Rules With Quadratic (2D) Replicators

[drc]

By "catalyst" I assume you mean some pattern than can cap off a replicator, like so?

Code: Select all

x = 26, y = 26, rule = B3-jq/S234i
14b2o$15bo$7b3o2b3o$12bo4$23bo$23bo$23bo$2o7b3o$obo6bobo$2bo6bo12b2o$
2b2o19bo$5b3o15bobo$5bo18b2o$2bo2b2o$2bo$2bo4$13bo$11b3o2b3o$10bo$10b
2o!

Reduced:

Code: Select all

x = 18, y = 18, rule = B3-jq/S234i
8b3o4$10b3o$9bo2bo$9bo$o8b2o$o16bo$o16bo$17bo7$7b3o!

[wildmyron]

If you thought my previous replicator was weird, take a look at this:

Code: Select all

rle: fractal generator

That is beautiful. There is a mesmerising, ethereal quality to the rule which is particularly evident when the diagonal B puffer doesn't appear:

Code: Select all

x = 3, y = 17, rule = B2ein3aei/S2-c3-c4-aew
o$bo$2bo$bo10$bo$2bo$bo$o!

Code: Select all

x = 4, y = 31, rule = B2ein3aei/S2-c3-c4-aew
3bo$obo$bo26$bo$obo$3bo!

I haven't found a way to sustain this growth pattern yet.

[AbhpzTa]

By "catalyst" I assume you mean some pattern than can cap off a replicator, like so?

Code: Select all

x = 26, y = 26, rule = B3-jq/S234i
14b2o$15bo$7b3o2b3o$12bo4$23bo$23bo$23bo$2o7b3o$obo6bobo$2bo6bo12b2o$
2b2o19bo$5b3o15bobo$5bo18b2o$2bo2b2o$2bo$2bo4$13bo$11b3o2b3o$10bo$10b
2o!

Reduced:

Code: Select all

x = 18, y = 18, rule = B3-jq/S234i
8b3o4$10b3o$9bo2bo$9bo$o8b2o$o16bo$o16bo$17bo7$7b3o!

Stable circuit:
Sides: repeat time 17
NE/SW corners: repeat time 28
SE corner: repeat time 17
NW corner: smaller variant of the SE corner: repeat time 18

Code: Select all

x = 39, y = 38, rule = B3-jq/S234i
10b2o8b2o8b2o$10b2o8b2o8b2o$b2o$bo4bo$7bo$7b2o$6b2o$2o35b2o$2o35b2o$
15b2o8b2o$15b2o8b2o2$9b2o17b2o$9b2o17b2o4$2o35b2o$2o35b2o4$9b2o17b2o$
9b2o17b2o2$12b2o8b2o$12b2o8b2o$2o35b2o$2o35b2o4$36b2o$36b2o$7b2o8b2o8b
2o$7b2o8b2o8bo3bo$28b3obo$28bo2b2o!

p80 gun:

Code: Select all

x = 41, y = 66, rule = B3-jq/S234i
32b2o$32b2o3$17b2o$17bo$18b3o$20bo18b2o$39b2o$30b2o$30bo$30b3o$19b2o$
19b2o$36bo2$6b3o23b3o2$29b3o4$17b2ob2o$2o8bo6b2ob2o$2o7b3o$9bo2bo$12b
2o$11b2o3$7b2o$7b2o2b2o$11bo$12bo$7b2o2b2o$7b2o3$11b2o$12b2o$9bo2bo$2o
7b3o$2o8bo6b2ob2o$17b2ob2o4$29b3o2$6b3o23b3o2$36bo$19b2o$19b2o$30b3o$
30bo$30b2o$39b2o$20bo18b2o$18b3o$17bo$17b2o3$32b2o$32b2o!

[drc]

AbhpzTa: The king of making cool contraptions for OCA

[toroidalet]

B3-q/S2-c3-ekn4ain has a replicator:

Code: Select all

x = 3, y = 3, rule = B3-q/S2-c3-ekn4ain
3o$obo$3o!

[muzik]

Interesting... that leaves a sort of linear fuse compared to the other one that leaves a quadratic agar type one.

[toroidalet]

Interesting... that leaves a sort of linear fuse compared to the other one that leaves a quadratic agar type one.

A variation of that replicator and another one I posted can be made to leave a decaying agar:

Code: Select all

x = 9, y = 9, rule = B3-q/S2-c3-ekn4ain
6b3o$6bobo$6b3o4$3o$obo$3o!

Code: Select all

x = 6, y = 6, rule = B2a/S2n3a4a
4b2o$4b2o3$2o$2o!

Also:

Code: Select all

x = 3, y = 3, rule = B3aij6i/S2aeik3-cky4i
3o$obo$obo!

[PHPBB12345]

Interesting... that leaves a sort of linear fuse compared to the other one that leaves a quadratic agar type one.

A variation of that replicator and another one I posted can be made to leave a decaying agar:

Code: Select all

x = 9, y = 9, rule = B3-q/S2-c3-ekn4ain
6b3o$6bobo$6b3o4$3o$obo$3o!

Code: Select all

x = 6, y = 6, rule = B2a/S2n3a4a
4b2o$4b2o3$2o$2o!

Also:

Code: Select all

x = 3, y = 3, rule = B3aij6i/S2aeik3-cky4i
3o$obo$obo!

P20:

Code: Select all

x = 28, y = 28, rule = B3aij6i/S2aeik3-cky4i
17b2o$17b2o2$17bo$16b3o$16bobo$6b2o5b2o5b2o$6b2o5b2o5b2o2$2o4b3o3b3o$
2o4bo7bo$6b3o3b3o2$6b2o5b2o5b2o$6b2o5b2o5b2o$10b2o4bobo$8b2obo4b3o$8b
2o7bo8b2o$8b2obo14b2o$10b2o$6b2o5b2o5b2o$6b2o5b2o5b2o5$9b2o$9b2o!

P28:

Code: Select all

x = 16, y = 16, rule = B3aij6i/S2-cn3-cky4i
6b2o$6b2o2$9bo$8bobo$7bo3bo$7bo3bo2b2o$7b2ob2o2b2o$2o$2o5$8b2o$8b2o!

P30:

Code: Select all

x = 28, y = 28, rule = B3aij6i/S2-cn3-cky4i
17b2o$17b2o5$6b2o5b2o5b2o$6b2o5b2o5b2o2$2o3b2o7b2o$2o2b2o9b2o$5b2o7b2o
2$6b2o5b2o5b2o$6b2o5b2o5b2o2$12b2o7b2o$11b2o9b2o2b2o$12b2o7b2o3b2o2$6b
2o5b2o5b2o$6b2o5b2o5b2o5$9b2o$9b2o!

P60:

Code: Select all

x = 28, y = 28, rule = B3aij6i/S2aeik3-cky4i
17b2o$17b2o5$6b2o5b2o5b2o$6b2o2bo2b2o5b2o$9bobo$2o6bo3bo$2o6bo3bo$8b2o
b2o2$6b2o5b2o5b2o$6b2o5b2o5b2o3$26b2o$26b2o2$6b2o5b2o5b2o$6b2o5b2o5b2o
5$9b2o$9b2o!

P72:

Code: Select all

x = 31, y = 28, rule = B3aij6i/S2-cn3-cky4i
20b2o$20b2o5$6b2o5b2ob2o5b2o$6b2o5b2ob2o5b2o2$2o12b2o$2o13b2o$14b2o2$
6b2o5b2ob2o5b2o$6b2o5b2ob2o5b2o3$29b2o$29b2o2$6b2o5b2ob2o5b2o$6b2o5b2o
b2o5b2o5$9b2o$9b2o!

[toroidalet]

2 more replicators:

Code: Select all

x = 3, y = 1, rule = B2a4i/S1e
3o!

Code: Select all

x = 3, y = 3, rule = B2a3in4it/S1e
3o$obo$3o!

[wildmyron]

Interesting... that leaves a sort of linear fuse compared to the other one that leaves a quadratic agar type one.

A variation of that replicator and another one I posted can be made to leave a decaying agar:

Code: Select all

x = 9, y = 9, rule = B3-q/S2-c3-ekn4ain
6b3o$6bobo$6b3o4$3o$obo$3o!

I find that rule rather mesmerizing to watch

Code: Select all

x = 8, y = 5, rule = B3-q/S2-c3-ekn4ain
2b4o$b6o$2o4b2o$b6o$2b4o!

My favourite linear growth patterns:

Code: Select all

x = 4, y = 3, rule = B3-q/S2-c3-ekn4ain
b3o$2obo$b3o!

Code: Select all

x = 11, y = 31, rule = B3-q/S2-c3-ekn4ain
3bo$3b2o$4b2o$3b2o$3bo4$2b3o$2bobo$2bo2$2o$2o$8b3o$8bobo$8b3o$2o$2o2$
2bo$2bobo$2b3o4$3bo$3b2o$4b2o$3b2o$3bo!

[Gamedziner]

My favourite linear growth patterns:

Code: Select all

x = 4, y = 3, rule = B3-q/S2-c3-ekn4ain
b3o$2obo$b3o!

Code: Select all

x = 11, y = 31, rule = B3-q/S2-c3-ekn4ain
3bo$3b2o$4b2o$3b2o$3bo4$2b3o$2bobo$2bo2$2o$2o$8b3o$8bobo$8b3o$2o$2o2$
2bo$2bobo$2b3o4$3bo$3b2o$4b2o$3b2o$3bo!

A gun and a rake, respectively.

[toroidalet]

Code: Select all

x = 3, y = 3, rule = B2e3ai4c6i/S2-c3eijnr4ijz
3o$obo$obo!

[drc]

Failed one, but an interesting one at that, because it reappears at ~gen 120 and 1360 and 2290 and more, to die off (10c/82d) again:

Code: Select all

x = 2, y = 4, rule = B3-y4ce6c8/S23-e
2o$bo$bo$o!

Lasts 4437 generations in total. And that's not the only 2D replicator in this rule (5c/13o):

Code: Select all

x = 3, y = 3, rule = B3-y4ce6c8/S23-e
3o$obo$3o!

That one's less interesting, though.

Have a 28-cell still life+junk predecessor:

Code: Select all

x = 13, y = 13, rule = B3-y4ce6c8/S23-e
bo$obo$bo8$11bo$10bobo$11bo!

[Rhombic]

Code: Select all

x = 13, y = 13, rule = B3-e4c5c/S2-i34i
3$4b3o$3bo2bo$3bo2bo$3bobo$4bo$3bobo$3bo2bo$3bo2bo$4b3o!

and

Code: Select all

x = 4, y = 5, rule = B34c/S2-i34wy5ay6i
b2o$2obo$o2bo$2obo$b2o!

[toroidalet]

Failed one, but an interesting one at that, because it reappears at ~gen 120 and 1360 and 2290 and more, to die off (10c/82d) again:

Code: Select all

x = 2, y = 4, rule = B3-y4ce6c8/S23-e
2o$bo$bo$o!

It's a real replicator in B3-y4ceq6c/S23-e5e:

Code: Select all

x = 3, y = 3, rule = B3-y4ceq6c/S23-e5e
3o$obo$obo!

[BlinkerSpawn]

Failed one, but an interesting one at that, because it reappears at ~gen 120 and 1360 and 2290 and more, to die off (10c/82d) again:

Code: Select all

x = 2, y = 4, rule = B3-y4ce6c8/S23-e
2o$bo$bo$o!

Rake in related rule:

Code: Select all

x = 89, y = 69, rule = B3-y4ce6c8/S23-e6c
33bo32b2o$32b2o32b2o$32bobo3$63bo$62b3o11bo$50bobo8b2ob2o9b2o2bo6bo$
49bo12b3o8b2o4bo6b2o$49bo13bo13bo9b2o$51bo26bo3bo3b2o$51bo21b2o7bo$50b
o3b3o17bo2bo$50bo3b3o18b2o$bo19bo19bo$obo17bobo17bobo$obo17bobo17bobo$
bo19bo19bo$50bo3b3o18b2o$50bo3b3o17bo2bo$51bo21b2o7bo$51bo26bo3bo3b2o$
49bo13bo13bo9b2o$49bo12b3o8b2o4bo6b2o$50bobo8b2ob2o9b2o2bo6bo$62b3o11b
o$63bo3$32bobo$32b2o32b2o$33bo32b2o6$27bo32b2o$26b2o32b2o$26bobo3$57bo
$56b3o11bo$44bobo8b2ob2o9b2o2bo6bo$43bo12b3o8b2o4bo6b2o$43bo13bo13bo9b
2o$45bo26bo3bo3b2o$45bo21b2o7bo$44bo3b3o17bo2bo$44bo3b3o18b2o$15bo19bo
$14bobo17bobo$14bobo17bobo$15bo19bo$44bo3b3o18b2o$44bo3b3o17bo2bo$45bo
21b2o7bo$45bo26bo3bo3b2o$43bo13bo13bo9b2o$43bo12b3o8b2o4bo6b2o$44bobo
8b2ob2o9b2o2bo6bo$56b3o11bo$57bo3$26bobo$26b2o32b2o$27bo32b2o!

[toroidalet]

Another replicator:

Code: Select all

x = 3, y = 3, rule = B34et5ky8/S234e8
3o$3o$3o!

[Saka]

Sifting through my old posts and I found that I made a rule with one of these, hope it's new...

Code: Select all

x = 5, y = 5, rule = B34ce/S12-a3
3o$o$o3bo$4bo$2b3o!

[muzik]

I'll update OP one of these days

[Bullet51]

P52 diamond:

Code: Select all

x = 15, y = 15, rule = B34e5r68_S2-n34n5e
2bo$bobo$obobo$bobo$2bo6$12bo$11bobo$10bobobo$11bobo$12bo!

[Saka]

A rule with 3

Code: Select all

x = 3, y = 3, rule = B2a3i6/S256
2o$2bo$2bo!

Code: Select all

x = 2, y = 2, rule = B2a3i6/S256
2o$2o!

Code: Select all

x = 4, y = 4, rule = B2a3i6/S256
2o$2o$2b2o$2b2o!

[apg]

A rule with 3

Impressive! Here's a rule with 4:

Code: Select all

x = 4, y = 6, rule = B1357/S02468
4o$b2o$b2o$b2o$b2o$4o!

Code: Select all

x = 7, y = 6, rule = B1357/S02468
7o$b2ob2o$b2ob2o$b2ob2o$b2ob2o$7o!

Code: Select all

x = 10, y = 6, rule = B1357/S02468
10o$b2ob2ob2o$b2ob2ob2o$b2ob2ob2o$b2ob2ob2o$10o!

Code: Select all

x = 10, y = 6, rule = B1357/S02468
6ob3o$b2obo3bo$b2o2bobo$b2o2bobo$b2o3bo$4o2bo!

[Saka]

A rule with 3

Impressive! Here's a rule with 4:

Code: Select all

x = 4, y = 6, rule = B1357/S02468
4o$b2o$b2o$b2o$b2o$4o!

Code: Select all

x = 7, y = 6, rule = B1357/S02468
7o$b2ob2o$b2ob2o$b2ob2o$b2ob2o$7o!

Code: Select all

x = 10, y = 6, rule = B1357/S02468
10o$b2ob2ob2o$b2ob2ob2o$b2ob2ob2o$b2ob2ob2o$10o!

Code: Select all

x = 10, y = 6, rule = B1357/S02468
6ob3o$b2obo3bo$b2o2bobo$b2o2bobo$b2o3bo$4o2bo!

I suspect that rule has an infinite number of replicators, because roman numerals are also infinite

[muzik]

For sake of brevity, rules with B0 or B1 will not be included

[Gamedziner]

I suspect that rule has an infinite number of replicators, because roman numerals are also infinite

EVERYTHING in that rule evolves into a replicator, except for zero cells:

Code: Select all

x = 4, y = 6, rule = B1357/S02468
o20b2o20b3o20b4o127b999o$12o2523b2345o$1337bo$1000b222o$123o$12o$o$49b126o!