ConwayLife.com

B468S02357 wrote: June 5th, 2026, 8:08 pm Do linear spacefillers exist? I've seen the normal quadratic ones, and sublinear ones consisting of a signal expanding an agar (or antivoid) in a spiral formation, but do any rules exist qith linear ones?

wildmyron wrote: February 18th, 2021, 9:35 am ...
However, A for Awesome did post this interesting linear growth spacefiller:

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x = 29, y = 29, rule = B2c3-cikn4-eijn5-akn6ein7c8/S01e2ei3-cen4-iqy5iknqr6ai7c8
29o$5ob23o$4obob22o$3ob3ob15o2b4o$3o5b15obob3o$23o4b2o$23obob3o$23o2b
4o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$29o$3o2b24o$2obob24o
$o4b16o5b3o$2obob16ob3ob3o$3o2b17obob4o$23ob5o$29o$29o!

...

melwin22 wrote: August 15th, 2019, 5:32 am ...
There also exists a linear spacefiller. Smallest predecessors in terms of bounding box (6x6) and population (12) are shown.

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x = 6, y = 6, rule = B3678/S135678
bob3o$6o$bob3o$3obo$6o$3obo!

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x = 8, y = 8, rule = B3678/S135678
bo$2obo2$bo2bo$3bo2bo2$4bob2o$6bo!

...

B468S02357 wrote: June 13th, 2026, 3:42 pm Does lowlife have any oblique ships?

I wrote: February 21st, 2026, 3:23 pm Out on a whim, I decided to do some knightship searching. Here was the best partial.

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x = 16, y = 14, rule = B3/S13
4b2o$4b3o$2bo4bo$b2o3b3o$o3bo4bo$o2bobo3bobo$o4b2o4bo$2b2o6bobo$b
3ob3o2b2ob2o$2b2o3bo2bob2o$3b2ob2o$2bo3bobo3bob2o$2b2o5b4obo$3b3ob
o3bobo!

ThePlayzr wrote: June 17th, 2026, 3:28 am Is it possible to make this signal turn, and thus make loops?

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x = 17, y = 17, rule = B2en3-acq6a7e/S2aek34a5aij6-e78
3b2ob2ob2ob2o$b15o$b15o$3o11b3o$3ob9ob3o$b2ob9ob2o$3ob2ob2ob3ob3o$3ob
3o4b2ob3o$b2ob3o3b3ob2o$3ob2o4b3ob3o$3ob3ob2ob2ob3o$b2ob9ob2o$3ob5ob3o
b3o$3o5bo5b3o$b8ob6o$b15o$3b2ob2ob2ob2o!

Change the rule all you want, so long as it's the same signal.

x = 16, y = 16, rule = B2e3akqy4knqrtw5ci6aen7/S012kn3eiky4acjkq5eij6-i78
o2bo2bo2bo2bo2bo$b14o$b14o$4ob6ob4o$b2obo6bob2o$b3ob6ob3o$4ob6ob4o$b
10ob3o$b2o3b5ob3o$4ob6ob4o$b3ob6ob3o$b2obo6bob2o$4ob6ob4o$b14o$b14o$o
2bo2bo2bo2bo2bo!

./lls -r pB2345678/S012345678 <path>/signal_turn.jdf

x = 16, y = 16, rule = B2ik3-nq4-ainry5acikn6ac7e/S0123-n4acejwyz5-nr6-e78
3bo2bo2bo2bo$b14o$b14o$3obob6ob3o$b5o5b4o$b3o2b4obob2o$11ob4o$b2o3b5ob
3o$b3ob6ob3o$4ob6ob4o$b2obob4o2b3o$b5o4b5o$3ob6obob3o$b14o$b14o$3bo2bo
2bo2bo!

NNlk05 wrote: June 22nd, 2026, 9:11 pm Can someone teach me how to make weighted neighborhoods rules?
LifeWiki is very unhelpful.

Rx, Cn, S…, B…, NW…

x = 1, y = 1, rule = R2, C2, S, B1, NW0010009090100010909000100
!

0 0 1 0 0
0 9 0 9 0
1 0 0 0 1
0 9 0 9 0
0 0 1 0 0

0  0 1  0 0
0 -1 0 -1 0
1  0 0  0 1
0 -1 0 -1 0
0  0 1  0 0

pifricted wrote: June 22nd, 2026, 9:27 pm *snip*

B468S02357 wrote: June 24th, 2026, 3:45 pm What's this osc's period

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x = 5, y = 5, rule = B3/S23Investigator|B34/S134Investigator
3.O$4.O$3A.O$ANA$3A!

Jasmine wrote: June 28th, 2026, 10:50 am Hello everyone! I'm new here. I have got basic knowledge of outer-totalistic rules, tried several tens of them, and am confused by two things:

1. Why is B37/S23 explosive but B357/S23 chaotic? I thought a more situation of born would make it more explosive, but it did vice versa.

2. Why is B3678/S235678 stable? Why those situations benefitting B and S altogether make it stable, even not chaotic? Even B3/S237 and B37/S23 is explosive!

I firstly supposed that one more number after B or S would never decrease the explosiveness/chaoticness, but it's false. Is there any theory to predicate character of rules with B3 and not B0/1/2? Or we don't have many ways indeed and need to try and try like chemists?

Jasmine wrote: June 28th, 2026, 10:50 am Hello everyone! I'm new here. I have got basic knowledge of outer-totalistic rules, tried several tens of them, and am confused by two things:

1. Why is B37/S23 explosive but B357/S23 chaotic? I thought a more situation of born would make it more explosive, but it did vice versa.

2. Why is B3678/S235678 stable? Why those situations benefitting B and S altogether make it stable, even not chaotic? Even B3/S237 and B37/S23 is explosive!

I firstly supposed that one more number after B or S would never decrease the explosiveness/chaoticness, but it's false. Is there any theory to predicate character of rules with B3 and not B0/1/2? Or we don't have many ways indeed and need to try and try like chemists?

NNlk05 wrote: June 29th, 2026, 12:51 am

Jasmine wrote: June 28th, 2026, 10:50 am Hello everyone! I'm new here. I have got basic knowledge of outer-totalistic rules, tried several tens of them, and am confused by two things:

1. Why is B37/S23 explosive but B357/S23 chaotic? I thought a more situation of born would make it more explosive, but it did vice versa.

2. Why is B3678/S235678 stable? Why those situations benefitting B and S altogether make it stable, even not chaotic? Even B3/S237 and B37/S23 is explosive!

I firstly supposed that one more number after B or S would never decrease the explosiveness/chaoticness, but it's false. Is there any theory to predicate character of rules with B3 and not B0/1/2? Or we don't have many ways indeed and need to try and try like chemists?

Welcome to the Forums!

I believe that adding B5 removes some bad-behaving patterns that makes the rule explosive.
Most OT rules had been explored throughout, and it seems like most discoveries had been discovered. You may want to try out INT instead.
However, still keep an eye out in OT, sometimes CA can surprise you...
-----
Was any B1e rule proven TC?

Jasmine wrote: June 29th, 2026, 3:26 am

NNlk05 wrote: June 29th, 2026, 12:51 am *snip*

Thank you. Your telling me they're explored throughout makes me surprised, for I haven't found much talk about them. LifeWiki doesn't say much, and I have only found separate information rather than lists on this forum.

Is there a list of chaotic OT rules, or discussions trying to predict their characters beyond their having to fall in either B3 type or B0 type?

Thank you. Your telling me they're explored throughout makes me surprised, for I haven't found much talk about them. LifeWiki doesn't say much, and I have only found separate information rather than lists on this forum.

Is there a list of chaotic OT rules, or discussions trying to predict their characters beyond their having to fall in either B3 type or B0 type?

LifeWiki, Life-like cellular automaton wrote: *snip*
There are 262144 (= 218) distinct Life-like rules. Each rule has a complementary rule which behaves identically under on-off reversal; namely the rule in which birth occurs on all N except those for which 8 - N is a survival condition in the original rule, and survival occurs on all N except those for which 8 - N is a birth condition in the original rule. For example, the rule complementary to Conway's Life is B0123478/S01234678. This however does not quite halve the number of effectively distinct rules, as there are 512 (= 29) self-complementary rules which are unaffected by on-off reversal.

Some straightforward inferences on the behavior of different kinds of rules can be made:

• In all rules where the lowest birth condition is 1 neighboring ON cell, all finite patterns grow at the speed of light in all directions. No still lifes, oscillators or spaceships are possible in these rules. Several have replicators, however. There are 65536 (= 216) rules of the B1 type.
• All rules where the lowest birth condition is 2 neighboring ON cells are exploding or expanding in character; this is largely due to the fact that a domino at the edge of a pattern will give rise to a new domino, also located at the edge of the daughter pattern. Spaceships (such as the moon) and oscillators (such as the duoplet) do exist in many of these rules. There are 32768 (= 215) rules of the B2 type.
• All rules where the lowest birth condition (if any) is 4 or more neighboring ON cells are stable in character, since no patterns can ever grow beyond their initial bounding box. In particular, no spaceships can exist. There are 16384 (= 214) rules of the B4+ type.
• In all rules where the lowest birth condition is 0 neighboring ON cells, and the highest survival condition is 8 neighboring ON cells, the vacuum is unstable and will be immediately filled (and remain filled) with ON cells; thus, there are no patterns that remain finite. All of these rules have distinct complementary rules, and they are not commonly studied on their own.
  
  This leaves 16384 rules in which the lowest birth condition is 3 neighboring ON cells, as well as 65536 rules in which the lowest birth condition is 0 neighboring cells, and 8 neighbors is not a survival condition. All chaotic rules must fall in either of these two areas of the rulespace. Most well-studied examples fall in the first one, since for long no commonly available software existed that could simulate the evolution of rules containing B0. Golly's QuickLife algorithm simulates them by converting them into equivalent rules to avoid having to simulate an infinite number of cells.

*snip*

gbagcn wrote: July 11th, 2010, 6:48 pm This is a type of cellular automata that I created is similar to both brains brain and star wars in that it creates alot of spaceships that travel at the speed of light. They start from an initial configuration of 2 cells that are horizontally next to each other and grow chaotically. These rules are created using weighted life (4 states) and general binary and use the MCell text format. The weights in the survives and born section can probably be cut down a bit since I left alot of information in them that made searching for new rules easier. Ok here they are:

1. Line ships: NW12,NN8,NE12,WW8,ME0,EE10,SW12,SS10,SE12,HI4,RS24,RS28,RS32,RB16,RB17,RB18,RB19,RB20,RB21,RB22,RB23,RB24,RB25,RB26,RB27,RB28,RB29,RB30,RB31,RB32,RB33

2. Rectangles:
NW4,NN5,NE6,WW4,ME0,EE4,SW6,SS5,SE5,HI4,RS12,RS16,RS20,RB8,RB9,RB10,RB11,RB12,RB13,RB14,RB15

3. Trickle Down: NW10,NN9,NE10,WW6,ME0,EE6,SW7,SS7,SE7,HI4,RS18,RS21,RS24,RB12,RB14,RB15,RB16,RB17,RB18,RB19,RB20,RB21,RB22,RB23,RB24,RB25,RB26

4. Weird:
NW4,NN4,NE5,WW4,ME3,EE4,SW4,SS4,SE4,HI4,RS12,RB6,RB7,RB8,RB9,RB13,RB14,RB15,RB16,RB17

5. Insects:
NW3,NN2,NE3,WW2,ME0,EE2,SW2,SS3,SE2,HI4,RS6,RS10,RB4,RB5,RB6,RB7

6. Random Triangle:
NW5,NN4,NE5,WW4,ME4,EE4,SW4,SS4,SE3,HI4,RS12,RB6,RB7,RB8,RB9,RB13,RB14,RB15,RB16,RB17

7. Weird Ships:
NW6,NN5,NE6,WW4,ME0,EE4,SW5,SS5,SE4,HI4,RS12,RS16,RS20,RB8,RB9,RB10,RB11,RB12,RB13,RB14,RB15

8. Weird Ships 2:
NW4,NN5,NE6,WW6,ME0,EE4,SW4,SS5,SE5,HI4,RS12,RS16,RS20,RB8,RB9,RB10,RB11,RB12,RB13,RB14,RB15

9. Bugs (gen binary):
C4,NM,S6ab5abab81ab15ab79abb30ab31a,B3ababbaabbab4abbab3ab8abbab3ab7ab15a3bab3ab7ab15ab32abbab3ab7ab15ab31ab63a

10. Solid insects (gen binary, start with 2x2 square, 2 states):
C0,NM,S7ab3aba3b3aba3ba7b3aba3ba7ba14b4aba3ba7ba14baa14ba7ba3bab6aba3ba7ba14baa14ba7ba3bab4a14ba7ba3bab3a7ba3bab3a3bab3ab7a,B3abaabb4ab11ab3ab19ab47ab15ab16ab62abb62a

NNlk05 wrote: June 22nd, 2026, 11:30 pm

pifricted wrote: June 22nd, 2026, 9:27 pm *snip*

For example, if I want to make a glider shaped cells be killed, otherwisely, behave exactly like CGoL, what do I do?

x = 103, y = 14, rule = R4,C2,S2-3,B3,NW100010001000000000000000000000000000100000001000000000000000000000000000100010001
48bo22bo22b2o$51bo20bobo20b4o$o22b2o21bo22bo5bo16b2o4b2o$obo20bobo19b
o7bo14bobo5bo14b4o4b2o$2o23bo18bo22bobo7bo12b4o6b2o$25b2o16bo3bo18bob
obo18b6o$o7bo14b2o6b2o13bo7bo12bobobo5bo12b6o4b2o$obo5bobo12bobo5bobo
11bo3bo18bobobo5bo12b6o4b2o$2o6b2o15bo7bo10bo3bo3bo14bobobobobo14b10o
$25b2o6b2o12bo3bo16bobobobobo14b10o$o3bo18b2o2b2o17bo3bo18bobobobo16b
8o$obobobo16bobobobo19bo20bobobo18b6o$2o2b2o19bo3bo43bo22b2o$25b2o2b2o
!

NNlk05 wrote: June 22nd, 2026, 11:30 pm

pifricted wrote: June 22nd, 2026, 9:27 pm *snip*

For example, if I want to make a glider shaped cells be killed, otherwisely, behave exactly like CGoL, what do I do?

WhiteHawk wrote: August 3rd, 2024, 3:17 pm How many oblique ship slopes are known, barring repeats like (2,1) and (3,6)?

yyh_baboon wrote: July 9th, 2026, 10:34 pm

WhiteHawk wrote: August 3rd, 2024, 3:17 pm How many oblique ship slopes are known, barring repeats like (2,1) and (3,6)?

Two years have passed, and definitely there are more slopes. So i will ask this question again

NNlk05 wrote: July 10th, 2026, 1:15 am speedydelete, can you look this up?

NNlk05 wrote: July 10th, 2026, 1:15 am

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yyh_baboon wrote: July 9th, 2026, 10:34 pm
Two years have passed, and definitely there are more slopes. So i will ask this question again

speedydelete, can you look this up?