HROT,NW (Higher-range outer-totalistic, weighted)

[confocaloid]

Code: Select all

x = 5, y = 5, rule = B3/S23
5o$5o$2ob2o$5o$5o!

What you have shown in the pattern is merely a 5-by-5 condition. I assume you meant that the following transition rule should be followed in this case? (T = 0 on the left, T = 1 on the right, state 4 = off, state 3 = on, state 2 = unspecified.)

Code: Select all

x = 11, y = 5, rule = LifeHistory
5C.5B$5C.5B$2CD2C.2BC2B$5C.5B$5C.5B!

For comparison, here is what happens in plain Life for the same condition:

Code: Select all

x = 11, y = 5, rule = LifeHistory
5C.5B$5C.5B$2CD2C.2BD2B$5C.5B$5C.5B!

It is obviously possible to define a cellular automaton that does this:

1. if a cell has exactly three alive range-1 Moore neighbours, then it lives in the next generation
2. otherwise, if a cell is alive and has exactly two alive range-1 Moore neighbours, then it lives in the next generation
3. otherwise, if a cell is dead and has 24 alive range-2 Moore neighbours, then it lives in the next generation
4. otherwise the cell dies or remains dead

To implement this cellular automaton in Golly/LifeViewer, it suffices to make a weighted range-2 neighbourhood where each of the 8 inner cells has weight 17 (decimal) = 11 (hexadecimal) and each of the 16 outer cells has weight 1:

Code: Select all

x = 5, y = 5, rule = R2,C0,S34-67,B51-67,152,NW01010101010111111101011100110101111111010101010101
5o$5o$2ob2o$5o$5o!

For comparison, an equivalent definition of plain Life with the same weighted neighbourhood (the toggled living condition is B152):

Code: Select all

x = 5, y = 5, rule = R2,C0,S34-67,B51-67,NW01010101010111111101011100110101111111010101010101
5o$5o$2ob2o$5o$5o!

However, I'm not currently sure whether that 5x5 condition can make a difference in evolution of patterns. (E.g. is there a glider synthesis that settles into two different objects in the two rules?)

[b-engine]

However, I'm not currently sure whether that 5x5 condition can make a difference in evolution of patterns. (E.g. is there a glider synthesis that settles into two different objects in the two rules?)

Even corder engines exists here:

Code: Select all

x = 8, y = 6, rule = R2,C2,S34-67,B51-67,NW01010101010111111101011100110101111111010101010101
6bo$4bob2o$4bobo$4bo$2bo$obo!

Honeyfarms evolves in a bit different way, but they can't affect the overall evolution at all.

[confocaloid]

You need to add the B152 condition to the ruleset (otherwise the rule is completely equivalent to Life). Common honeyfarm predecessors still evolve the same way:

Code: Select all

x = 60, y = 6, rule = R2,C0,S34-67,B51-67,152,NW01010101010111111101011100110101111111010101010101
6bo23b5o23b2o$4bob2o22b5o22bobo$4bobo23b2ob2o22bobo$4bo25b5o23bo$2bo
27b5o$obo!

I think the rulespace defined by that weighted neighbourhood includes 2^306 CA rules. The state of the middle cell ranges from 0 through 1, the "inner count" ranges from 0 through 8, the "outer count" ranges from 0 through 16; 2 x 9 x 17 = 306; with the given weighted neighbourhood, two different combinations can never produce the same weighted sum.

[muzik]

There're 136 neighbors in the weighted neighborhood, but LifeViewer says the maximum neighbors a cell can have is 8.

This appears to work:

Code: Select all

x = 0, y = 0, rule = R2,C2,S2-3,B3,136,NW08080808080801010108080100010808010101080808080808
5o$5o$2ob2o$5o$5o!

[H. H. P. M. P. Cole]

I am trying to explore this weighted neighbourhood:

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00 00 00 01 00 00 00
00 00 00 05 00 00 00
00 00 00 19 00 00 00
01 05 19 00 19 05 01
00 00 00 19 00 00 00
00 00 00 05 00 00 00
00 00 00 01 00 00 00

My wish was to explore INT R3 Cross, but since LifeViewer does not support CAViewer or Durnak-Cole, this is the closest I can go.

Some 1-condition objects (WARNING: long):

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x = 31, y = 10, rule = R3,C2,S,B2,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
13bo13bo3$o9bo5bo7bo5bo3$3bo9bo3$24bo5bo!

Code: Select all

#has many more objects
x = 39, y = 15, rule = R3,C2,S,B6,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
b2o6$o10bo17bo2$3bo10bo11bo5bo2$17bo11bo5bo2$20bo11bo5bo2$35bo!

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x = 6, y = 4, rule = R3,C2,S,B7,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o3$o4bo!

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x = 21, y = 7, rule = R3,C2,S,B10,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
9bo8bo2$o6bo3bo4bo3bo2$2bo6bo2$16bo3bo!

Code: Select all

x = 6, y = 3, rule = R3,C2,S,B11,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o2$o4bo!

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x = 6, y = 6, rule = R3,C2,S,B12,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o2$o4bo$o4bo2$2b2o!

Code: Select all

#what? a ship?
x = 7, y = 4, rule = R3,C2,S,B25,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obobo2$6bo$bobobo!

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#has many more objects
x = 23, y = 8, rule = R3,C2,S,B26,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bobo7bobo6bobo$11bobo6bobo$20bobo4$o$3bo!

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x = 5, y = 4, rule = R3,C2,S,B27,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bobo3$o3bo!

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x = 3, y = 8, rule = R3,C2,S,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
b2o6$o$2bo!

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x = 6, y = 19, rule = R3,C2,S,B31,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o3$bo2bo6$2b2o$o4bo6$bobo2$o3bo!

Code: Select all

x = 6, y = 5, rule = R3,C2,S,B32,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o$o4bo2$o4bo$2b2o!

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x = 4, y = 3, rule = R3,C2,S,B35,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
b2o2$o2bo!

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x = 6, y = 4, rule = R3,C2,S,B36,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o$o4bo$o4bo$2b2o!

Code: Select all

x = 8, y = 3, rule = R3,C2,S,B50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bo4bo$o4bobo$6bo!

Code: Select all

x = 5, y = 2, rule = R3,C2,S,B51,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bobo$o3bo!

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x = 5, y = 5, rule = R3,C2,S,B52,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bobo$o3bo2$o3bo$bobo!

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x = 4, y = 2, rule = R3,C2,S,B55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
b2o$o2bo!

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x = 5, y = 4, rule = R3,C2,S,B56,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bobo$o3bo$o3bo$bobo!

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x = 4, y = 4, rule = R3,C2,S,B60,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
b2o$o2bo$o2bo$b2o!

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x = 1, y = 1, rule = R3,C2,S0,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o!

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x = 4, y = 1, rule = R3,C2,S1,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo!

Code: Select all

x = 47, y = 10, rule = R3,C2,S2,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo6bo2bo2bo5bo2bo2bo2bo5bo2bo2bo3$o2bo6bo5bo5bo8bo5bo5bo2bo3$10bo2b
o2bo5bo2bo2bo2bo5bo2bo5bo3$40bo2bo2bo!

Code: Select all

x = 3, y = 1, rule = R3,C2,S5,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obo!

Code: Select all

x = 45, y = 9, rule = R3,C2,S6,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo6bo2bobo5bo2bobo2bobo5bo2bobo2$o2bo6bo10bo15bo$15bo15bo10bobo2$10b
obo2bo5bobo2bobo2bo5bobo$44bo2$39bobo2bo!

Code: Select all

x = 34, y = 7, rule = R3,C2,S10,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obo4bobobo4bobobobo4bobobo2$obo4bo3bo4bo5bo4bo3bobo2$7bobobo4bobobobo
4bobo3bo2$29bobobo!

Code: Select all

x = 2, y = 1, rule = R3,C2,S25,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

Code: Select all

x = 43, y = 8, rule = R3,C2,S26,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo6bo2b2o7bo2b2o2b2o6bo2b2o$o2bo6bo11bo14bo2$14bo15bo10b2o$10b2o2bo
7b2o2b2o2bo6b2o2$42bo$38b2o2bo!

Code: Select all

x = 3, y = 2, rule = R3,C2,S30,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obo$obo!

Code: Select all

x = 2, y = 2, rule = R3,C2,S50,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o$2o!

Notice a few things:
- The B6 condition on its own can produce, of all things, Margolus oscillators.
- von Neumann rules can be emulated as follows: do not change the neighbourhood counts for expansion factor 3, but multiply them by 5 for expansion factor 2. I can't find a way to do expansion factor 1. For example, B24/S134V with expansion factor 2 is R3,C2,S5,15,20,B10,20,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000, and B2/S2V with expansion factor 3 is R3,C2,S2,B2,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000. The soup must be expanded, NOT inflated (there must be empty space between the cells). This is an expanded soup with expansion factor 3:

Code: Select all

x = 22, y = 22, rule = R3,C2,S1,3-4,B2,4,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
3bo8bo2bo5bo3$3bo2bo8bo2bo2bo3$o5bo2bo8bo3$o2bo5bo8bo3$o2bo2bo2bo5bo2b
o2bo3$o2bo2bo2bo5bo2bo3$o5bo5bo3$3bo2bo14bo!

- If two emulation media coexist, all objects in the expansion factor 3 emulated rule exist, but only some in the expansion factor 2 emulated rule can exist:

Code: Select all

x = 80, y = 24, rule = R3,C2,S1,3-5,15,20,B2,4,10,20,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o6bo9bobo7bobo11bo3bo8bobobobo9bobo2$o8bo9bo21bo3bo10bobo11bo5bo2$29b
obo9bo3bo8bobobobo15bo2$72bobo8$o6bo9bo2bo6bo2bo10bo5bo6bo2bo2bo2bo6b
o2bo3$o9bo9bo20bo5bo9bo2bo9bo8bo3$30bo2bo7bo5bo6bo2bo2bo2bo15bo3$73bo
2bo!

- S6 and S26 produce 'lopsided' SLs which have a similar structure (same adjacency graph*) to their non-lopsided counterparts in B/S2V.
- B25 without B26 gives a strangely B0-like effect (see below)

Code: Select all

x = 4, y = 3, rule = R3,C2,S50,B25,50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2$3bo!

To escape bounding box, one must have either of B1, B5, B6, B25, B26, B30, B31. All seven expand bounding diamond as well. (B1 and B5 generally produce explosive rules.)

I hope that others can join in...

*If one creates a graph of which cells are adjacent to each other (with respect to some neighbourhood) in a SL, one obtains the adjacency graph of the cells in that SL. For example, the adjacency graph of the block in Life is the tetrahedral graph, and that of the block in B/S2V (or Factorio) is the square graph.

[confocaloid]

[...] My wish was to explore INT R3 Cross, but since LifeViewer does not support CAViewer or Durnak-Cole, this is the closest I can go. [...]

It's possible to go a bit closer to INT R3 Cross, using an "atlas" of multiple overlapping rulespaces, with each "chart" in the "atlas" defined by a weighted neighbourhood like this:

Code: Select all

00 00 00 01 00 00 00
00 00 00 0F 00 00 00
00 00 00 2D 00 00 00
01 05 2D 00 2D 05 01
00 00 00 2D 00 00 00
00 00 00 0F 00 00 00
00 00 00 01 00 00 00

R1 neighbours and R3 neighbours are treated as before. The four R2 neighbours are split into two pairs, allowing to distinguish the situation "two alive R2 neighbours opposite each other" from the situation "two non-opposite alive R2 neighbours". One needs to be careful to choose living conditions so that the resulting CA is isotropic (for example if B58 is included then B78 also should be). Otherwise it seems to work:

Code: Select all

#what? a ship?
x = 7, y = 4, rule = R3,C2,S,B25,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obobo2$6bo$bobobo!

Code: Select all

#C Some ships, including a diagonal 3c/16 spaceship
#C Rulegolfed from a CA with an orthogonal 8c/8
#C https://conwaylife.com/forums/viewtopic.php?p=182653#p182653
#C
#C Despite using a weighted neighbourhood that distinguishes
#C horizontal from vertical, this CA is isotropic:
#C S6 = one R3 alive cell, one horizontal R2 alive cell, middle cell alive
#C S16 = one R3 alive cell, one vertical R2 alive cell, middle cell alive
#C B45 = one R1 alive cell, middle cell dead
#C B145 = three R1 alive cells, two horizontal R2 alive cells, middle cell dead
#C B165 = three R1 alive cells, two vertical R2 alive cells, middle cell dead
x = 92, y = 73, rule = R3,C0,S6,16,B45,145,165,NW000000010000000000000F0000000000002D00000001052D002D05010000002D0000000000000F00000000000001000000
2obo11bob3o7bo3bo6b2o3bo2bobob4o3bo2bo2bo3b2ob3obo4bob3obobo2bo$bobo5b
4o3b3obo2b3o3b2ob3o2b2obo4b2o2bo3b3obobob7o2bo2b2ob6obobo2b4o$3b2obo2b
o4bob2o2bo4b2o5bob3ob2obo3b3o4bo3bo2bo2bob2o3bobobob2obob4obo3b3o$o4bo
3b2o2bo2bo6bo2bo2bobobob2obo3bo3b2o2bo2bo3b3o6bob2o2bob3obo2bob4obo2bo
$2ob3obo3bo2b2obob2o2b2ob3obo5b3o2bob2ob2obobobob2o8bobobobob2o2bobo2b
2obobo$bob3ob2o5b4o5bo3bo8bobobo2bo2b2ob3obo3bo5bo3b3o2b4obobob2o5b4o$
2ob2ob3ob2o2bob2obobo2b3o2b3ob2o2b2obob3obo2b2o2bobobob2o2b4obo4b5ob5o
b3ob2o$3bo2b4ob2o2b2obob6o2b3o2bo4b2ob3obo2b3o3bobobobobo4b3o2bo3b3ob
2obob3o3bo$bo7bob2obobo4bo2bobob4obobobo3bob5o3b4o2bobobo3b4o2b3obobo
2bobob2o2b2obo$2ob4ob5obo2bob3o3bo2b2ob2o2bobob3o2bobo2b6obobobobobo3b
4o2b2obob2obo2b2o3bo$2o5b3o3b3o6b2ob2ob2ob4o7b2ob2o3bobobo4b6o4bob2o4b
obo5b4obo$b4o2b6o2b2o4b7o9bob2o2bo5b2obobo2bo2bob2obo9bobob4obobo2bo$o
b3o2b3o3b3ob3ob6o3b3obobo2b2o2bo4bo3bo3bob2obo3b3o3b3o2b2o3bo2bob3ob2o
$obob3o2b2ob3o9bobo8bo2bo4b2ob2o2b2ob2o3b3ob2obobob2o2b2obob2o3b2o2bob
o$3b2obob7o2bo5b3obo2bo2b2o2bo3bobobo2b3o2bo4bo4bo2b2obo5bob3o2bob2o3b
2o$3o6bo2b2obobo3bob3ob6ob4obo2b2obobo3bobob3obo2b2o2b2o2b2ob2o2bo2bo
2b3o2bo2bo$ob4o2b2o2bobobo4bobob3obo3bo2b3obo2b3o3bo4bob2o2bo3b2obob3o
bob5obo2bobo3bo$b3o2bo2bobo4b2o2bobob4o2b6ob5o2bob3obo2bo8bo5b2o2b4obo
3bo2b3o3bo$2o2b3o2bo2bo2bob5obobo2b3o3bo6bob2obob2obo2bobo2b2o2b2o2b5o
b2ob2o3b6ob4o$2bob2obobo2bobo3b2o4b2ob3ob2o3b5obo2b2obo2b10o3bo4b2obo
3bo2b2ob2o2bobob2o$3b2o4b4ob2o3bo2bo5bo4b3o8bob2o2b3ob3ob2o2b2o2bob2o
4b2o2bo2bob2obobo2bo$ob3o2bo3bobob2obo3b4ob3ob2o4bob4o6bob2obob5ob3o3b
o5b2ob2o2bo2bobo2bo$b3ob4ob3obo3bobobob2o3bobo4bob4ob3o3bobobo3b3o4b2o
b3obobo4b2o4bo4bobo$b7obobob3obob3o2bobo2b2o2bo2b2obo2bobo2bob2obo2bob
2o2b2o4bo2b2o2b5obobo2bo2b2obo$4b8ob4ob2ob2o6b2obob4ob6o2b2o2b4o2bobob
o2b2obo2b2obob2o3bo2bob2o4bo$o2b3obo6bobo4b6o3b6obo3bo5b2obobob2ob2obo
2bo5b3o2bo4bobo5b2o2bo$2bobobo2bobo2bobo3b2o4bo3bo2bobob4o4b2ob3ob3o3b
2o3bobobob2o3b7o2b2obob2obo$2b4o4b3o4bo2b3obobo6b3obo7bo2b4o3bobobo2bo
b2obob3o2bob2ob3obobo4bo$b5ob2o2bobo2b2obo5bobob7o3b2o4b2o6b2obobo2b5o
2bo2b2ob4o5bobo3bobo$bo3b2o3b2ob2o3b4obo4b2ob5obo2b2o2bobo2b3obob3o2b
2ob2ob4o3b3o3b2o2b2o2b2o$bob3obobob2o2b2ob2o2b3o2bobob2o5bo3bo7bob4ob
2o4b2o2b7obo3bob2ob3o2bobo$4bobo3b4o2bo2b2obo2b3o3b3o2bobo2bob2ob3ob2o
bo2b4obob2o2b4obob2ob2o3b2obo4b2o$bobob2ob3ob2obob2ob2ob2o2b2obo4bob2o
5b2o3bo2bobob2obobob4o2bo3bo2b6ob3o4b2o$bo2bo2bob7ob2ob2o2bo2b5obo2b2o
bo2b2ob4o2b3o2bobo6b5obob2obo3b2ob3obob2o$4b2o2b2o2b2o3b2o5bobob2o3bo
4b3o2bob2ob2o6bob3o3b2ob8o6bo2bobobo2bo$2b4o2bo11b4ob3o4bobobob2obo3b
2ob2obobob4obo3bobo3bobo3bo2b2obo3b2o3bo$b3ob6ob2o3bo2b4ob2o3bob2o3bob
2obob2o3b2obo2bobo2b2ob2o2bo2bo2b2o3b3o3bo2b2o$4bobob2ob4o3bo4b5ob2obo
2b2o10bo2b2ob2o4b3obo2b3o3b3ob2obob2o2b2obo$2bobobobobob2ob3obo3bobobo
bob4o3bo2b3o3b4obo2b2o2bo2bo2b3o2b4o5bo2bo3bob2o$2o2bo4bobo3bobob2o2bo
5b2o2bob2ob4o2bob2o2b2o2bobo3bobob2o2bo2b2o2bobobobo3bob5o$b2obobo2b2o
b2ob5ob2obob2o2b3ob2o3b6ob2ob2o2bo3b4obob2o5b2ob2obobo3b2obo2bo$8bo2b
2obobobob2o2bo2b3obo2b6o2b3ob7ob3o2bobobob2obo3b5o3b3o6bo$o2bo3b2o3b2o
2bob3o2bob5obob4obob2o3bo3b2ob11o3b3o2b2o3bo2bo5bo2b4o$o4b3obob5o2bob
5o2bob3o2bo2b3ob5ob2o6bo2bob2ob2o2b3ob2ob5o3b2ob2o2bobo$2o2bo5bo3b2ob
2obob2obo2b4obo3b3o2b2o7bo2bo2bob2obo2b5o2bobobob3obob2o2bo$o3bob3o2bo
bob4o2bob4obob2obo2b3obo2b4obobob2ob2o3b2obob2obo4b2o2b2o2b2ob2ob3obo$
6obobo3bob6o4b2ob3o3bo2b2ob3o2b2obobobo3bo4bob3obo2b2o10b3obo4bo$3o2b
2obo2b3ob3ob2o5bo2bo4b2obobob4o2bobo2bobo9b2o2bo2bobo3bo2b2o2b4ob3o$o
3bo4bo2b2obob2ob4obo2b4obobobo3bo2bo3b5o8bo3bobo2bobobob2o2bobob2obo2b
o$4b3obobo3b2ob4ob2o2bob2o2bo2b4o2bobob4o5bob2o3bo5b4ob3o3bob2obo4bo2b
o$4bob4o2bo2b2o2b5ob3obo3b2ob3obobo2bo5bob2o2bob2ob2o2b2o2bobo2b4o4b2o
4b2o$o5bo3b3o3bob2ob3o4bobobo4b2o2bo2b3o2bo2b2o3b2obob3o3bo4b2o3bob3ob
4o2bo$2b2o2b2ob3ob7o3bo2b4o6bo5bob3o2b3ob2o5bo2b3o3b3o2bo2b3o4bo5b2o$o
2bobo7bo5bo5bob2ob3o3b3o3b11o3bo2bo2b2o4bobob3o2b5o2bo2bo3bo$2bo4b2obo
2b2o2bob9obo3b3ob5ob2obo3bo3bo2bo5b3obo6b4o3b2ob8o$o2bob2o2bo3bo4b4o2b
3o3bob2ob3o2b7o4bo7b3o2bob2o2bo3bo5bo2bob2ob2o$o4b2o7b2o2b3o3bo2b10o2b
ob2o3b3o3b8o4bob2obo3b3o2bob3ob2o2b2o$ob3o2b2o2b3o4bobob3ob3o2b2ob4obo
2bo2b3o2bob2o2bo3b3obob3o2bo2b2ob3o3bo3b4o$2bo2bo2bo5bobobobo4b3o3b6o
5b7ob2o3bobo2b2ob3o3b4o3bob3o4b2obo2bo$3bob2ob2o2bo3bobo2b5obobobo2b2o
b5o10b4o3bo4b2ob2ob3o3b4ob4o2bob3o$5bo3b2o3b2obo2b3o2bo5b5ob2ob3o3bo3b
ob2obobo4b4ob2o4bo6b2o3b3ob3o$ob2o2bo2bo2b2ob2ob6ob2obo8bobob2obo3b5ob
2ob2o2bob3o5bob6obo2b4o2b3o$b2ob3ob6o2b3o4b2o2b2obob2obo3b3o3b3o2bobo
2b4o2b2obobobo2bo2b3ob2o2b2ob4o$b4ob4obob4ob2ob3o2bo7bobob7ob2o2bob5o
2b3ob2o4b2o5bo2b2o2bob2ob4o$2ob2o4b3obobobobob2o3bo3bobo2bo2bob3obo3b
3ob2obo2b2o5b3o4b2o3bobobob8o$b2obo2bo2bob3o2b2obo2bobo3b2obo3b4ob2ob
7ob6o2b2ob7o2bo7bo5b3ob2o$ob2o2b3o4bobob2o4b2o2bobobo2b2o2b2o6bo5b2obo
3b2o2bo4bo3b6o3bobo2bo3bo$3b3obobo2b3obobo4b9obo2b5o3b2o2b2ob2o3b2obo
3b2obo2b5o2bo4bob3o2b4o$o2b4o2b2o3bobo3b2obob3o5b2o2bo3b2obo4bo7bo5bo
3b4obo6bobo2bob2ob2o$4ob2obo2b2obo2b2o3b3obo2b2obob2ob2o2bo2b2ob6ob4o
3bo2bobobo2b6o4b2o3bob2obo$ob3ob2o8bobo5bo4bo2bo2b3o5b4o2b2ob4ob3o3b2o
bo2b2o3bob4obo4bo2bobo$bobo2b3ob8o3bob2o2b3ob3o3b2o4b4o4bobob3o3bo3b4o
b3o4b2o2bob3o2b2o$o4b2o3bo3bobobobobo2bo2bo2b2o2bobob3ob3o4b2obob2obo
3bob3o3bo3b2o5b2o4bob3o!

That "distinguishing trick" could be performed for any one of three ranges, and would work in Golly/LifeViewer.
I think it's also possible to do that for two ranges at once. However, one would need to use the highest weight on the remaining range where all four neighbours have the same weight.
It appears to be impossible to perform the "distinguishing trick" on all three ranges at once. That would require some cells to be weighted 243. Currently Golly/LifeViewer only allows weights from -127 to 127 (signed two-digit hexadecimal).

[lemon41625]

Found these c/3o and 4c/6o ships in FarCorners Life using cfind.

Code: Select all

x = 9, y = 8, rule = R2,C2,S2-3,B3,N@891891
4bo$2b2ob2o$3bobo$4bo$o7bo$3o3b3o$bo5bo$2bo3bo!

Code: Select all

x = 8, y = 6, rule = R2,C2,S2-3,B3,N@891891
b6o$2ob2ob2o$2o4b2o$3o2b3o$3b2o$2bo2bo!

Some c/2os

Code: Select all

x = 0, y = 0, rule = R2,C2,S2-3,B3,N@891891
4bo$3b3o$2bo3bo$bo2bo2bo$bo2bo2bo$bobobobo$2o5b2o$obobobobo$2bo3bo$3bob
o2$4bo!

Code: Select all

x = 0, y = 0, rule = R2,C2,S2-3,B3,N@891891
7bo$5b5o$5b2ob2o$4b2o3b2o$4bob3obo$3b2o5b2o$3b3obob3o2$bo3bo3bo3bo$b2o9b
2o$3bo3bo3bo$2o11b2o$ob2o7b2obo$o13bo!

[lemon41625]

I've been exploring a variant of Minibugs lately (R2,C2,S6-9,14-20,B7-8,15-24,NM or r2bffc0c0s0fe1e0).

The rule has photons of many periods, with periods 1, 2, 3, 4, 6, 8, 9, 10, 12, 13, 14, 33, 40 and 88 known.

Code: Select all

x = 429, y = 109, rule = R2,C2,S6-9,14-20,B7-8,15-24
127bobobo32bo3bo32bobobo31bobobo22bobobo23bo2bobobo24bo2bobobo19bo2bo
3bo14bobobo2bobobo31bo3bo2bobobo$85bobobo$27bo103bo32bo3bo32bo35bo3bo
22bo3bo23bo2bo3bo24bo6bo19bo2bo3bo18bo6bo31bo3bo2bo3bo$89bo$27bo99bob
obo32bobobo32bobobo31bobobo22bobobo23bo2bo3bo24bo2bobobo19bo2bobobo14b
obobo2bobobo31bobobo2bo3bo$85bobobo$27bo103bo36bo32bo3bo31bo3bo26bo23b
o2bo3bo24bo6bo19bo6bo18bo6bo35bo2bo3bo$85bo$27bo99bobobo36bo32bobobo31b
obobo22bobobo23bo2bobobo24bo2bobobo19bo6bo14bobobo2bobobo35bo2bobobo$
85bobobo$27bo3$125b3o$78b3o43b5o12b3o15b3o11b3o$77b5o13b3o25b2o3b2o10b
5o13b5o9b5o18b3o12b3o19b3o12b3o16b3o19b3o12b3o14b3o13b3o16b3o21b3o$13b
3o10b3o10b3o34b2o3b2o11b5o24bob3obo9b2o3b2o11b2o3b2o7b2o3b2o16b5o10b5o
17b5o10b5o14b5o17b5o10b5o12b5o11b5o14b5o19b5o38b3o$12b5o8b5o8b5o33bob
3obo10b2o3b2o22bob5obo8bob3obo11bob3obo7bob3obo15b2o3b2o8b2o3b2o15b2o
3b2o8b2o3b2o12b2o3b2o15b2o3b2o8b2o3b2o10b2o3b2o9b2o3b2o12b2o3b2o17b2o
3b2o36b5o$11b2o3b2o6b2o3b2o6b2o3b2o31bob5obo9bob3obo22bob5obo7bob5obo
9bob5obo5bob4obo15bob3obo8bob3obo15bob3obo8bob3obo12bob3obo15bob3obo8b
ob3obo10bob3obo9bob3obo12bob3obo17bob3obo35b2o3b2o$11bob3obo6bob3obo6b
ob3obo31bob5obo8bob5obo21b4ob3obo6bob5obo9bob5obo5bob4obo14bob5obo6bo
b5obo13bob5obo6bob5obo10bob5obo14bob3obo8bob3obo10bob3obo8bob3o14bob3o
19bob5obo34bob3obo$11bob3obo6bob4obo4bob5obo29bob3ob2obo8bob5obo22b7o
bo5bob3ob2obo9bob2ob2obo8b3obo14bob5obo6bob5obo13bob5obo6bob5obo10bob
5obo14bobobobo8bob3obo10bobobobo8bob3o14bob3o19bob5obo34bob3obo$11bob
obobo6bob4obo4bob5obo29bob6obo10b2ob2obo23b4o3bo5bob6obo9bob5obo10bob
o14b4ob4o6bob2ob3obo11bob2o2b4o6bob2ob2obo10bob2ob2obo14bob3obo9b5o11b
ob4o8bob4obo11bob4obo20b3o37bobobo2bo$11bobobobo6bob3o7bob5obo29bob4o
bobo11b4obo21bo8bo5bob4obobo9bo3bo3bo12bo14b9o6bob6o13bob2o3b2obo5bob
2ob2obo10bob5o2b2o13b4obo7bob5obo9bob4obo6bob4o13bob4o20bo5bo35bob4ob
o$11bo5bo6bobo3bo9bo33bo8bo9bo2bo3bo22bo4bobo6bo8bo13bo12b2o2bo16b2ob
2o8bobob3obo12bob7obo8b3o13bobobo4b2o11bob4obo7bob2ob2obo9bob4obo5bob
4o13bob5o20bo5bo36b5obo$12bobobo7bo50bo4bob2o53bo8bo45bob5obo6bo20bo3b
2o4bo6bo2bo2bo11bo8b2o11bob5o8bob5obo10b2ob2obo5bob4o13bob4o22bobobo35b
ob6obo$24bo2b2o66bob2o40b2ob3o50b3o9b2obo3bo13bo9bo7b2ob2o12b2obobo2b
o2bo10bob2ob2obo7b3ob3o12b4obo5bob3o14bob4o20bob2ob2obo33bob2o2b2obo$
24b2o167bo5bo29bob2o3b2o8b2ob2o35b6obo5bob7obo10b2o3bo5bo5bo12bob3obo
18bo3bobo3bo32b4o2b4o$26bo168b3o86bob3ob3o6bob2o3b2obo8bo6bo5bo5bo12b
obo3bo18bo9bo31bobo6bobo$3b3o12b3o12b3o11b3o38b3o40b3o79b3o68bob2ob4o
bo4bob2o3b2obo8b2o2b2o8bob3o13bo24b2ob5ob2o31bob3o2b3obo$2b5o10b5o10b
5o9b5o36b5o12b3o23b5o25b3o12b3o35b3o68bob2o3b2obo4bob7obo41bob2o62bo2b
6o2bo$b2o3b2o8b2o3b2o8b2o3b2o7b2o3b2o19b3o12b2o3b2o10b5o21b2o3b2o23b5o
10b5o33b2ob2o67bobob5obo4bo3bobo3bo64bo11bo30b2ob6ob2o$bob3obo8bob3ob
o8bob3obo7bob3obo18b5o11bob3obo9b2o3b2o20bob3obo22b2o3b2o8b2o3b2o32bo
3bo67bo3b3obobo4b2o7b2o65bob7obo31b2o8b2o$bob3obo7bob4obo8bob3obo6bob
5obo16b2o3b2o9bob5obo8bob3obo19bob4obo22bob3obo8bob3obo32bo3bo68bobo6b
o5bo3bo3bo65bo11bo31bo8bo$bob3obo7bob4obo8bobobobo6bob5obo16bob3obo9b
ob5obo7bob5obo18bob4obo22bob3obo7bob5obo18b3o11bobo75bob2o123b2o6b2o$
2b5o8bob4obo8bobobobo5bob3ob3obo15bob3obo9bob2ob3obo6bob5obo18bob4obo
22bobobobo7bob5obo17b5o11bo16b3o58bo83b3o3b3o34bob4obo$ob5obo6bobo4bo
8bo2bo2bo5bob7obo15bobobobo9bob6obo6bob2ob2obo18bobo4bo22bob3obo6bob2o
3b2obo15b2o3b2o26b5o10b3o171bo6bo$ob2ob2obo6bo6bo8bo5bo5bo3b3o3bo15bo
b3obo9bobob2o3bo6bob5obo18bo6bo23b4obo6bob3ob3obo15bob3obo25b2o3b2o8b
5o171b2o2b2o$9o7bob2obo9bo2bo2bo5bo9bo15bob4o10bo8bo6bobobo3bo18bo5bo
22bob5o7bo3b5obo14bob5obo24bob3obo7b2o3b2o172b2o$b3ob3o24b2ob2o7bobo3b
obo16bob4obo8bo7bo7bo7bo18b2o27bob5obo5bo9bo14bob5obo24bob3obo7bob3ob
o$b7o62b5obo8b3o13b2obobo2bo20bo26bob2ob2obo7b2o20bob3ob4o24bobobobo7b
ob4obo$2b5o61bob2ob2obo31b2o47bob5obo11b3o15bob7o25bob4o12b2obo125b3o
3b3o$o7bo59bob6o31b2o48bo3bo3bo29b5ob3o25bob4obo9b4obo123b3o5b3o$bo5b
o60b4ob3obo83bo33b4ob4o25bob4obo7bob4obo123b2o7b2o$14b3o24b3o23bob7ob
o119b6o26bob4obo9b5obo122b2o2bobo2b2o$13b5o9b3o10b5o22bob3o2b2obo117b
o8bo24bo4bobo7bob2ob2obo124bob3obo$12b2o3b2o7b5o8b2o3b2o21bob7obo151b
o6bo7bob5obo125b5o$12bob3obo6b2o3b2o7bob3obo21bobob3obobo119b2ob3o27b
o4bo9bo2bobobo125b5o$12bob3obo6bob3obo6bob4obo21bo9bo167bo6bo127bo$12b
obobobo6bob4obo5bob3o25bo8bo171bob2o$12bob4o7bob4obo5bob3o32bo$12bob4o
bo5bob4obo5bobo3bo$12bob4obo5bo6bo5bo4bo$12bob4obo6bo4bo7bob2o$12bo6b
o$12bo6bo$13bob2obo8$370b3o3bo7bo3b3o$369b2o2bo2bo7bo2bo2b2o$369b3o5b
7o5b3o$370b6o9b6o$376bob5obo$377bo5bo$377b2o3b2o$379bobo2$373b3o9b3o$
373b3o9b3o$373b3o9b3o26$376b2o5b2o$375b3o5b3o$375b3o5b3o$374bo11bo$373b
o13bo$373b3o4bo4b3o$373bo2bo3bo3bo2bo$373bo2b2o2bo2b2o2bo$374b2o9b2o!

Some other ships are known naturally (from left to right, c/3d, c/4d, 8c/88d, 2c/3o, c/2o, 4c/10o, 2c/5o, c/5o)

Code: Select all

x = 87, y = 27, rule = R2,C2,S6-9,14-20,B7-8,15-24
30b3o12b5o11b4o9bo8b3o$29b5o9b2o5b2o9b2ob2o6b2ob2o6b3o$17b3o9b2ob2o7b
2ob7ob2o11bo6b2ob2o5bo3bo$15b2o3b2o7bo3bo7bob9obo6bo3b2o6bobobo6b3o$15b
2obob2o8bobo7bob11obo6b4o8b3o$16b2ob3o18bob11obo$17b3o20bo3b7o3bo$41b
o11bo$42b2o7b2o$45b5o6$9b3o$8b4o$8b2o$9b3o3$4bo$3b3o$2b2obo$b2o2bo$2o
3bo$b4o!

Using cfind, I've also found a number of c/2os, including higher-period ones (with the help of apgsearch), some new 2c/3os and a c/3o.

Code: Select all

x = 203, y = 61, rule = R2,C2,S6-9,14-20,B7-8,15-24
6b3o$4b3ob3o23b8o$3b3obob3o21b2o2b2o2b2o16b4o4b4o12b3o6b3o$b3o2bobo2b
3o18bob8obo14b2ob2ob2ob2ob2o10b4o6b4o$2o3b5o3b2o16bob10obo12b2o2b2ob2o
b2o2b2o8bo5b4o5bo12b3o3b3o15b3o6b3o48b7o$o4b5o4bo15bob3o6b3obo10b2o14b
2o7bob3obo2bob3obo11b4o3b4o13b4o6b4o46bo3bo3bo$3obo5bob3o15bob12obo10b
2o2b3ob2ob3o2b2o6bob4o6b4obo9bo5bo5bo11b2o2bo6bo2b2o17b2o7b2o16bo2b5o
2bo$30bob12obo34bob5o4b5obo9bobobo3bobobo12bo3b2o2b2o3bo17b3o7b3o14bo
b9obo$30bobobo6bobobo34bob14obo9bob9obo13b2ob6ob2o17b2ob3o3b3ob2o13bo
b9obo$30bobo4b2o4bobo38b10o12bob11obo16b4o21bobo4bo4bobo13bob9obo$30b
o2b2o6b2o2bo35bo6b2o6bo9bob3ob3ob3obo15b6o20bobob2o3b2obobo13bobobo3b
obobo$30b2obo8bob2o42b2o16bob3obobob3obo15b6o20bob11obo14bo4bo4bo$8b3o
21bo10bo12b3o7b3o17bo4bo14bo2b9o2bo17b2o22bob11obo15b2ob3ob2o$7b5o44b
4o5b4o19b2o17bo3b5o3bo42bob11obo$7b2ob2o43bo3bo5bo3bo39bo2b3o2bo49b5o
$7bo3bo43bo13bo94bo9bo$6bo5bo43b2o9b2o43b3o$5bo7bo43bo9bo99bo3bo$5b3o
3b3o46bo3bo80b3o3b3o12bob3obo$4bo2b5o2bo14b4o8b4o15b5o79b4o3b4o11b2o3b
2o$4b2o7b2o14b4o8b4o12b2o7b2o75bo5bo5bo10bobobobo$5bob5obo14bo16bo10b
2o2b5o2b2o13b3o4b3o10b3o3b3o32bobobo3bobobo9bo2b3o2bo$34bo4bo16bob9ob
o12b4o4b4o8b4o3b4o31bob9obo9bo2b3o2bo$30b2ob8ob2o12bob9obo12bo2bo4bo2b
o7bo5bo5bo29bob11obo8bob5obo$30bo5b2o5bo12bob3obob3obo12bob2o4b2obo7b
obobo3bobobo29bob11obo8b4ob4o$56bobob5obobo13bob6obo8bob9obo29bob4obo
b4obo9b2o3b2o$29bo3bob4obo3bo11bo4b3o4bo13bo2bo2bo2bo7bob11obo28bob4o
bob4obo9b2o3b2o$28bob2o2bo4bo2b2obo11bo9bo15b8o8bob3ob3ob3obo28bo3b7o
3bo8bob5obo$30b2o10b2o14b2ob3ob2o16bob4obo8bob3ob3ob3obo29bo2b7o2bo9b
ob5obo$28bobo2bo6bo2bobo13b7o17bo6bo8bob3ob3ob3obo33b5o14bo2bo2bo$28b
o3bo8bo3bo12bo2bobo2bo35b9o37b3o16b2ob2o$29b2o12b2o14b3ob3o38b5o$105b
3o40bobo$102b2o5b2o$76b3o3b3o21bo$75b4o3b4o$74bo5bo5bo$74bobobo3bobob
o$42bo10bo20bob9obo45b4o4b4o$40b4o8b4o17bob11obo43b2ob2ob2ob2ob2o$39b
2o3b3o2b3o3b2o16bob11obo17bo10bo13b2o2b2ob2ob2o2b2o$39bo3bo8bo3bo16bo
b4obob4obo15b4o8b4o10b2o14b2o$39bob14obo16bob4obob4obo14b2o3b3o2b3o3b
2o9b2o2b3ob2ob3o2b2o$39bobob10obobo16bo3b7o3bo14bo3bo8bo3bo$39bob14ob
o17bo2b7o2bo15bob14obo$39bob14obo21b5o19bobob10obobo13b2o6b2o$39bob4o
6b4obo18bo9bo16bob14obo$39bobobo8bobobo17bo11bo15bob5o4b5obo13b10o$39b
o3bo8bo3bo16bobo3bobo3bobo18b4o2b4o16b2o8b2o$39b2o14b2o16bob2o7b2obo15b
obob8obobo13bob8obo$43b2ob4ob2o22bo2bo3bo2bo18bo2b8o2bo14bob8obo$41bo
b2ob4ob2obo18bobo2bo3bo2bobo44bob3o2b3obo$42bobo6bobo19bo3bo5bo3bo18b
3o4b3o16bob8obo$41b2ob3o2b3ob2o19b2o9b2o23b2o25b2o$42b2o8b2o56b2o22b2o
4b2o$43bo8bo56b4o$108b2o2b2o$109bo2bo$107b2ob2ob2o$107b2ob2ob2o$108b2o
2b2o!

I've also tried looking for 3c/4os but no success yet. Here are some partials.

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,14-20,B7-8,15-24,NM
4b2o4b2o$3b3o4b3o$2b2o3b2o3b2o$b2o4b2o4b2o$b2o3b4o3b2o$2bo10bo$2b3o6b3o
$3bo8bo$4b3o2b3o$2bo10bo$bo12bo$bo2bo6bo2bo$bob2o6b2obo$bo2b2o4b2o2bo$
3b4o2b4o$bob4o2b4obo$2bo10bo$b2o10b2o$bo5b2o5bo$4b3o2b3o$16o!

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,14-20,B7-8,15-24,NM
6b3o$5b5o$4b2o3b2o$4b2o3b2o$4b3ob3o$4b2obob2o$5b5o$5b2ob2o$4b2obob2o$4b
o5bo$3bo7bo$3bo2bobo2bo$3bo7bo$2bo9bo$2b2o7b2o$2b3o2bo2b3o$2bo2b5o2bo$
2bo9bo$3bobo3bobo$3bob2ob2obo$3bo3bo3bo$3bob2ob2obo$b5obob5o3$obo4bo4b
obo$obob2o3b2obobo$2obob2ob2obob2o!

Finally, here are some oscillators in the rule.

Code: Select all

x = 74, y = 49, rule = R2,C2,S6-9,14-20,B7-8,15-24
7b2ob2o$6bob2o2bo12bobo41b3o$5bob5obo10bobobo13b2o12b4o8b2o2bo$6b6obo
9b2obob2o11bob3o9b6o7bo3b2o$5b7obo9b2obob2o10bo3b2o22b2o3bo$2bob6o2bo
10b2obob2o10bo4bo7b2o2b2o2b2o6bo2b2o$bob5o3bo12bobobo11bo2b3o7b2o2b2o
2b2o7b3o$ob6obo15bobo13b3o$6o49b6o$b5obo48b4o$ob3o$ob3obo$bo3bo63b4o$
2b3o64bo2b2o$68b2o3bo$23b18o27bo4bo$22bo3bo10bo3bo6b5o16bob3o$22bob16o
bo6bo3bo17b2o$22bob5o6b5obo6bo3bo$22bob16obo6bo3bo$8b4o10bob4o8b4obo6b
5o$7bo4b2o9bo5b6o5bo21b4o$6bob4o12b3o10b3o21bo4bo$6bob5obo47b4obo$8b5o
bo44bo2b4obo$7bob4o45bob6obo$10b3o44bob6obo$10b3o44bob4o2bo$10b3o27b4o
b4o8bob4o$7bob4o26bo9bo8bo4bo$8b5obo23bob8obo9b4o$6bob5obo23bob8obo$6b
ob4o26bob8obo$7bo4b2o24bob7obo$8b4o11b3o13bo2bo5bo$22bo3bo13b7o$21bob
3obo$21bob3obo$23b4o$23b4obo$21bob4o$21bob5o2bo$22bob5o3b2o$25b7o2bo$
24bob8obo$25bob7obo$28b6obo$27bo6bo$28b2o2b2o!

In addition, here are some more 2c/3o partials in Minibugs from cfind.

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,B7-8,NM
5b4o2b4o$4b2o8b2o$3b2o3b4o3b2o$3b2o3bo2bo3b2o$3b3o2bo2bo2b3o$3b2obo2b2o
2bob2o2$9b2o$6bo6bo$4b2o2bo2bo2b2o$3b3o2bo2bo2b3o$8b4o$3bo4b4o4bo$2b2o
3b6o3b2o$3b2o2b6o2b2o$6b2o4b2o2$6b2o4b2o$2b3o10b3o$b2o14b2o$2o3bobo4bo
bo3b2o$2o3b3ob2ob3o3b2o$2b4obo4bob4o!

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,B7-8,NM
3bo11bo$2b3o9b3o$b2ob2o7b2ob2o$2o3b3o3b3o3b2o$bo15bo$6b2o3b2o$3b2o2b5o2b
2o$4bo3bobo3bo$4b2ob2ob2ob2o2$3b2o9b2o$3b3ob2ob2ob3o$b3ob4ob4ob3o$obob
o2bobobo2bobobo$3o4bobobo4b3o$4bo4bo4bo$4bo2bo3bo2bo$4bo2b2ob2o2bo$3o2b
o7bo2b3o$b2o4bo3bo4b2o$6b2o3b2o$2bob11obo!

Code: Select all

x = 0, y = 0, rule = R2,C2,S6-9,B7-8,NM
9b3o$8b2ob2o$7b2o3b2o$8bo3bo$6b3o3b3o$3b3o2b5o2b3o$2b3o2bo5bo2b3o$b2o2b
2o7b2o2b2o$6bo7bo$bo4b2o5b2o4bo$2o2b2o9b2o2b2o$o4b5ob5o4bo$b8o3b8o$7b2o
3b2o$2b2o13b2o$5b3o5b3o$7b7o2$2b3o3b5o3b3o$3obo2b7o2bob3o$b2o6b3o6b2o$
2obo13bob2o$2bo2bo9bo2bo$2bo2b2o2b3o2b2o2bo$2ob2o11b2ob2o$3ob2obob3obo
b2ob3o!

EDIT: Forgot to mention this c/2o wickstrecher that was found because cfind's tranposition table broke.

Code: Select all

x = 105, y = 14, rule = R2,C2,S6-9,14-20,B7-8,15-24
13b79o$2b3o7b2o77b2o7b3o$2o3b3o4bob77obo4b3o3b2o$2obo4bo3b2o77b2o3bo4b
ob2o$b2o3bo2bo3b79o3bo2bo3b2o$2bo3b2o89b2o3bo$6b2o89b2o$6b2o89b2o$2bo
3b2o89b2o3bo$b2o3bo2bo3b79o3bo2bo3b2o$2obo4bo3b2o77b2o3bo4bob2o$2o3b3o
4bob77obo4b3o3b2o$2b3o7b2o77b2o7b3o$13b79o!

[hotcrystal0]

new r2 neighborhood

heatmap! :D

01210
12321
23032
12321
01210

0121012321230321232101210

b6,s4567heatmap seems to be stable

This rule has a common P31, a less common P16, and a c spaceship:

Code: Select all

x = 33, y = 22, rule = R2,C2,S3,B5,12,NW0121012321230321232101210
o2$bo$bo2$o11$28bo3bo$28bo3bo$2o2$o27bo3bo$bo26bo3bo!

[H. H. P. M. P. Cole]

I am trying to explore this weighted neighbourhood:

Code: Select all

00 00 00 01 00 00 00
00 00 00 05 00 00 00
00 00 00 19 00 00 00
01 05 19 00 19 05 01
00 00 00 19 00 00 00
00 00 00 05 00 00 00
00 00 00 01 00 00 00

My wish was to explore INT R3 Cross, but since LifeViewer does not support CAViewer or Durnak-Cole, this is the closest I can go.

Here are all the objects I have found in this rulespace where every phase of the object fits within a 4x1 box.

Code: Select all

index,rle,xdisplacement,period,rule
1,o!,0,1,"R3,C2,S0,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
2,2o!,0,1,"R3,C2,S25,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
3,2o!,0,2,"R3,C2,S,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
4,2o!,0,2,"R3,C2,S25,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
5,2o!,0,3,"R3,C2,S25,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
6,2o!,0,3,"R3,C2,S1,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
7,obo!,0,1,"R3,C2,S5,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
8,obo!,0,2,"R3,C2,S5,30,B50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
9,3o!,0,1,"R3,C2,S30,50,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
8,3o!,0,2,"R3,C2,S5,30,B50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
10,o2bo!,0,1,"R3,C2,S1,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
3,o2bo!,0,2,"R3,C2,S,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
11,o2bo!,0,2,"R3,C2,S1,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
5,o2bo!,0,3,"R3,C2,S25,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
6,o2bo!,0,3,"R3,C2,S1,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
12,ob2o!,0,1,"R3,C2,S6,26,30,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
13,ob2o!,-1,1,"R3,C2,S30,B26,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
14,ob2o!,1,1,"R3,C2,S26,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
15,ob2o!,2,1,"R3,C2,S30,B6,30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
16,ob2o!,0,2,"R3,C2,S6,30,B26,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
17,ob2o!,0,2,"R3,C2,S6,26,B55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
18,ob2o!,0,2,"R3,C2,S30,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
19,ob2o!,0,2,"R3,C2,S26,30,B6,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
20,4o!,0,1,"R3,C2,S31,55,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
4,4o!,0,2,"R3,C2,S25,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
11,4o!,0,2,"R3,C2,S1,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
5,4o!,0,3,"R3,C2,S25,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"
6,4o!,0,3,"R3,C2,S1,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000"

The index number is for itemizing the objects.

As one can see, ob2o! has the largest number of mod-1 objects, with a whopping 8 of them.

Here are all 20 objects, in RLE form:
1.

Code: Select all

x = 1, y = 1, rule = R3,C2,S0,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o!

2.

Code: Select all

x = 2, y = 1, rule = R3,C2,S25,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

3.

Code: Select all

x = 2, y = 1, rule = R3,C2,S,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

4.

Code: Select all

x = 2, y = 1, rule = R3,C2,S25,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

5.

Code: Select all

x = 2, y = 1, rule = R3,C2,S25,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

6.

Code: Select all

x = 2, y = 1, rule = R3,C2,S1,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2o!

7.

Code: Select all

x = 3, y = 1, rule = R3,C2,S5,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obo!

8.

Code: Select all

x = 3, y = 1, rule = R3,C2,S5,30,B50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
obo!

9.

Code: Select all

x = 3, y = 1, rule = R3,C2,S30,50,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
3o!

10.

Code: Select all

x = 4, y = 1, rule = R3,C2,S1,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo!

11.

Code: Select all

x = 4, y = 1, rule = R3,C2,S1,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o2bo!

12.

Code: Select all

x = 4, y = 1, rule = R3,C2,S6,26,30,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

13.

Code: Select all

x = 4, y = 1, rule = R3,C2,S30,B26,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

14.

Code: Select all

x = 4, y = 1, rule = R3,C2,S26,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

15.

Code: Select all

x = 4, y = 1, rule = R3,C2,S30,B6,30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

16.

Code: Select all

x = 4, y = 1, rule = R3,C2,S6,30,B26,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

17.

Code: Select all

x = 4, y = 1, rule = R3,C2,S6,26,B55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

18.

Code: Select all

x = 4, y = 1, rule = R3,C2,S30,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

19.

Code: Select all

x = 4, y = 1, rule = R3,C2,S26,30,B6,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
ob2o!

20.

Code: Select all

x = 4, y = 1, rule = R3,C2,S31,55,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
4o!

Of these 20 rules, rules 3, 4, 5, 6, 11, 13, 14, 15, 16, 18, and 19 can expand their bounding box. ob2o! in rules 13, 14, and 15 is a ship. Rule 15 is explosive.

Other ships:
Rule 4 (the first ship works in rule 5):

Code: Select all

x = 21, y = 4, rule = R3,C2,S25,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2bo15bo$2bobo11b2o$o16bob2o$18bo!

Rule 5 (this ship works in rule 4):

Code: Select all

x = 5, y = 3, rule = R3,C2,S25,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2bo$2bobo$o!

Rule 6 (this ship works in rule 11):

Code: Select all

x = 4, y = 2, rule = R3,C2,S1,55,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bo$o2bo!

Rule 11 (this ship works in rule 6):

Code: Select all

x = 4, y = 2, rule = R3,C2,S1,31,B30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
bo$o2bo!

Rule 18:

Code: Select all

x = 4, y = 3, rule = R3,C2,S30,B30,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
2b2o$b2o$o!

[H. H. P. M. P. Cole]

I am trying to explore this weighted neighbourhood:

Code: Select all

00 00 00 01 00 00 00
00 00 00 05 00 00 00
00 00 00 19 00 00 00
01 05 19 00 19 05 01
00 00 00 19 00 00 00
00 00 00 05 00 00 00
00 00 00 01 00 00 00

This rule has c/1os, c/2os, and a very impressive slope-9 rake which can be made into a cordership:

Code: Select all

x = 166, y = 92, rule = R3,C2,S1,5,25,30,B10,26,50,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
162bo$162bo$162bo$165bo$85bo6bo11bo8bo2bo10bo7bo11bo11bo$49bob2o$44bo
2bo37bo6bo11bo8bo2bo10bo7bo2bo5bo2bo2bo8bo$47bo37bo6bo11bo9bo$47b2o46b
o5bo5bo$47bo79bo7bo11bo11bo$24bob2o$19bo2bo24bo$22bo$22b2o$22bo21b2o$
53bo31bo6bo11bo$22bo30bo$85bo6bo11bo$85bo6bo11bo$5bob2o10b2o74bo5bo5b
o$o2bo24bo$3bo24bo$3b2o80bo6bo11bo$3bo2$3bo$47bo$47bo$2o$9bo$9bo$22bo
44bo$22bo44bo2$65bobo$65bo$42bo$42bo2$40bobo$3bo36bo$3bo3$49bo$49bo4$
49b3o3bo5$24b3o3bo$49b3o3bo3$5bo$5bo$24b3o3bo7$27b3o3bo2$12bo$11bo3$13b
o13b3o3bo2$9bo3bo$15bo2$9bobo$9bo9$14bo2b2o3$19b2o!

cata

EDIT: 2-engine (2,18)c/48 ship, 1 engine smaller than the 3-engine solution above

Code: Select all

x = 47, y = 40, rule = R3,C2,S1,5,25,30,B10,26,50,55,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
26b2obo2$29b2o10$44bo2$10b2o$o$o43bo$44bo$o38b2o3bo$3bo$b4obo14b2o2$9b
o$bo7bo7$34b2o2$24bo$23bo$24b2o3bo$24b2o3bo$25b2o18b2o$31bo$33bo$25bo
3bo2bo!

[iddi01]

I surprisingly found a highly Life-like cross-neighborhood rule: R2,C0,S3-4,6,B0-7,N+

Initially, it would seem like Factorio, due to these things:

Code: Select all

x = 32, y = 19, rule = R2,C0,S3-4,6,B0-7,N+
3$14bo6bo2bo2$15bo6bo5$2bo2b2o!

But then, it would appear to be closer to CGoL, for being quite chaotic, having not-so-sparse ash, and small sequences that last quite a while:

Code: Select all

x = 28, y = 21, rule = R2,C0,S3-4,6,B0-7,N+
6$3bo$3bo$21bobo2$3bo19bo2$4bo!

However, this rule has some unique features that neither CGoL nor Factorio could ever have imagined:

First, since this rule is strobing, it's self-complementary in some sense, and large solid blocks last quite a while:

Code: Select all

x = 118, y = 50, rule = R2,C0,S3-4,6,B0-7,N+:T118,50
47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$
47b71o$47b71o$47b71o$5bo41b71o$5bo41b71o$5bo41b71o$47b71o$5bo41b71o$
47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$
47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$
47b7ob2o2b59o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$47b71o$
47b71o$47b71o$47b71o!

This rule has many types of natural puffers/rakes, lowest period 22, highest period 1584:

Code: Select all

x = 173, y = 125, rule = R2,C0,S3-4,6,B0-7,N+
14$12bo$12bo$12bo2$12bo$14bo$12bo5$13bobo$13bobobo$12b4obo$17bo$13b5o$
15b2o11$14b4o11$15b2o11$14b4o2$28bo$28bo$28bo2$28bo$26bo3bo$30b2o2$30b
2o$15b2o2$105bo29bo$105bo29bo26bo$135bo26bo$31bo$105bo29bo$30bo76bo29b
o24bo$31bo128bo3bo$135bo29bo$137bo$14b4o6bo3bo108bo26bo$24bobob3o104b
3o25bo2bo$24bobobobobo104bo27bobo$27b7o101bobo$24bo4bobo105bo$29bo2bo
104bo$135bo2$137bo!

There are also many distinct (periods of) natural spaceships, with all of them being "photons" except for a 2c/48 slow ship:

Code: Select all

x = 169, y = 62, rule = R2,C0,S3-4,6,B0-7,N+
7$58bo15bo37bo$58bo15bo37bo53bo$58bo15bo37bo53bo$41bo51bo70bobo$41bo
16bo15bo18bo18bo53bo$10bo7bo11bo10bo16b2o14bobo35bobo50b2o$10bo7bo9bob
obo30bo100bo$18bo9b5o8bo16b2o3bo10bobo16bo18bobo$30bo11bo20bo27bo3bo
23bo$10bo7bo9bobobo8b2o76bo$16bo3bo20b2o20bo55bo$40b4o31b2o14bo3bo$40b
ob2o32b2o41bo$75bobo15$133b2o3bobobobobo$133bo5bo5b3o$134bobo2b3o2b2ob
o$134bobo5b2obo2bo$133bob2ob5obo2bo$135b3o4b5o$135b2obo3b2o2bo$133bob
3o5b2obobo$135b8o2b2obo$141bob3ob2o$133b2o3b3obobob3o$134b3ob2ob4o3bo$
134b4o2b6obo$133bo2b2ob2o4bo2bo$134b3o3bobo2b4o$135b3ob7ob2o!

(That soup generates a corderization of the common puffer.)
All the common or notable natural oscillators (including an extensible margolus one):

Code: Select all

x = 269, y = 35, rule = R2,C0,S3-4,6,B0-7,N+
10$247bo2$234bobo12bo$185bob2obo43bo$187b2o27bob2o12bob3o14bo$186b4o$
162bo54bo4bo7b3obo18bo$147bo39b2o10b2o6b2o23bo$95bo2bo61bo38b2o2b2o2b
2o11b2obo6bobo22bo$99bo7bo2b2o8bo3b4o3bo13bob2o13bo$75b2o7b2o7bo12bobo
11bo10bo11bob3o109bo$110bobo7bo10bo14b3obo13bo$11b4o5bobo6bo24bo5bo6b
2o6b2o7b3o12bo7b2o2bo8bo10bo13b2obo110bo$2b2o7b4o5b3o5bo8bo8b2o5bo4bo
8b2o24bo72bo$11b4o5b3o10bo33bo7b2o8b2o7bo2bo48bo114bo$11b4o5bobo16bo5b
3o6bo5bo$32bo!
#C [[ GPS 8 AUTOSTART ]]

This rule also have some unique and interesting reactions.

Pushing reaction, eaters, and spaceship technology:

Code: Select all

x = 154, y = 95, rule = R2,C0,S3-4,6,B0-7,N+
9$48bo3$48bo$48bo9$100bo2$100bo$100bo2$36bo2b2o7bob2obo7b2o5b2o5b2o7b
2o7b2o5bo$152b2o3$133bo2b2o5$152b2o3$94bo$21bo2b2o27bo2b2o17b2o17bo4$
31bo$31bo3$31bo21bo2b2o18b2o2bo$26bo$26bo3$26bo11$71bo$71bo3$71bo3$8bo
bo$16b2o$10bo12$70bo$70bo3$70bo!

One-time reflectors:

Code: Select all

x = 59, y = 45, rule = R2,C0,S3-4,6,B0-7,N+
18$43bo4b2o2bo$42bo9$16bo$16bo2$41bo$48b2o2bo$39bo2bo$12bob3o!

The best methuselah so far (3,000 generations):

Code: Select all

x = 15, y = 17, rule = R2,C0,S3-4,6,B0-7,N+
2$5bobo$5bo$3bob3o2$b3obo$3bo$bobo$12bobo$12bo$10bob3o2$8b3obo$10bo$8b
obo!

Due to lack of catalysts, this rule is currently lacking two important things, guns and reflectors. With the high potential of this rule however, i think both won't be hard to discover.
This rule (i called it CrossLife) is now officially my favorite LtL rule.

If you wish to apgsearch this rule, use this ruletable:

Code: Select all

@RULE CrossLife

@COLORS
0 0 0 0
1 255 255 255

# This ruletable is automatically generated by CAViewer
# Note that is ruletable may not work properly in Golly as it is meant to be run by lifelib.
# If this ruletable operates in with a range 1 neighbourhood, switch neighbourhood:... with neighbourhood:Moore or any other appropriate neighbourhood to run it in Golly

@TABLE
n_states:3
neighborhood:[(0, 0), (-2, 0), (-1, 0), (0, -2), (0, -1), (0, 1), (0, 2), (1, 0), (2, 0), (0, 0)]
symmetries:permute

var _any.0.0 = {0, 1}
var _any.1.0 = _any.0.0
var _any.2.0 = _any.0.0
var _any.3.0 = _any.0.0
var _any.4.0 = _any.0.0
var _any.5.0 = _any.0.0
var _any.6.0 = _any.0.0
var _any.7.0 = _any.0.0

0, 0, 0, 0, 0, 0, 0, 0, 0, 0
0, 1, 0, 0, 0, 0, 0, 0, 0, 0
0, 1, 1, 0, 0, 0, 0, 0, 0, 0
0, 1, 1, 1, 0, 0, 0, 0, 0, 0
0, 1, 1, 1, 1, 0, 0, 0, 0, 0
0, 1, 1, 1, 1, 1, 0, 0, 0, 0
0, 1, 1, 1, 1, 1, 1, 0, 0, 0
0, 1, 1, 1, 1, 1, 1, 1, 0, 0
1, 1, 1, 1, 0, 0, 0, 0, 0, 0
1, 1, 1, 1, 1, 0, 0, 0, 0, 0
1, 1, 1, 1, 1, 1, 1, 0, 0, 0
1, _any.0.0, _any.1.0, _any.2.0, _any.3.0, _any.4.0, _any.5.0, _any.6.0, _any.7.0, 2
0, _any.0.0, _any.1.0, _any.2.0, _any.3.0, _any.4.0, _any.5.0, _any.6.0, _any.7.0, 2
1, _any.0.0, _any.1.0, _any.2.0, _any.3.0, _any.4.0, _any.5.0, _any.6.0, _any.7.0, 0

var _any.0.1 = {0, 2}
var _any.1.1 = _any.0.1
var _any.2.1 = _any.0.1
var _any.3.1 = _any.0.1
var _any.4.1 = _any.0.1
var _any.5.1 = _any.0.1
var _any.6.1 = _any.0.1
var _any.7.1 = _any.0.1

2, 2, 2, 2, 2, 2, 2, 2, 2, 1
2, 0, 2, 2, 2, 2, 2, 2, 2, 1
2, 0, 0, 2, 2, 2, 2, 2, 2, 1
2, 0, 0, 0, 2, 2, 2, 2, 2, 1
2, 0, 0, 0, 0, 2, 2, 2, 2, 1
2, 0, 0, 0, 0, 0, 2, 2, 2, 1
2, 0, 0, 0, 0, 0, 0, 2, 2, 1
2, 0, 0, 0, 0, 0, 0, 0, 2, 1
0, 0, 0, 0, 2, 2, 2, 2, 2, 1
0, 0, 0, 0, 0, 2, 2, 2, 2, 1
0, 0, 0, 0, 0, 0, 0, 2, 2, 1
0, _any.0.1, _any.1.1, _any.2.1, _any.3.1, _any.4.1, _any.5.1, _any.6.1, _any.7.1, 0
2, _any.0.1, _any.1.1, _any.2.1, _any.3.1, _any.4.1, _any.5.1, _any.6.1, _any.7.1, 0
0, _any.0.1, _any.1.1, _any.2.1, _any.3.1, _any.4.1, _any.5.1, _any.6.1, _any.7.1, 1

Off-topic:
Try to guess (without quoting this post) if i used code tags or pattern tags in this post. (bet you can't (: )

[confocaloid]

.

[b-engine]

A way to simulate an INT rule using NW:

Code: Select all

x = 16, y = 18, rule = R1,C2,S1,5,B2,10,NW010501050005010501
6bobo$3o5bo5b2o3$7bo$8bo$7bo$2o$2bo$2bo11bo$15bo$6bo7bo$7bo$6bo2$5bo8b
o$6bo8bo$5bo8bo!

[b-engine]

(Revival)
I'm finding a range-2 equivalent of W110, end up I stumbled over this "class 3.5" rule:

Code: Select all

x=0,y=0,rule = R2,C2,S,B4-6,7-12,NW0000011722000000000000000
2o!
[[ THEME OCCUPIED ]]

EDIT:
Add B3 makes it class 4:

Code: Select all

x = 7, y = 1, rule = R2,C2,S,B3-12,NW0000011722000000000000000
2ob2obo!

Anyone like Cook want to prove the rule Turing complete?

[lemon41625]

I surprisingly found a highly Life-like cross-neighborhood rule: R2,C0,S3-4,6,B0-7,N+

c/4o

Code: Select all

x = 0, y = 0, rule = R2,C2,S3-4,6,B0-7,N+
o5bo$o2bo2bo$ob3obo$bobobo$7o$7o$b2ob2o$2bobo!

[b-engine]

c/4o

Code: Select all

x = 0, y = 0, rule = R2,C2,S3-4,6,B0-7,N+
o5bo$o2bo2bo$ob3obo$bobobo$7o$7o$b2ob2o$2bobo!

Catchover "photon" turning reaction:

Code: Select all

x = 10, y = 55, rule = R2,C2,S3-4,6,B0-7,N+
3bo5bo$3bo2bo2bo$3bob3obo$4bobobo$3b7o$3b7o$4b2ob2o$5bobo43$o$o3$o! 

Your large spaceship actually travels at c/2, as the rule is strobing and everything only propagate every 2 generatons.

[H. H. P. M. P. Cole]

A rule (generated by a beta version of a rule generator that I am planning to release soon) discovered accidentally that has 5 unreduced ship speeds and 6 total:

The speeds are c/1o, 3c/5o, 3c/7o, 3c/9o, c/2d, and 3c/6d.

Code: Select all

x = 57, y = 21, rule = R3,C2,S9,13,23,42,62,64,65,71,76,109,123,B6,9,21,23,26,37,51,86,90,96,119,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
48bo$47bo$o7bo10bo11bo7bo6bobo$22bobo7bo5bo8bo$o7bo10bo26bo$22bobo20b
o$o7bo16bo5bo7bo$11bo$21bo2$o30bo$38bo$39bo9bo$38bo9b2o$31bo7bo8bo$52b
o3bo$45bo$50bo$39bo13bo$38bo$53bo!

cata

Minrule of all the ships:

Code: Select all

x = 57, y = 21, rule = R3,C2,S,B6,26,51,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
48bo$47bo$o7bo10bo11bo7bo6bobo$22bobo7bo5bo8bo$o7bo10bo26bo$22bobo20b
o$o7bo16bo5bo7bo$11bo$21bo2$o30bo$38bo$39bo9bo$38bo9b2o$31bo7bo8bo$52b
o3bo$45bo$50bo$39bo13bo$38bo$53bo!

===========================================================

This rule has lower-density soups that are long-living as although the rule B26,50 on its own is explosive (in lower densities), the S15 condition tames the explosions, though only ever so slightly, making this rule apgsearchable.

Code: Select all

x = 61, y = 30, rule = R3,C2,S15,B26,50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o14bo17bo10bo12bo2$o14bo17bo10bo12bo$18bo11bo5bo10bo6bo5bo2$44bo12bo$
o5$o14bo17bo10bo12bo2$o14bo17bo10bo12bo$18bo28bo6bo5bo$19bobo$20bobo$
o32bo10bo12bo$bobo28bobo8bobo10bobo$2bobo6$o$3bo$4bo2$4bo!

Code: Select all

x = 64, y = 64, rule = R3,C2,S,B26,50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
!
[[ RANDOMIZE RANDFILL 25 ]]

Code: Select all

x = 64, y = 64, rule = R3,C2,S15,B26,50,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
!
[[ RANDOMIZE RANDFILL 25 ]]

cata (for R3,C2,S15,B26,30,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000)

Crosspost:

[...]
37+3/4. Why is there no extension of the Weighted format to add larger weights than +127? One can just add more digits per weight of cell. (There might be some difficulty I had probably overlooked.)
[...]

Indeed it would be relatively straightforward to extend the weighted neighbourhoods syntax to allow 2^n digits per weight of cell (n = 0, 1, 2, 3, ...)
As far as I can see, the big difficulty would be that the number of distinguishable conditions would become very high, very quickly. A consequence would be that many rulestrings would get extremely long.

For example, with four hexadecimal digits per cell weight, it would be possible to have hexadecimal weights 0001, 0002, 0004, 0008, 0010, 0020, 0040, 0080, 0100, 0200, 0400, 0800, assigned to 12 different neighbours (each weight assigned to exactly one neighbour cell). Then it would be possible to refer to every possible configuration in those 12 cells, distinguishing it from all other possible configurations; there would be 2^12 = 4096 possibilities for the current states of neighbours of the cell, multiplied by 2 possibilities for the current state of the cell itself. That would lead to a rulespace with 2^13 = 8192 fully-specified living conditions, each of which would be individually toggleable.
Now imagine writing a rulestring with multiple ranges of birth conditions and multiple ranges of survival conditions, something that would look like this:

Code: Select all

R2,C0,S1-2,4-5,7-8,10-12,14-16,18-20,(trimmed for brevity),4080-4085,4090-4095,B1-2,4-5,7-8,10-12,14-16,18-20,(trimmed for brevity),4080-4085,4090-4095,NW0000000000010000000000000002000400080000001000200000004000800000010002000400000000000000080000000000

EDIT: The B6,31/S30 space houses a small replicator, and so far I cannot find a rule which destroys the replicator while making the rule nonexplosive:

Code: Select all

x = 3, y = 1, rule = R3,C2,S30,B6,31,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
3o!

[confocaloid]

Honeyfarm neighbourhood:

Code: Select all

x = 16, y = 29, rule = R6,C0,S3,B3,N@0200280140040000301A42580C0000200280140040
5bo2bo2bo2bo$o3$o$15bo2$o$15bo2$o$15bo3$15bo$bo2bo2bo2bo11$4bo$5b2o$4bo!
#C [[ ZOOM 4 THEME MCell ]]

canvas.png (69.68 KiB) Viewed 4104 times

[confocaloid]

What are known explored CA with negatively-weighted neighbours?
The NW... neighbourhood format allows to specify negative weights ("[...] The hexadecimal representation has the MSB as the sign bit [...]"). However, there seems to be little evidence of people actually using that feature.

[H. H. P. M. P. Cole]

A 1D object that stays 1D in the NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000-space exists in a rulespace that is more than or equal to 2^196 rules large, as there are, maximally 54 conditions:

Code: Select all

B0-2,5-7,10-12,25-27,30-32,35-37,50-52,55-57,60-62
S0-2,5-7,10-12,25-27,30-32,35-37,50-52,55-57,60-62

that must remain untoggleable. Here is a 1D quasi-SL where all 54 of the conditions stated above must remain untoggleable for it to remain a SL:

Code: Select all

x = 121, y = 1, rule = R3,C2,S0-2,5-7,10-12,25-27,30-32,35-37,50-52,55-57,60-62,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o5b2o4bobo4b3o3bo2bo3bob2o3b2obo3b4o2bo2b2o2bobobo2bob3o2b2ob2o2b3obo
2b5obobob2obob4ob2ob3ob7o!

This is generated by this website, and I am very sure it can be made smaller. Here is an obvious 3-cell reduction:

Code: Select all

x = 114, y = 1, rule = R3,C2,S0-2,5-7,10-12,25-27,30-32,35-37,50-52,55-57,60-62,B,NW00000001000000000000050000000000001900000001051900190501000000190000000000000500000000000001000000
o5b2o4bobo4b3o3bo2bo3bob2o3b4o2bo2b2o2bobobo2bob3o2b2ob2o2b3obo2b5obo
bob2obob4ob2ob3ob7o!

Are there any other (semi-)obvious reductions I have missed?

[CARuler]

Rake

Code: Select all

x = 37, y = 87, rule = R3,C2,S6,16,B45,145,165,NW000000010000000000000f0000000000002d00000001052d002d05010000002d0000000000000f00000000000001000000
28$16bo2$14bo$15bobobo7bobobo$32bo$17bo$22bobobobobo$27bo2$19bobo3bob
o$16bobo3bobo2$14bo7bobo$15bobobobo2$17bobobo!

[ThrashBin]

This neighbourhood:

Code: Select all

x = 5, y = 5, rule = B/S012345678History
3.A$4A$.ABA$.4A$.A!
#C state 2 is the center cell

Rule:

Code: Select all

x = 64, y = 64, rule = R2,C2,S0-12,B5,NW0001011110010100111101000
!

[[ RANDOMIZE ]]

Example rule also has an knight wickstretcher:

Code: Select all

x = 18, y = 18, rule = R2,C2,S0-12,B5,NW0001011110010100111101000
7b11o$6b2ob6ob2o$6b11o$5b2ob6ob2o$5b11o$4b2ob6ob2o$4b11o$3b2ob6ob2o$3b
11o$2b2ob6ob2o$2b11o$b2ob6ob2o$b11o$2ob6ob2o$b10o$2b6ob2o$3b7o$4b3ob2o
!

Some methuselahs:

Code: Select all

x = 107, y = 7, rule = R2,C2,S0-12,B5,NW0001011110010100111101000
2o98bob2ob2o$o2bo96bob2o$3b2o97b2ob2o$2ob4o93b2o4bo$2bobobo94bob2obo$
bo2b3o93bo2bobo$3obobo94b2ob3o!

For those counting in dozenal, i have reached my 10th post! Yay!