob7o2bobo$3bobob2o2bob3o2bo2bo2b3o2b2ob2o2b2obobob3o4b7obo
2bo$ob3ob2o3bo2bob3ob2obobo2bo3b2ob2ob2o5bo2b2obo2bo3b2ob3o$2bobo2bo2b
o3bob3o2bobob3o2bob3ob3o2bo2bo3bobob3ob3obo2bo$3bo3bo4bo3b2ob2o2bob3o
bob3ob2obo5b2o2b3o3b2o2b3o2bo$o2b2ob5ob3o5bob2o4b2ob6obo2bobobobob3o2b
o2bobo3bo$2b3ob2o2bo3bob2o2b3obob5o3bob2o2b2o2b4o3b3o4bo3b2o$bobob2ob
2obob4obob4o10bo3b2o3bob2ob2o2bobob2o2bob2o$bobo2b3o6bo2b3o2b2obobo3b
3obo3b3o2b3o2b3ob4ob3obo$ob10ob6o2b3ob5ob2obob5o5b2obob2o2b2obo2b3o$2o
b6o4b10obobobobo3b3o2bobob4obo4bob2obo2b3o$o3b2obo2b4o3b5o2bob6o2bo4b
4obo2b2o7b5o$ob3o2bo2b3ob2o4b4o4bo2b3obo2b2ob4ob2o2bo4b2o4bobo$3bo3b3o
5bo5bo3bo2b2o3bobobobo2b3obob2o2b5ob3ob2o$3bo3b2obob2obobo2b4obobo2b2o
6bobo3bo4b6o2b2o3b2o$6b2ob3o2bob2obob5o2bob3obobo3bob2o2b2ob2o4b2o2b2o
$bobob2ob2obob2o4bob3ob3obob2o2b5o2bob3ob5obo2bo3bobo$b8ob3ob2obobo2b
5o3b2o3bobo6b2o2bo4bo2b3o3bo$b4o3bobob2o3b4o2b3o2b3o2bo2b5obobob4o2b5o
2bo3bo$2bob4o3b2o2bo2b2o2bobobobobo2b2o2b2o2b5ob2o2b3o4bo3b2o$3b3obo2b
2o5bo3bob2obobo3b4o2bo2bob2o3b3obo2b2obobo2bo$b5o6b3obo2b4obob3obo5bo
3b2ob9obob2o3bo2bo$b2o5b2obobo3b4obobob2obo2b4o4b5o3b2o2bo5bob2obo$2o
b6o2bob3ob4ob3o2b4obobob2o2b2obobo2bo2bob3o3b2obo!
weird

Code: Select all

x = 8, y = 12, rule = R4,C2,S2-3,B3,N@000000038181c0000005
obo$b2o$bo8$6b2o$6b2o!
User avatar
R2INT
Posts: 972
Joined: July 2nd, 2024, 7:42 pm

Re: Rules with interesting dynamics

Post by R2INT »

I think I just discovered like Whitespace but in the zebra stripes agar:

Code: Select all

#R B1e2in3jy4a5ce/S1e2ai3ekry4ar5j:T512,512
!
# [[ RANDOMIZE ]]
Unfortunately, the rule is explosive due to increased activity. I may need to remove some transitions to make the dynamics more obvious.

Code: Select all

x = 768, y = 767, rule = B1e2in3jy4a5ce/S1e2ai3ekry4ar5j:T768,768
768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$325obob2o2bobo2bo2b
5ob2o5bobo2bob2o2bob2obo3bob393o$326bo2b2o2bob3o3bo2bo2bobo2b3obo2bo2b
o2bo3bo2b2obo$325obobo3b2o3b3o2b2obo2bobobob5o4bobo2bob3obob392o$325b
obo3bobo2bob2obobo5b4o3bo2bob2ob4ob2obob2o$326ob2o2b3obo4bobob5ob3obo
bo2b5o2bobo2b2ob394o$325bo2bo2bo7bob2obo2bo2b3obob2obob3ob2o2bo2b2o$326o
b2obob2o3b2ob3obobob3o2bo2bobo2b3ob2obobob2o2b392o$327b2o2bobo2b3obob
obobo3bo3b4o3b5obobo2b4o$325o2b3o3bo5b4o4b2o3b2o2b4obobobobo2bo2b395o
$325b3ob2o3bob4ob2obo2b2obo4bo3bob2obobo3b3ob2o$329obob3ob2obo4b2ob2o
b3obob3ob2ob3obo2bob2ob393o$329bo2bobo2bob3o2b3o4bob2o3bo2bo2bo3bobob
2obo$326ob2o4b4obo3b3obobo2bob3obobob5o3b2o2bo2b392o$326bobo2b2o3b2o2b
ob2o2b3o2bob2o3b2o2b2obob4o2bobo$325obobo3b2obo2b2o3bobobobobo3bo4b3o
4bobo2bo2b393o$325b5o2bob3o2bobo5b4ob2obo3b8obo2b2o$326obo2bob2o2bob2o
7b3obo4b3obob2obob2ob2o2b394o$325b3ob3o2b2o3b2ob3o2b2o4bob5o2b3ob4obo
bo$329o2bob2o5b2o3b5obo2bo2b2o4bob3ob2ob2o2b392o$325bobo3b2ob6o2b5o2b
5o2b3ob2o2b3o3b2o2b2o$328o3b3o4bo3bo2bo4b3ob5o4bob2obo2bo2b394o$325b2o
2bobob5ob4ob2o2b3obob4o2bo5bob2o2b3o$325ob3o2b4o10b2o2bo4b2ob4obob3o2b
obobob393o$325b2obobob2o3b6obo3b3obobob4ob2ob4o7bo$325ob2o3bo3bob3obo
2bob4ob2obobo2b2obo2bob2ob3o2b393o$325bob2o2b5o4bo2bo9bobo5b2o3bob3ob
4o$325obobob3obob4ob2o2b4obo2b2o2bo2b3ob2o2b2o2b2ob393o$325b4ob4obo3b
2o4b2obobobo2bobobo2bobo5b2o$325o2b2o2b4obo2b4ob2obobo4b2ob2o3b2o2b7o
b394o$325b3ob6o2bo2bob4o3bo4bobobo2b3ob4obo3bo$326o5bo3bo3bob2o3bobob
obo3b3obo2b3ob2obobob394o$327bob3ob3o2bobob2obo3bobo3b2o3b3o6bo3bobo$
326o2bob4o3b2o3b2ob4o4b3ob2ob4ob5ob3ob393o$325bobobo2b2obobo2bob3o2b2o
7b3o3b2ob4o2b2ob2o$329obob4o2bob2ob3o12bobob2ob2obo2b4ob392o$327bo3b2o
2bobobo2b2ob2obobo4bobobob2o4b2ob3ob2o$326obob6o2bo4b3o4b2o2bob2obo2b
2o2bo2b2o2b396o$326b4obo2b3ob2ob3o9b2ob3ob4o2bobo2bo2bo$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o2$768o
2$768o2$768o2$768o2$768o2$768o2$768o!
EDIT: Natural gun for a chiral c/3o spaceship:

Code: Select all

x = 11, y = 17, rule = B1e2ein3jy4at5c6ce/S1e2aci3ery4ajr5ajy6-in
obobobobobo$obobobobobo$obobobobobo$obobobobobo$obobo3bobo$obo4b2obo$
obo3bobobo$obo5bobo$obo5bobo$obo2b4obo$obob2o2bobo$obobobobobo$obobob
obobo$obobobobobo$obobobobobo$obobobobobo$obobobobobo!
EDIT2: Progress on taming the whitespace rule

Code: Select all

x = 3, y = 2, rule = B1e2ikn3jy4a5acen/S1e2ai3ekry4aejr5j:T1024,1024
2bo$o!
Range-2 INT
R2INT's Rule Collection

3-state rules are the final frontier.
User avatar
LaundryPizza03
Posts: 2652
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: Rules with interesting dynamics

Post by LaundryPizza03 »

Produces dense ash that slowly stabilizes into spaghetti, including rapidly on the edge of a soup.

Code: Select all

x = 0, y = 0, rule = B2c3aj4akq5jn6ac7e/S12cik3-ciky4aijkr5i6c7
b!
# C [[ RANDOMIZE ]]

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
LaundryPizza03 at Wikipedia
User avatar
R2INT
Posts: 972
Joined: July 2nd, 2024, 7:42 pm

Re: Rules with interesting dynamics

Post by R2INT »

Maze vs. Strobing Checkerboard:

Code: Select all

x = 64, y = 64, rule = B2ek3aeijn4ej5cqy6ck7c/S1e23-cnqy4ijkrtwz5knqry6-ik7c8
3b3ob8obob2ob4ob3ob5ob3o4b5ob2o4b2o3bo$4bobo2b2o3bob2obo3bobobo2b5ob2o
2bo7bo3bobo2bobo2bo$2bo3bo4bo5b2obob2o2bo2bobob2o2bo8bobob3o5b3o2bo$2o
2bobo8bobo2b5obobo2bobobob2ob2obobo4b3o4b2o3b2o$9bob3obobo4b3obo4b2ob
obob2obob2o2b2o6bob5o$b4ob4obobo3b2ob7ob3ob5ob2ob2obobo2bob2obob2o2bo
2bo$bo4b2o2b2obob2obobob4o2b5obob2obo3bo4b4obo2b6obo$2o9b3o4bo3bo4bob
2ob4ob4obo3b5obobo2bo5bo$ob4ob4o4b2o3b2o2bo2bob2o4bobob2ob2obo2b2o2bo
b3o5b2o$ob2o2b2o2b3obob2o6b3ob3o2b2obo2bo2bo4bo3bobobob2o3bo$ob3o2b4o
bobob2ob3ob2obo3bobo4bo3bobobo3bobob4o2b2ob2o$2o2b2ob2ob2ob5obob2ob2o
bobo2b3obobobob3o4b2o2b3o2bobobo$5b5o5bob3ob3o2b2o2b4ob2obobo2b2ob4ob
2o3b2ob3obo$obo2b3ob4o2b2o3bo6bo3bob2o6b2o3bo2b4obob3o3bo$4o2bo3b2o2b
2obo3b3o3bob3ob2ob3o3bo2bo3bobobob4o2b3o$3o5b3ob3o5bob8o2bo2bob2o2b2o
2b2ob3obo3b2ob2o2bo$2ob3obo2bo2b2o3bobobo2bo4b2ob2o10b2ob4o3b2o3bobo$
obo2b2o2b2o4bobo2b3o4b2o2bo2bob2o2bobobob5o3bo2b2o3b2o$obo3b2o4bo8bob
3o2bobob3obo3b3ob4ob2ob4o3b3o$2b3o9b4o2bobo4b2o2bo3b2obo2b5o2bob2o2b2o
bo3bobo$b3o3b6obo2bobo2bob2ob4ob2ob3ob8obob2ob3ob4o2bo$bo3b3o2bob2o2b
3o2bobo3b2o3b2ob2obob3ob2o5bob4obo2bo$2o3bo2b3obobo8b2o2bobobo4bo2b3o
b2ob2obo4bo2bo3b2o$ob2obobobob4o2bobo5bob3o2bob3obo4bobobobo2b2obob3o
3bo$2obob2o2bo5b3ob2obobob2obo3bo2b3obob2o3b3ob2o3b3o2bobo$3o3b2obo5b
o2b2o2bobob2o8b3ob2obob2o3bo2bo3b2o3b2o$3bo2bo8b2o2b3ob3ob2obo5b2ob3o
b2o2bo2b2o2b2o2bob4o$b2o2b4obo2b2obobo2bo2b2o2bobobobo4bob2ob7ob2ob3o
2bobo$2o2b5ob2ob7o2bo2b3o3b2obo2b2obobobobobobobob5ob2o$2b2ob3o2b3ob2o
2b2o6bo2bob4obo2bobo4b2o2b2obob2ob2obo$2bobob2o5b2obob7o7bobo5bo6b3ob
5ob2ob2obo$2o3b2o3b3o2bobo2b2o2bob6ob6ob2ob2ob2obobob2o3bo3b2o$2obo2b
ob2o3bo2b2o2bo2bo6b5ob2o2b2o2bo5bo3b6o2bo$o2b2o4bo2bob5ob3obobo2bo5bo
bo2b3o2bo4bo2bob5o3bo$bob4o2bob3ob2o3b6obobo4b6ob3o3b2ob2o2bobob4o$7b
o4bo3bobo2bo2b2o2bob3o5b2o3bobo5b3ob7obo$2ob2obobo2b2o2bobo2b2ob2obob
3obobo2bo2b2ob6o2bobob2ob3o2bo$b2ob4obo2bo2bob3o4bo2bo4b2ob2o2bo2b2o2b
2o4bob4o3b2o$bob2obo2b2obo2b3ob2o4b4o3b2obob4o3b4obo3b2obob2ob2o$2obo
3b4obo3bo6bo4b2o2b8o3bo6bo5b2o3bo$2bo3b10o7b2ob2o2b2o2bo6b2o2b2obobo2b
o2b3o2bo$2obob2ob2obobob9ob3ob2obo3b2o2bob2o2bob2o2b4ob3o2bo$3bo4b2ob
2o3bobo3bo2bob3o4b2o4b3o6b5ob2o2b4o$b3ob7ob2obo3b6o4bo4b4ob4obo3b3o2b
3obo3bo$2obobo3bobobob4o2bobo4bobo2b5o4bobob2ob3o2b5o2b2o$2o2b2o2b5ob
ob2o2b2o2b2obo2bo5b2ob4o2b3o9b3obo$2ob3ob4o4bo3b2obob2o2b2o2bob2o2b4o
bo2b4o2b4ob4o2bo$2o3b3o3b2ob3o4b3ob2o6bo2bo2bo2bo2bobo5b2o2b2ob2o$o5b
o4bobo3bob4obo4b2ob2o2b2o2bobobob3ob3ob4obo$o3b2ob2o3bob3o3bo2b2o2b2o
bo3b2o2b3obob2ob2obob2ob4o2bo$3o7bo2bobob3obob4ob2ob2o2bob2ob2o3b2o5b
o4b4ob2o$2o2bo2b7ob3ob3o4bo2b4o2b8o4bobo4b2o4bo$bobob2obo2bo9bo2b3ob4o
4b4o4bob3obo2b6o4bo$bobobobo2bobob2obo2b4o2bo2bobo2b3obo3bo6b3ob4o2bo
2bo$o2b3o2b2o3bo2bo3bo8b3ob4obobobo2b4obob9ob2o$2bo2bob6o2bobo8b3o3bo
2bob7o2bob5o9b2o$obo2bo3bo2bob2obobobo2bob2ob5ob2obo6bobobobobo3bobo2b
2o$2b2o5bob2o3b4ob2ob2obo3b3o2b6ob2o2bo9b4obo$ob3o4bo4bo2bo4b5ob4obob
o6b4o2b5o3bo4bobo$2bo2b3obo2bob2o3bo2bob2obo2b2o4b2ob3ob3o3b2obo6bob3o
$bo3bobo5b2o6b4o2bo2bobo2b4o2b2obobo3b2o5b3ob3o$b3o5bobo7bo5b3obo2bob
2o3b2o2b3ob2o3bo6b5o$2b2obobo2b2o7b3obo9b2o3b2ob2obo3bobo2b2o2b2obobo
$b2ob2obobo3b4obob2obo2b7o3b2o2b2o4bo7b4obobo!
# [[ RANDOMIZE  ]]
EDIT: Maze but it leaves little patches of strobing checkerboard

Code: Select all

x = 64, y = 64, rule = B2ek3aeijn4ejr5cqy6ck7c/S1e23-cnq4ijkrtwz5knqry6-ik7c8
5bo3b2ob2o10b5o3b3ob4o3bo2b2obob4obob2obobo$ob2obobob4ob2o3bob4ob4o2b
2obo2b3ob3o3bob2o2bo2bo2bo$ob3obo4bo2b4ob2obobo5b4o5b4o2b3obo2b6o2bo$
bo7bo3bo3bo3b4obo3bobob2ob5o2b3ob2ob3o2b2ob4o$b3o2bob7obobob3obobobo2b
2ob3o2bobo3b3o5b3o4b4o$2b3o4b2obo4b3obo2bobob2o4b3obob2ob3ob2o2bobob2o
bo3b2o$b2o2bobo7bo2bobob3o2bo5b2o3b2ob5o3bob2o4bobob3o$o2bo2bob3ob2ob
3o2bo2bo2b3ob5ob3o3b2o2b2o4bo4b2o4bo$2ob3o2bob2ob2o7bobobo2b2obo4bobo
b3o3b4o3bob4o2bo$3bobo2bobobo2bo2bo2bob3obo3bo2b3o2b2o2bo4bo5b3o3b3o$
bo2b3obob4o3bo2bo2b3obo3b4o2b2o3bo2bob3obo3bo3b2obo$4o2b2obo3bo4bo3bo
5b5ob2o2b2ob2ob7o2bo2b3o4bo$3bob3obo2bobob5obo2b2ob2o3b4o3b2o3b2o5b2o
bo2bo2bo$bob2ob4o2bobo2bo2bobobob2obo5bo3bo2b3o5b2o3b2o2bob3o$4o2bo2b
3o3bobo3b6obobo2bo3b5obobobob2o2b2ob3obo2bo$5obo3bobob2o2b2ob2o2bobo2b
o3bobob3o3b3obob2o3bob5obo$b2ob2ob7obobobo4b7o3b4o2bob4obobo2bo2b2obo
b2obo$2o5b3ob4o2bob2o2bob7o3bo2b5obo2b2o4bob5ob3o$2b4ob3o4bo3bob2o2bo
bob2o3b4ob2obo3b3obo3bo2bo2b3o$3o2b2ob4o4b2obobo3bo3b4ob3obo7bo7b7obo
$2b3obobobo2b4obo2bo2bo12bo4b5ob2o3b4obo2b3o$2ob2ob5ob3ob4o2bo4bob2ob
2o2b2obob2obobo6bobobo2b2o$obo4b4o4b2obob3o4b2o3bo5bob5ob2o5bo2bo2b5o
$5bob2ob2ob5o4bo3b2ob2o4bobo2b2o6bo2bobob4ob2obo$ob8o2b3ob3obobob2obo
b7o6bo2bo4bo2b5o2bo2bo$ob4ob2o2bobobob3o3b4obo2bobob3ob2obobobo2b2o2b
o7b3o$4o2b2ob3obobobobob6o2bo2b3obo2bobob2ob2o5bo5bo3bo$2bobob10o7bob
obobo2b2o3bobobo4bob5obobo2b3obo$bo2b4o2b7obobo2b4obob4ob5ob3ob2o3b2o
bo2bob2o2b2o$ob2o2b2o2b2o4bob5o2bob2o2bo2bo2b3ob2o2b4o2bobo2b2o2bob2o
$o2b2o2bobob2o2bo4b4o2b2obob5ob4obo4bob2obo5b2ob3o$b2o2bob3obob4obob4o
2bo2bo2bob2o3bo2b2o2b4obo2bob3obobo$2obo3bo2b2o2bo3b2ob3obob8obo2b3o3b
o3bo2bo$3ob4ob4obo2b2o4b3o4b2o2bobo2b3o2bo2b2o2bo10b2o$ob2o5b2obob3ob
ob6obobo2b2ob4o4bo2b3o4bobobo2b2o$bob3obobobo5bo2bob4o4b2ob2ob4o3bobo
3b2o2b2o4b4o$4bo2bobo2b3obobob2o2bob5ob2o2bob7o2bobob4o2bob2ob2o$b2o2b
2o4b2ob2obo2b5o5bo3bob6ob2obobob4obobobo2bo$b4o3bobo3b2obo2bob2o3bo3b
obo3b4o4b4o5bobob2o2bo$bo4b2o5bo3bo4b3o2b2o4b5ob3o6bobo3bo2b3o$o6bo2b
o2bo4b2o2bo2bob3ob2o6bob5o2b4o2bobo3bob2o$b4obob2o3bo2b2obo5b2ob3o4bo
3b2obo5bobo2b5o3bo$obobob2obo3b3o2b3o3bob3obob3o2bob2obobo2bo3bobo2b2o
2bob2o$ob2obo2bo6b3obob4o7bo4bo2b3o4b3o3b2o2b2obob2o$b6ob4obobo2bob3o
b2o2b2ob2o3bo2bob8obobo2b2obob2obo$b2obo2bob2o5b2obob2obo3b3obo5b2obo
b2ob3o3b2o2b3o4bo$3bobo4b5o2bo3b2ob2obob2ob2o3b2o3bo2b2obob4obobobob3o
$4obobo2bo3bobobobob4o2b2obobo3b3ob2o2b2o2b2obo2b4o3bo$2o2b2ob2o2bob2o
b2o4bo2bo2b3o2bobob2ob5o2bo3bobo8b2o$ob2o2bo2b3ob5obobo3bo2b3obo2b6ob
o3b2o7bob6o$2o2bo3bo4bob2ob2o4b4o5bo7b4obo2bobobobo4bo2bo$3b2o2bobobo
b2o3bo3bobobo4b2ob3o3b2o2b5o3bob2ob3ob3o$2b2o2b2o4bob2ob2o2bob2obo2bo
b4o2bobob3obobobobob3o$4o2bobobo3b3o3b2o2bobob5obo2b3obo2b2ob4ob3ob4o
2bo$2o2bob6o3bobob2o2bobobo2b4obo2b3obobo5bo4bo4b2o$2b3obo3bob2obobob
2obo3b2ob6obob4obobob3o5b2o2b2obo$4ob2o2b6o5b5o3bo2bobob7o3b7obo4b2ob
3o$2bobobo2bob2obo2bob5ob7o3b3ob2obo2bob9ob7o$4ob2o3bobob2o2b2o3bo3bo
2b5obobobobo2b7obo4b2obobo$4o2b2ob2ob2o2bob2ob2o2b4obob3o2bobo3bob2ob
2o3b3ob3ob2o$b5o2bo2bo3bo4b4o2bobo2b3o3bob3ob2o6b2ob2obo$4ob2obob2obo
2bob3o2bo5bobo8bo2bob2o2b3ob3o2bo2bobo$6o2bo2b2obo2bo3bobobo5bobo3bob
ob3o4bo2bo4bo4b2o$b2o2bobob7o3b3o3bo3b2o2b3o9b2o3bo4bo3bob3o!
# [[ RANDOMIZE  ]]
EDIT2: Strobing checkerboard wins

Code: Select all

x = 64, y = 64, rule = B2ek3aeijn4ejnr5cqy6ck7c/S1e23-cknq4ijkrtwz5knqry6-ik7c8
3obobo3bobob2obo3bob3o3bo2b4obob4o2b6obob2obobobo$b4obob4o4b5o2b2ob2o
bob3o3b2ob3obobobo3b2o2b2o3b2o$4bobobo2b2o2bo2b2obo2b2obobob2o2b3obob
2o4bobobobo5bobo$5obo3b3o3bob3o2b6o3bob5o3b2o2bobobobob3o4bo$2o7b4ob2o
b2ob2o2b4o5bobobo2b5o6bo2bob3ob2o$2b2o4bob2ob3ob6o3bo4bo2bo2b3o5bobo4b
3obo5b2o$bobob3ob2o4b2o4b2ob4o3bob2o2bobobo2b3o3bobo4bob2o2bo$3b5o6bo
5bob5obo3bo4b2obo5bob3o3b3o3bobo$o3b3ob2o2b7o3bo2b2o3bo2bo2bo2b3o2bob
3o2bo3b2obobobo$bo3b2o6bo6bobob3ob3obobo3b2o2b3ob2o2b2ob2o2b3ob3o$obo
2bo2bobob4obo3b5obobobobo3bob6ob4obo4bo4bobo$3o3b3o2b4o3b2o3b2obobo2b
3o2b6obo3b2obo5bob2obobo$b3o3b3o4b2o4bo2b2o4bo2b6ob4o2bo3b3o4b2ob2o2b
o$o2bo4bo3bob5o3bob2o7bobobob3o2bob2o6bo2bo2b4o$ob6o2bobobobob2o6bo3b
o2bobo4b4obob2obob3o2b3ob2o$b2o4b10o2bobob2o2b2o2bob2o3b3o6bob3ob3obo
b4o$b2o2bobo2bo2b2ob3ob2o4b2ob4o4b2ob2o3bo2bobo2bo4bo3bo$o2bo8b2ob2o3b
obo2bob3o4bo2bo2b2obob3ob2obob3ob3ob2o$2o2bo2bobobo3bo2b3ob2obo3bo2bo
4b3o2bobob2o3bo3bobo4bo$5bo2b4ob2o2b4o2b3o2bo2b2ob2o3bob4ob4o4b5o2b2o
$b2o4bob2o3b2ob3o4b2obo4b2o4b7obo4b2obobob2o$ob2o3b2o2bobob2ob3obobob
o2bob2o3bobobo2bo4bobo2bo2bo2bobobo$b3o2b5ob2o2bo2b3ob2ob2o3bob2obobo
2bobob2o2b6ob2o2b2o$ob3ob2obob3obo2bo4bobo7bob5ob2obo4bobo2bo2bo3bobo
$2bobobobo2bo2bo3bo4bo4b2obo2bob3o3b4o3b5obo2b3ob2o$b2obo5b5ob6o2bobo
bob4o5b2ob2ob3ob2o3b2ob2o4bo$3obo2bob2o2bob3ob4ob3o3b4o2bobo2b2obo2b2o
b3obo4bo2bo$o4bo3b2o4bo2bo2b2obobo3bob2ob2o2b2ob3obobobo2b3ob2ob3o$b5o
2b2o3b2o2bo2bobobobobob3o2bo7b2obob5ob3o4b3o$o2bob3o4b2o3bobobo4b2ob4o
2b3obo2b4obob3o3bob2ob3o$b3o2bo2b4o3bo5b2o2bob3o3b2ob2o2b5o5bobo2b3ob
2obo$bo2bobo3bo2bob2o2bobo3b2o2bo3bo4bob4o2b3o4b2ob3ob4o$5obobo3b3ob2o
2b2ob2ob2o2bobo5b2o3bobob7o2bob2o2bo$ob2o6b2ob2obo2bob2ob2o2b6ob2obo3b
3obo2bo2b5o2b2obo$2o3b4obob2ob5o2b2obob2obob2o2bo4bob4ob5o2bo3bob3o$2b
6obo2b2o3b2o2bobob3o2bo5b2ob2o2b3ob5obo4bob2obo$3obob2ob3o3bob2obo2b2o
2bo2bo2bobob2o2b2ob2ob2ob2o3b2ob3obo$5bo4b2o5b2o2bob3o2b3obob2o5b6ob5o
bo2b4o$o2b2o2bo2bo2b2o3b2o2b2ob3obob5o2b2o2b4obob3o2b3ob2obo$ob3o2b5o
bo2bo3bob4ob2ob2o2bobob5obo2b5obo2bobo3b2o$b2obobob3ob2obo4bob2obob5o
4b2o3bobo2b3ob4o2b2ob2ob2o$ob3o2b2ob2obo2b2o2bo3b4obo2b2obobo2b2o4bo3b
3o4bobo3bo$2o7bo6b6o6b7obobob2obo3bobo3bo2bo2b2o2bo$b2o2bo2b2obobo4bo
2b2o2b3ob2obobob3o2b3obo2b2ob7obobo$bo3bobob2o2b3o2bob2o3b2ob2obo3b2o
bobobo2b3ob2o3bo3bob2o$ob2o4b2ob2o4b5o2b2o3bobob2o2b3o3bo4bob2obo2bo2b
ob2o$b2obo9bobob2o5b7o2b2ob3o2bob5ob3o3b3obob2o$obobob3o2bo6b2ob2ob5o
b2o11b4o2b2o4b2o2b4o$6o5bobo4bobob3obob3ob2o3bo2bob2o2b6o3bob4ob2o$o3b
3ob2o2bob3ob5o4b2obobobo3b2o2b2obobo2b2obob3ob2o2bo$o3b7obob3obob2obo
b4o2bobo2bobobobob2o2b7ob3obobo$2b3o2b2ob2o2bob9o2b3ob4obobobob2obo2b
4obo4bo2b3o$3obobo2b2o2b2obob4obob4o3b2o5bo3b2o2bob7o2bob2obo$obo2b2o
b2o3b2o2bo2b2ob2ob2ob2ob2o3bo2bo3b2o3b2ob2o3bo2bobo$4bo2bobob2o2b2o5b
obob4ob2o5b4ob3o2b2obo2b2obo4bo$obob2ob2o3b2ob2o2b4o3b6o3bobo2b4ob3o2b
2o2bobo4b3o$3o2b4o2b9ob2o4b5o2b2ob2ob2obobo3b3o2b3ob2obo$4bo4b2ob5obo
bo2b3o2b3o2b2o4bobo3bob3o2bob2obo2bo2bo$o7bo2bobobobob2o2bo2b3ob4obo3b
obo7bobo2bob4ob2o$2bo3bo3bo2b4obob2o2bobo2b2obo2bo4b2o2bobobobo3b3ob4o
$2bob3o5b4obo3b3ob2ob3ob2obo2bo5bob7o2b3o5bo$o4bob4obo2b9o2bo2bo3b3ob
2ob5obob5ob5o2bobo$ob2o2bob2obob3o2bobob7o11bob3obob2ob2o4b3o2b2o$3bo
bob4ob2o4bobo4b2o2bo5b3obob3o2bo2bobobobo4bobo!
# [[ RANDOMIZE  ]]
EDIT3: Longer-lived battle, but the checkerboard still wins

Code: Select all

x = 64, y = 64, rule = B2ek3aeijn4ejnr5cq6ck7c/S1e23-cknq4ijrtwz5knqry6-ik7c8
b2ob3o5bobo4b2o2b2ob5o3b2ob5o3b4o2b3o2b2obob2o$obob2obob3obob2ob2obo3b
o2bo4bobobob3ob3o3b2ob4o2bo$2b2ob2ob3obob2o5b2o2bo3bo9bobo4bo2bo5bo2b
2ob2o$2bob2o4b2obo2b3o3bo2b2o6bobob3ob2obobobob2o5bo2bo2bo$2o2b4obo3b
ob5o5b4obo2bo2bo2b2o3b3o3bo2b3ob2obobo$3obo5bo4bobobo2bo3b2o2bo2b3ob2o
2bo2b2obobob3o3b2o3bo$2bo5bobobo2b3o3b4o3bo2b3ob6o3b2o2bobo3bo4bobobo
$2o3bob5o2bo2bob2obob2o2b2obobo4b4ob2o4bobobobo2b3obo$3ob4o3bo5b2o2bo
bo2bobob3ob3ob2obo2b2ob3o5b9o$b2obobobo3b3o2b2o5bobo2b6ob4ob2o5b2ob2o
bob2ob3o$bo2bob3o2bobobo4b5ob2obob2obo2b7obobo3bobobo3b3o$3o2bo3bob2o
3b3ob2o6bo3bo4bo3b3obo2bo4bob2ob2ob3o$3ob4obob4o3b2obob2ob2o2b2ob5obo
bo3b2obobo3b2o2bo3bo$2b2ob2o2bo3b2o3b3obobob5ob3ob2o2b3o5bo2b3o2b3ob2o
bo$ob3o3bo3bo3b3o3bob2o2bobo2bobo2bo2bo2b4ob3ob2o5b2o$bobobo2bo5b2o2b
o3bobo5b3o3b6ob2obo3bo5bobobob2o$b3obob2o2bo5b3o2b3obo2bobob2ob2ob2o4b
o3bo3bo2b3o2bobo$4b4ob3ob4o5bo2bo3b2o2bo2b2obobo2b2o2bo4b3obob4o$o3bo
bo3bo2b2ob2ob2ob3ob2o3b3ob2obo2bo6b4obo7b3o$obo2bo3b2o2b4o3bob3obo4b2o
bo3b3obo5bo2b2ob5o$3o6b6obo3b5ob2ob2o4bo2bo2b3o6b3o2b4o2b2o$bob2obobo
bobobo3bob5o5b5ob2o2b3obo2b2o2bo2bobo3bob2o$o2bobo2b2ob2ob3ob3o2bo4bo
bo4bobobo5b2o2b2o3b3o3bo2bo$o2bob3obobo7bobo3b2o2b3ob6ob2o2bob2obo4bo
2b2obobo$b2ob5o6b3o2b2o2bo2bo5b2o4b2obo3bo2b2obobo5bob2o$bo2bob2obobo
2bob2ob2obo2b2o2bo2b4obobobob6ob2o4b4o3bo$b4obobo2bob2ob3o2bo3b3ob2o4b
o2bo2b3o2b5obobo2b4o$8o4b2o2bo5b3o2b2ob2o2b4ob2o7b2obob2obob5o$bobo2b
2o2b3o4bobobo4b4obobob2obob2o4b2o3b5o2bob3o$6obobob2o2bo3b2o3b7obo3bo
2bo4bo4bobob2o2bobob2o$2ob2o2bob3obob2o5b2o2b5obob4ob2obo2bobo2b2obo3b
3o$b2o3b2o2bob4obob3o3b3o4bo3bo5b2obo3b3o5b2o2b3o$o2b2ob2o2b2o5b3obob
o2b5ob2ob2o3bob2o2bob2o4b5obo$o3bobo2bobob3o2bobobo2bob5obobo3b3obo3b
5o2b3ob2obo$o2bo2bo4b5o4bo2bo2bob2obob2o2b2o3b2o4b5o3b2o4bo$bo2b2ob2o
bo3b2o3b2o2bob2obob3o2bob5ob5ob5o2b2obob3o$b5obob3obobob3ob3o3bobo2b2o
bob2o2bo3b2obobobobob2obo2bo$5bo2b4o4b2obob3ob3o2b2obob2obo4b4ob3obob
o5bobo$4b2obo2bobob2ob2ob4obo3bob3o7b3obo3b2obo2bo2bobo2bo$6bob6ob2o2b
o2b3ob2o5b2obob5o2b2ob2ob5obo3bo$2o3bo2b2ob2o13bob5ob2obob2o3bo5bob3o
bob2o$o3b3o2bo3b2o4b2ob2o3b2obob2o3b4ob2o3b2obobo2b2obob4o$ob3obo2bo3b
o2b2o2bo2b3o2b6obobob2obobo3bobo2b2ob4o$bo2bob4ob2o4b2o3b3o2b2ob3o2bo
3bo2b2ob3ob5o3bobo3bo$2ob2ob2ob3o2b2ob3ob2obobo2bobob3ob2o3bob3ob2ob2o
bobo2bo$b3o2b3ob2obo6b2o3b3ob3o2b2ob2o2b2o2bo2b3o2b3ob2o3b2o$2o4bobob
2ob4o3bo2bobob2o2bo3b2ob4obo2b3o3b7obobo$4o2bob2o2bo6bobobobo3b2o2bob
o2b2ob2ob2o3bobobobo3b2obo$ob3o4bo3b7o4bob3ob4obo2bob2obo2bo4b5o3b5o$
4o4b4ob2obob2ob3o2bobo6b4o4b2o2b2ob2obobo2b3o2bo$bob2o2bob2obo3b2obob
2ob2o4bobo3bobo3b4o2bo6bobo3b3o$2bob2o2bobobo3bob2o3b2obo2b2o3bo2b2ob
o5b2ob2obob4ob2ob2o$4ob4obob2ob2ob5o2bobo2bob2o2bo6b6o3b2ob3ob2o$obob
obo2bobobob3o2b2o4b2ob2obo4b2obob2o5bo3b4o3b4o$3o3bob2obob6obo2b2obo2b
2obo3b3o2b2ob3o3b2obo2b2ob4o$o5b4ob4o3bobo2bobo3b3o4b2o3b2o2bo3bob2ob
o4bo3bo$b2o4b3ob2ob3ob2ob2o2bob3o2b2o2bo3bobobo4bo4bo2b3o2bo$ob2ob3o3b
5obo2b9o5bob2o3b3o2bo3bo2b2o3bobobo$bob2obobobobob3o2b2o2bobo2b2ob6o2b
2ob4obob3ob2o5b4o$2bo2b2o2bobobo3bo2b2obo2b5ob2ob3o3bo4b6o2bobobob2ob
o$3o3b3obob4o4b3obo2b2ob4o5b2o4b2ob2o3b2o2bobob2o$obobo3bobo5bo2bobob
2obo3b2ob3ob3ob2obo2bobob3obob3obo$11obo2b3ob2o5bob2ob4obobo3bo2b6o2b
ob2o3b2obo$ob7obo6b2o5bo3bo2b4o3b3o3bo2b5ob2ob3ob2o!
# [[ RANDOMIZE  ]]
Range-2 INT
R2INT's Rule Collection

3-state rules are the final frontier.
OogaBooga_
Posts: 87
Joined: February 7th, 2026, 8:34 pm
Location: Quantum Superposition

Re: Rules with interesting dynamics

Post by OogaBooga_ »

LaundryPizza03 wrote: November 6th, 2026, 12:58 pm Produces dense ash that slowly stabilizes into spaghetti, including rapidly on the edge of a soup.

Code: Select all

x = 0, y = 0, rule = B2c3aj4akq5jn6ac7e/S12cik3-ciky4aijkr5i6c7
b!
# C [[ RANDOMIZE ]]
Natural 4c/1316 in that rule:

Code: Select all

x = 6, y = 3, rule = B2c3aj4akq5jn6ac7e/S12cik3-ciky4aijkr5i6c7
5o$5bo$4o!

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
Post Reply