## New method of classifying two-dimensional replicators

For discussion of other cellular automata.

### New method of classifying two-dimensional replicators

We first set the requirements that the replicator be a sawtooth, hereby excluding U-class, X-class, and failed replicators, and that it must be a square, rectangle or rhombus.

These replicators can be classified using the notation (E,C), where:

E - Edge rule; the one-dimensional rule which is simulated by the edge of the replicator

C - Core rule; the one-dimensional rule found on the diagonal of the square.
`x = 46, y = 17, rule = bs012345678History24.A\$23.3A\$22.A3.A\$21.2A.A.2A\$20.A.A.A.A.A\$3C9.3C4.3A5.3A\$C11.C.C3.A5.A5.A\$C3.3C.3C.3C2.2C.2C.3C.2C.CE\$C3.C.C.C3.C5.A5.A5.E\$3C.3C.C3.3C4.3A5.2AE\$20.A.A.A.A.E\$21.2A.A.AE\$22.A3.E4.3E3.E5.3E\$23.2AE5.E5.E5.E.E\$24.E6.3E.3E.3E.3E\$31.E3.E.E3.E.E\$31.3E.3E.3E.3E!`

Through these, we can currently identify four classes of replicators:

90,90 (includes all S, R and Q-class replicators):
`x = 1, y = 1, rule = B1e/So!`

90,150
`x = 1, y = 1, rule = B1e/S04eo!`

150,90
`x = 1, y = 1, rule = B13ci/So!`

150,150
`x = 1, y = 1, rule = B13i/S08o!`

150,1721342310
`x = 65, y = 55, rule = R2,C0,S1,3,5,7,9,11,B1,3,5,7,9,11,NNo!`

150,2523490710
`x = 65, y = 55, rule = R2,C0,S0,2,4,6,8,10,12,B1,3,5,7,9,11,NNo!`

2523490710,1721342310
`x = 1, y = 1, rule = r2b555555s555555o!`

2523490710,2523490710
`x = 1, y = 1, rule = r2b555555saaaaaazo!`

199931532107794273605284333428918544790,140117185019831836588493434554119984790
`x = 1, y = 1, rule = r3b555555555555s555555555555o!`

199931532107794273605284333428918544790,199931532107794273605284333428918544790
`x = 1, y = 1, rule = r3b555555555555saaaaaaaaaaaazo!`

0-fold and 1-fold replication rules have been excluded.
Last edited by muzik on January 26th, 2019, 12:22 pm, edited 6 times in total.
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muzik

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### Re: New method of classifying two-dimensional replicators

Examples of replicators:

90,90:

step2
`x = 2, y = 2, rule = B2a/S3a4a2o\$2o!`

step18
`x = 3, y = 5, rule = B2e3aijkq4ac7c/S2-an3-abo\$obo\$3o\$obo\$bo!`

step24
`x = 7, y = 7, rule = B3578/S233o\$obo\$3o2\$4b3o\$bo2bobo\$4b3o!`

90,150:

step2
`x = 2, y = 2, rule = B2a3i4w/S3a4a7c2o\$2o!`
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muzik

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### Re: New method of classifying two-dimensional replicators

Why exclude so many of them?

Here are some replicators that have an "Edge rule" and "Core rule." However, they are not saw-tooths:

`x = 512, y = 512, rule = B12c4e/S1e2c4cooo\$obo\$ooo\$! `

`x = 512, y = 512, rule = B1e2i4te/Sbo\$obo\$bo\$! `
Layz Boi

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Joined: October 25th, 2018, 3:57 pm

### Re: New method of classifying two-dimensional replicators

These classes also match up with "Replicator"-type rules:

`x = 16, y = 16, rule = B1e2ak3einqy4jnry5einqy6ak7e/S1e2ak3einqy4jnry5einqy6ak7e3b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$ob2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2obobo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obobob3o\$8b4obobo!`

`x = 16, y = 16, rule = B1e2ak3einqy4jnry5einqy6ak7e/S01c2-ak3acjkr4-jnry5acjkr6-ak7c83b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$ob2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2obobo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obobob3o\$8b4obobo!`

`x = 16, y = 16, rule = B1357/S13573b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$ob2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2obobo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obobob3o\$8b4obobo!`

`x = 16, y = 16, rule = B1357/S024683b2ob2obo3bobo\$bo3b2o4bobo\$o3b3o2bob2obo\$3bo6b2o2b2o\$bob3ob2obob2obo\$ob2ob2o2bob2ob2o\$obobo2b2o2b2obo\$b2o2b2ob5obo\$bo4b2obobo2bo\$2o2b2o2b2obobo\$3bo2bo3b3o2bo\$3o2bobo2b2obobo\$2b2obob2o3b2o\$bo2b3o2bo2b4o\$2o4b2obobob3o\$8b4obobo!`

It is possible to see such behaviour in some S-class replicators:
`x = 5, y = 6, rule = B1e2ak3einqy4jnry5einqy6ak7e/S1e2ak3einqy4jnry5einqy6ak7e2bo\$3bo\$obobo\$bo\$2bo\$3bo!`

`x = 47, y = 55, rule = B3578/S2324b3o\$24bobo\$24b3o2\$28b3o\$25bo2bobo\$28b3o2\$32b3o\$32bobo\$32b3o2\$36b3o\$33bo2bobo\$36b3o2\$24b3o13b3o\$24bobo2bo10bobo\$24b3o13b3o2\$28b3o13b3o\$28bobo10bo2bobo\$28b3o13b3o2\$3o13b3o\$obo2bo10bobo\$3o13b3o2\$4b3o13b3o\$4bobo10bo2bobo\$4b3o13b3o2\$8b3o\$8bobo2bo\$8b3o2\$12b3o\$12bobo\$12b3o2\$16b3o\$16bobo2bo\$16b3o2\$20b3o\$20bobo\$20b3o2\$24b3o\$24bobo2bo\$24b3o2\$28b3o\$28bobo\$28b3o!`
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muzik

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### Re: New method of classifying two-dimensional replicators

What i believe to be the first five iterations of the 2523490710,1721342310 replication habit, as seen in R2B(1,3,5,7,9,11,13,15,17,19,21,23)/S(1,3,5,7,9,11,13,15,17,19,21,23):

`x = 17, y = 129, rule = W08bo28\$6b5o\$6b5o\$6b2ob2o\$6b5o\$6b5o24\$4bobobobobo2\$4bobobobobo2\$4bobo3bobo2\$4bobobobobo2\$4bobobobobo20\$2b2o2bobobo2b2o\$2b2o2bobobo2b2o\$4bobobobobo2\$2b3ob5ob3o\$6b5o\$2b3ob2ob2ob3o\$6b5o\$2b3ob5ob3o2\$4bobobobobo\$2b2o2bobobo2b2o\$2b2o2bobobo2b2o16\$o3bo3bo3bo3bo4\$o3bo3bo3bo3bo4\$o3bo7bo3bo4\$o3bo3bo3bo3bo4\$o3bo3bo3bo3bo!`

Is there anything that can simulate such rules?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: New method of classifying two-dimensional replicators

From what I can tell:
E90 basically does this:
`000A000B0`

Or this:
`000000A0B`

E150 does this:
`000000ABC`

C90 does this:
`000A0B000`

Or this:
`A0000000B`

C150 does this:
`A000B000C`

Or this:
`000ABC000`

So I think XOR 4 edge would do the following:
`00000000000000000000AB0CD`

Center:
`0000000000AB0CD0000000000`

`A00000B00000000000C00000D`

I also think that the results of all the inputs are XORd.
And no, I am not going to go through all 2D range 2 neighborhoods.
UPDATE:
It's a bit more complicated, you OR the neighborhoods, then take the XOR of that.
`x = 23, y = 10, rule = B1357S02468History4.A3.3A3.A5.3A\$.D2.AD3.D3.DA5.ACA\$3A.A9.A5.3A5\$A5.A\$.C3.C\$2.A.A!`

So...this is probably what muzik is looking for.
`x = 39, y = 13, rule = BS012345678History13B.7B\$B4.AB5.B.BA4.B\$B4.AB5.B.B.A3.B5.D\$B2.D.AB2.D2.B.B2.D2.B6.D4.7B\$B4.AB5.B.B3.A.B7.D3.B5AB\$B4.AB5AB.B4.AB8.D2.B2A.2AB\$13B.7B.9D.BA.D.AB\$B5ABA4.B.B4.AB8.D2.B2A.2AB\$B5.BA4.B.B3.A.B7.D3.B5AB\$B2.D2.BA.D2.B.B2.D2.B6.D4.7B\$B5.BA4.B.B.A3.B5.D\$B5.BA4.B.BA4.B\$13B.7B!`

wwei23

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### Re: New method of classifying two-dimensional replicators

While I've yet to modify the classification system that integrates these, here are the rule tales for modulo-n replicators generated by FredkinModN-gen.py:

`@RULE Fredkin_mod3_vonNeumann@TREEnum_states=3num_neighbors=4num_nodes=131 0 0 01 1 1 11 2 2 22 0 1 22 1 2 02 2 0 13 3 4 53 4 5 33 5 3 44 6 7 84 7 8 64 8 6 75 9 10 11`

`@RULE Fredkin_mod4_vonNeumann@TREEnum_states=4num_neighbors=4num_nodes=171 0 0 0 01 1 1 1 11 2 2 2 21 3 3 3 32 0 1 2 32 1 2 3 02 2 3 0 12 3 0 1 23 4 5 6 73 5 6 7 43 6 7 4 53 7 4 5 64 8 9 10 114 9 10 11 84 10 11 8 94 11 8 9 105 12 13 14 15`

`@RULE Fredkin_mod5_vonNeumann@TREEnum_states=5num_neighbors=4num_nodes=211 0 0 0 0 01 1 1 1 1 11 2 2 2 2 21 3 3 3 3 31 4 4 4 4 42 0 1 2 3 42 1 2 3 4 02 2 3 4 0 12 3 4 0 1 22 4 0 1 2 33 5 6 7 8 93 6 7 8 9 53 7 8 9 5 63 8 9 5 6 73 9 5 6 7 84 10 11 12 13 144 11 12 13 14 104 12 13 14 10 114 13 14 10 11 124 14 10 11 12 135 15 16 17 18 19`

`@RULE Fredkin_mod6_vonNeumann@TREEnum_states=6num_neighbors=4num_nodes=251 0 0 0 0 0 01 1 1 1 1 1 11 2 2 2 2 2 21 3 3 3 3 3 31 4 4 4 4 4 41 5 5 5 5 5 52 0 1 2 3 4 52 1 2 3 4 5 02 2 3 4 5 0 12 3 4 5 0 1 22 4 5 0 1 2 32 5 0 1 2 3 43 6 7 8 9 10 113 7 8 9 10 11 63 8 9 10 11 6 73 9 10 11 6 7 83 10 11 6 7 8 93 11 6 7 8 9 104 12 13 14 15 16 174 13 14 15 16 17 124 14 15 16 17 12 134 15 16 17 12 13 144 16 17 12 13 14 154 17 12 13 14 15 165 18 19 20 21 22 23`

`@RULE Fredkin_mod7_vonNeumann@TREEnum_states=7num_neighbors=4num_nodes=291 0 0 0 0 0 0 01 1 1 1 1 1 1 11 2 2 2 2 2 2 21 3 3 3 3 3 3 31 4 4 4 4 4 4 41 5 5 5 5 5 5 51 6 6 6 6 6 6 62 0 1 2 3 4 5 62 1 2 3 4 5 6 02 2 3 4 5 6 0 12 3 4 5 6 0 1 22 4 5 6 0 1 2 32 5 6 0 1 2 3 42 6 0 1 2 3 4 53 7 8 9 10 11 12 133 8 9 10 11 12 13 73 9 10 11 12 13 7 83 10 11 12 13 7 8 93 11 12 13 7 8 9 103 12 13 7 8 9 10 113 13 7 8 9 10 11 124 14 15 16 17 18 19 204 15 16 17 18 19 20 144 16 17 18 19 20 14 154 17 18 19 20 14 15 164 18 19 20 14 15 16 174 19 20 14 15 16 17 184 20 14 15 16 17 18 195 21 22 23 24 25 26 27`

`@RULE Fredkin_mod8_vonNeumann@TREEnum_states=8num_neighbors=4num_nodes=331 0 0 0 0 0 0 0 01 1 1 1 1 1 1 1 11 2 2 2 2 2 2 2 21 3 3 3 3 3 3 3 31 4 4 4 4 4 4 4 41 5 5 5 5 5 5 5 51 6 6 6 6 6 6 6 61 7 7 7 7 7 7 7 72 0 1 2 3 4 5 6 72 1 2 3 4 5 6 7 02 2 3 4 5 6 7 0 12 3 4 5 6 7 0 1 22 4 5 6 7 0 1 2 32 5 6 7 0 1 2 3 42 6 7 0 1 2 3 4 52 7 0 1 2 3 4 5 63 8 9 10 11 12 13 14 153 9 10 11 12 13 14 15 83 10 11 12 13 14 15 8 93 11 12 13 14 15 8 9 103 12 13 14 15 8 9 10 113 13 14 15 8 9 10 11 123 14 15 8 9 10 11 12 133 15 8 9 10 11 12 13 144 16 17 18 19 20 21 22 234 17 18 19 20 21 22 23 164 18 19 20 21 22 23 16 174 19 20 21 22 23 16 17 184 20 21 22 23 16 17 18 194 21 22 23 16 17 18 19 204 22 23 16 17 18 19 20 214 23 16 17 18 19 20 21 225 24 25 26 27 28 29 30 31`

`@RULE Fredkin_mod9_vonNeumann@TREEnum_states=9num_neighbors=4num_nodes=371 0 0 0 0 0 0 0 0 01 1 1 1 1 1 1 1 1 11 2 2 2 2 2 2 2 2 21 3 3 3 3 3 3 3 3 31 4 4 4 4 4 4 4 4 41 5 5 5 5 5 5 5 5 51 6 6 6 6 6 6 6 6 61 7 7 7 7 7 7 7 7 71 8 8 8 8 8 8 8 8 82 0 1 2 3 4 5 6 7 82 1 2 3 4 5 6 7 8 02 2 3 4 5 6 7 8 0 12 3 4 5 6 7 8 0 1 22 4 5 6 7 8 0 1 2 32 5 6 7 8 0 1 2 3 42 6 7 8 0 1 2 3 4 52 7 8 0 1 2 3 4 5 62 8 0 1 2 3 4 5 6 73 9 10 11 12 13 14 15 16 173 10 11 12 13 14 15 16 17 93 11 12 13 14 15 16 17 9 103 12 13 14 15 16 17 9 10 113 13 14 15 16 17 9 10 11 123 14 15 16 17 9 10 11 12 133 15 16 17 9 10 11 12 13 143 16 17 9 10 11 12 13 14 153 17 9 10 11 12 13 14 15 164 18 19 20 21 22 23 24 25 264 19 20 21 22 23 24 25 26 184 20 21 22 23 24 25 26 18 194 21 22 23 24 25 26 18 19 204 22 23 24 25 26 18 19 20 214 23 24 25 26 18 19 20 21 224 24 25 26 18 19 20 21 22 234 25 26 18 19 20 21 22 23 244 26 18 19 20 21 22 23 24 255 27 28 29 30 31 32 33 34 35`

To my knowledge, no replicators have been found in any 2-state CA that are bound by these rules (indeed, no one-dimensional replicators that truly follow a composite Pascal triangle, either).
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muzik

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### Re: New method of classifying two-dimensional replicators

"Range-3 Moore" seems to be bound by the following edge rule:
`x = 55, y = 28, rule = Fredkin_mod3_Moore27.A\$26.3A\$25.AB.BA\$24.A2.A2.A\$23.9A\$22.AB7.BA\$21.A2.B5.B2.A\$20.3A3B3.3B3A\$19.AB.AB.AB.BA.BA.BA\$18.A8.A8.A\$17.3A6.3A6.3A\$16.AB.BA4.AB.BA4.AB.BA\$15.A2.A2.A2.A2.A2.A2.A2.A2.A\$14.27A\$13.AB25.BA\$12.A2.B23.B2.A\$11.3A3B21.3B3A\$10.AB.AB.AB19.BA.BA.BA\$9.A8.B17.B8.A\$8.3A6.3B15.3B6.3A\$7.AB.BA4.BA.AB13.BA.AB4.AB.BA\$6.A2.A2.A2.B2.B2.B11.B2.B2.B2.A2.A2.A\$5.9A9B9.9B9A\$4.AB7.AB7.AB7.BA7.BA7.BA\$3.A2.B5.A2.B5.A2.B5.B2.A5.B2.A5.B2.A\$2.3A3B3.3A3B3.3A3B3.3B3A3.3B3A3.3B3A\$.AB.AB.AB.AB.AB.AB.AB.AB.AB.BA.BA.BA.BA.BA.BA.BA.BA.BA\$A26.A26.A!`

and this core rule:
`x = 55, y = 28, rule = Fredkin_mod3_Moore27.A\$26.A.A\$25.A3BA\$24.A5.A\$23.A.A3.A.A\$22.A2B.B.B.2BA\$21.A2.B2.B2.B2.A\$20.A.AB.2B.2B.BA.A\$19.A2B.9A.2BA\$18.A17.A\$17.A.A15.A.A\$16.A3BA13.A3BA\$15.A5.A11.A5.A\$14.A.A3.A.A9.A.A3.A.A\$13.A2B.B.B.B.B7.B.B.B.B.2BA\$12.A2.B2.B5.B5.B5.B2.B2.A\$11.A.AB.2B.B3.B.B3.B.B3.B.2B.BA.A\$10.A2B.5AB2.A.2AB.B2A.A2.B5A.2BA\$9.A8.B8.B8.B8.A\$8.A.A6.B.B6.B.B6.B.B6.A.A\$7.A3BA4.B3AB4.B3AB4.B3AB4.A3BA\$6.A5.A2.B5.B2.B5.B2.B5.B2.A5.A\$5.A.A3.A.AB.B3.B.2B.B3.B.2B.B3.B.BA.A3.A.A\$4.A2B.B.B.B.2A.A.A.4A.A.A.4A.A.A.2A.B.B.B.2BA\$3.A2.B2.B5.A2.A2.A2.A2.A2.A2.A2.A2.A5.B2.B2.A\$2.A.AB.2B.B3.A.2A.2A.2A.2A.2A.2A.2A.2A.A3.B.2B.BA.A\$.A2B.5AB2.A27BA2.B5A.2BA\$A53.A!`

What Wolfram 3-state rule integers do these rules have?
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

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### Re: New method of classifying two-dimensional replicators

A bunch of (90,90)s (which I'm considering changing to (2,2), since these rulestrings can get unwieldy)

`x = 35, y = 19, rule = B2k3578/S3-e456k83o13b3o13b3o\$3o13b3o13b3o\$obo13bobo13bobo4\$obo5bobo5bobo13bobo\$3o5b3o5b3o13b3o\$3o5b3o5b3o13b3o8\$3o13b3o13b3o\$3o13b3o13b3o\$obo13bobo13bobo!`

`x = 104, y = 104, rule = B34-ac/S2333b3o\$32bo3bo\$32bo4bo\$33b3o2bo\$35b2o2bo\$36bo2bo\$36bo2bo\$37b2o3\$23b2o\$22bo2bo\$22bo2bo\$22bo2b2o\$23bo2b3o\$24bo4bo\$25bo3bo\$26b3o9\$39b2o\$38bo2bo\$38bo2bo\$38bo2b2o\$39bo2b3o\$40bo4bo\$b3o37bo3bo19b3o\$o3bo37b3o19bo3bo\$o4bo58bo4bo\$b3o2bo58b3o2bo\$3b2o2bo59b2o2bo\$4bo2bo60bo2bo\$4bo2bo60bo2bo\$5b2o62b2o3\$55b2o\$54bo2bo\$54bo2bo\$54bo2b2o\$55bo2b3o\$56bo4bo\$57bo3bo\$58b3o15\$33b3o61b3o\$32bo3bo59bo3bo\$32bo4bo58bo4bo\$33b3o2bo58b3o2bo\$35b2o2bo59b2o2bo\$36bo2bo60bo2bo\$36bo2bo60bo2bo\$37b2o62b2o3\$87b2o\$86bo2bo\$86bo2bo\$86bo2b2o\$87bo2b3o\$88bo4bo\$89bo3bo\$90b3o15\$65b3o\$64bo3bo\$64bo4bo\$65b3o2bo\$67b2o2bo\$68bo2bo\$68bo2bo\$69b2o!`

`x = 54, y = 37, rule = B2in3aijr4eq5j6c/S2-in3ijnqr4i5cnr6k7b3o\$7bobo\$6b2obo4\$29b3o\$29bobo\$28b2obo\$5bob2o\$5bobo\$5b3o\$16bob2o31b3o\$16bobo32bobo\$16b3o31b2obo\$27bob2o\$27bobo\$27b3o4\$49bob2o\$b3o45bobo\$bobo45b3o\$2obo4\$23b3o\$23bobo\$22b2obo4\$45b3o\$45bobo\$44b2obo!`

`x = 73, y = 35, rule = B3578/S23-c2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o14\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o\$2o5b2o7b2o5b2o7b2o5b2o23b2o5b2o14\$2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o\$2o5b2o23b2o5b2o23b2o5b2o!`

`x = 79, y = 40, rule = B34jy6n/S2-i32b3o33b3o33b3o\$bo3bo31bo3bo31bo3bo\$o5bo29bo5bo29bo5bo\$b2ob2o31b2ob2o31b2ob2o18\$b2ob2o13b2ob2o13b2ob2o31b2ob2o\$o5bo11bo5bo11bo5bo29bo5bo\$bo3bo13bo3bo13bo3bo31bo3bo\$2b3o15b3o15b3o33b3o12\$2b3o33b3o33b3o\$bo3bo31bo3bo31bo3bo\$o5bo29bo5bo29bo5bo\$b2ob2o31b2ob2o31b2ob2o!`

`x = 55, y = 55, rule = B3578/S2320b3o\$20bobo\$20b3o2\$16b3o\$16bobo2bo\$16b3o2\$12b3o\$12bobo\$12b3o2\$8b3o\$8bobo2bo\$8b3o2\$4b3o13b3o13b3o\$4bobo10bo2bobo10bo2bobo\$4b3o13b3o13b3o2\$3o13b3o13b3o\$obo2bo10bobo13bobo\$3o13b3o13b3o2\$28b3o\$28bobo\$28b3o2\$24b3o\$24bobo2bo\$24b3o2\$20b3o29b3o\$17bo2bobo29bobo\$20b3o29b3o2\$16b3o29b3o\$16bobo29bobo2bo\$16b3o29b3o2\$44b3o\$41bo2bobo\$44b3o2\$40b3o\$40bobo\$40b3o2\$36b3o\$36bobo\$36b3o2\$32b3o\$32bobo2bo\$32b3o!`

`x = 103, y = 50, rule = B3-y5a/S234c5ekbo3bo43bo3bo43bo3bo\$3ob3o41b3ob3o41b3ob3o24\$3ob3o17b3ob3o17b3ob3o41b3ob3o\$bo3bo19bo3bo19bo3bo43bo3bo22\$bo3bo43bo3bo43bo3bo\$3ob3o41b3ob3o41b3ob3o!`

`x = 31, y = 24, rule = B3-nq4nt5ar/S2-k34aiw6bo\$5b2o\$4b2o\$5b2o\$18bo\$17b2o\$4bo11b2o\$3b2o12b2o\$2b2o3b2o21bo\$3b2o3b2o19b2o\$7b2o7bo11b2o\$7bo7b2o12b2o\$2bo11b2o\$b2o12b2o\$2o26bo\$b2o24b2o\$14bo11b2o\$13b2o12b2o\$12b2o\$13b2o\$26bo\$25b2o\$24b2o\$25b2o!`

`x = 51, y = 26, rule = B3-jny/S1c23bo23bo23bo\$3o21b3o21b3o10\$3o9b3o9b3o21b3o\$bo11bo11bo23bo12\$bo23bo23bo\$3o21b3o21b3o!`

`x = 81, y = 81, rule = B34e5-ey7e8/S2330b3o\$30b3o\$30b3o4\$24b3o\$24b3o\$24b3o4\$18b3o\$18b3o\$18b3o4\$12b3o\$12b3o\$12b3o4\$6b3o21b3o21b3o\$6b3o21b3o21b3o\$6b3o21b3o21b3o4\$3o21b3o21b3o\$3o21b3o21b3o\$3o21b3o21b3o4\$42b3o\$42b3o\$42b3o4\$36b3o\$36b3o\$36b3o4\$30b3o45b3o\$30b3o45b3o\$30b3o45b3o4\$24b3o45b3o\$24b3o45b3o\$24b3o45b3o4\$66b3o\$66b3o\$66b3o4\$60b3o\$60b3o\$60b3o4\$54b3o\$54b3o\$54b3o4\$48b3o\$48b3o\$48b3o!`

`x = 173, y = 89, rule = B3/S23-ac4eiy62bo83bo83bo\$b3o81b3o81b3o\$2ob2o79b2ob2o79b2ob2o\$bobo81bobo81bobo\$2bo83bo83bo38\$2bo41bo41bo83bo\$bobo39bobo39bobo81bobo\$2ob2o37b2ob2o37b2ob2o79b2ob2o\$b3o39b3o39b3o81b3o\$2bo41bo41bo83bo38\$2bo83bo83bo\$b3o81b3o81b3o\$2ob2o79b2ob2o79b2ob2o\$bobo81bobo81bobo\$2bo83bo83bo!`

`x = 117, y = 66, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i2bo\$b3o\$2obo52bo\$55b3o\$54b2obo52bo\$3bob2o102b3o\$3b3o102b2obo\$4bo52bob2o\$57b3o\$58bo52bob2o\$111b3o\$112bo16\$3bo\$2b3o25bo\$b2obo24b3o25bo\$28b2obo24b3o\$55b2obo52bo\$4bob2o102b3o\$4b3o24bob2o74b2obo\$5bo25b3o24bob2o\$32bo25b3o\$59bo52bob2o\$112b3o\$113bo16\$4bo\$3b3o\$2b2obo52bo\$57b3o\$56b2obo52bo\$5bob2o102b3o\$5b3o102b2obo\$6bo52bob2o\$59b3o\$60bo52bob2o\$113b3o\$114bo!`

`x = 43, y = 23, rule = B2ei3/S1e23o17b3o17b3o\$obo17bobo17bobo\$obo17bobo17bobo8\$obo7bobo7bobo17bobo\$obo7bobo7bobo17bobo\$3o7b3o7b3o17b3o8\$3o17b3o17b3o\$obo17bobo17bobo\$obo17bobo17bobo!`

`x = 96, y = 96, rule = B3-ckq6/S2-c34ci629b3o\$28bo2bo\$28bo2bo\$28b3o5\$37b3o\$36bo2bo\$36bo2bo\$36b3o3\$15b3o\$14bo2bo\$14bo2bo\$14b3o5\$23b3o\$22bo2bo\$22bo2bo\$22b3o3\$b3o25b3o25b3o\$o2bo24bo2bo24bo2bo\$o2bo24bo2bo24bo2bo\$3o25b3o25b3o5\$9b3o25b3o25b3o\$8bo2bo24bo2bo24bo2bo\$8bo2bo24bo2bo24bo2bo\$8b3o25b3o25b3o3\$43b3o\$42bo2bo\$42bo2bo\$42b3o5\$51b3o\$50bo2bo\$50bo2bo\$50b3o3\$29b3o53b3o\$28bo2bo52bo2bo\$28bo2bo52bo2bo\$28b3o53b3o5\$37b3o53b3o\$36bo2bo52bo2bo\$36bo2bo52bo2bo\$36b3o53b3o3\$71b3o\$70bo2bo\$70bo2bo\$70b3o5\$79b3o\$78bo2bo\$78bo2bo\$78b3o3\$57b3o\$56bo2bo\$56bo2bo\$56b3o5\$65b3o\$64bo2bo\$64bo2bo\$64b3o!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland

### Re: New method of classifying two-dimensional replicators

Some more:

`x = 61, y = 32, rule = B2i3-ekny4z5r7/S2-cn3-ace4eiz5ejknq6i2bo27bo27bo\$b3o25b3o25b3o\$o3bo23bo3bo23bo3bo\$2ob2o23b2ob2o23b2ob2o8\$2ob2o9b2ob2o9b2ob2o23b2ob2o\$o3bo9bo3bo9bo3bo23bo3bo\$b3o11b3o11b3o25b3o\$2bo13bo13bo27bo14\$2bo27bo27bo\$b3o25b3o25b3o\$o3bo23bo3bo23bo3bo\$2ob2o23b2ob2o23b2ob2o!`

`x = 52, y = 52, rule = B3-n4a/S1e2-a3ijnr33bo\$32b2o\$33b3o\$34bo5\$41bo\$40b2o\$41b3o\$42bo5\$17bo31bo\$16b2o30b2o\$17b3o29b3o\$18bo31bo5\$25bo\$24b2o\$25b3o\$26bo5\$bo31bo\$2o14bo15b2o\$b3o11b3o15b3o\$2bo14b2o15bo\$17bo4\$9bo\$8b2o\$9b3o\$10bo5\$17bo\$16b2o\$17b3o\$18bo!`

`x = 81, y = 81, rule = B34ew/S2324b3o\$24b3o\$24b3o4\$30b3o\$30b3o\$30b3o4\$12b3o\$12b3o\$12b3o4\$18b3o\$18b3o\$18b3o4\$3o21b3o21b3o\$3o21b3o21b3o\$3o21b3o21b3o4\$6b3o21b3o21b3o\$6b3o21b3o21b3o\$6b3o21b3o21b3o4\$36b3o\$36b3o\$36b3o4\$42b3o\$42b3o\$42b3o4\$24b3o45b3o\$24b3o45b3o\$24b3o45b3o4\$30b3o45b3o\$30b3o45b3o\$30b3o45b3o4\$60b3o\$60b3o\$60b3o4\$66b3o\$66b3o\$66b3o4\$48b3o\$48b3o\$48b3o4\$54b3o\$54b3o\$54b3o!`

`x = 76, y = 52, rule = B2ac3e/S1e5i27bo\$27bo\$24bo\$24bo5\$15bo\$15bo\$12bo\$12bo5\$3bo23bo23bo\$3bo23bo23bo\$o23bo23bo\$o23bo23bo5\$39bo\$39bo\$36bo\$36bo5\$27bo47bo\$27bo47bo\$24bo47bo\$24bo47bo5\$63bo\$63bo\$60bo\$60bo5\$51bo\$51bo\$48bo\$48bo!`

`x = 43, y = 25, rule = B2e3aijkq4ac7c/S2-an3-abo19bo19bo\$obo17bobo17bobo\$3o17b3o17b3o\$obo17bobo17bobo\$bo19bo19bo6\$bo9bo9bo19bo\$obo7bobo7bobo17bobo\$3o7b3o7b3o17b3o\$obo7bobo7bobo17bobo\$bo9bo9bo19bo6\$bo19bo19bo\$obo17bobo17bobo\$3o17b3o17b3o\$obo17bobo17bobo\$bo19bo19bo!`

`x = 52, y = 29, rule = B34c/S2-i34wy5ay6ib2o22b2o22b2o\$2obo20b2obo20b2obo\$o2bo20bo2bo20bo2bo\$2obo20b2obo20b2obo\$b2o22b2o22b2o8\$b2o7b2o13b2o22b2o\$2obo5bob2o11b2obo20b2obo\$o2bo5bo2bo11bo2bo20bo2bo\$2obo5bob2o11b2obo20b2obo\$b2o7b2o13b2o22b2o8\$b2o22b2o22b2o\$2obo20b2obo20b2obo\$o2bo20bo2bo20bo2bo\$2obo20b2obo20b2obo\$b2o22b2o22b2o!`

`x = 109, y = 79, rule = B34ej5y6n/S232bo\$b3o\$2o2bo3\$7bobo\$5b5o\$5b3o\$3b5o\$3bobo3\$8bo2b2o\$9b3o\$10bo2\$46bo\$45b3o\$44b2o2bo2\$30bo2b2o\$31b3o17bobo\$32bo16b5o\$49b3o\$47b5o\$47bobo3\$52bo2b2o\$53b3o\$54bo2\$90bo\$89b3o\$88b2o2bo3\$95bobo\$93b5o\$93b3o\$91b5o\$91bobo3\$18bo77bo2b2o\$17b3o77b3o\$16b2o2bo77bo14\$62bo\$61b3o\$60b2o2bo14\$106bo\$105b3o\$104b2o2bo!`
Bored of using the Moore neighbourhood for everything? Introducing the Range-2 von Neumann isotropic non-totalistic rulespace!
muzik

Posts: 3310
Joined: January 28th, 2016, 2:47 pm
Location: Scotland