Margolus-neighborhood rules

muzik · Post by **muzik** » July 4th, 2024, 10:55 am

x = 32, y = 352, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o
$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$32o$
32o$32o!

That object that gets created on the right just makes me want an increased Identify limit that much more. It must be periodic. What period is it?

Code: Select all

x = 23, y = 16, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
14b2o$14bo$10b2obob2o$9b4obob3o$6b2o2b4o3b3o$5bob3ob4o2bob2o$2b4ob5ob
3o3bobo$b5obobob3ob2o2bo2bo$b5obobob3ob2o2bo2bo$2b4ob5ob3o3bobo$5bob3o
b4o2bob2o$6b2o2b4o3b3o$9b4obob3o$10b2obob2o$14bo$14b2o!

ababa11e · Post by **ababa11e** » August 6th, 2024, 3:20 am

This rule forms moving 'waves' moving at c/3 diagonal, which after a long time, degrade into c/3d spaceships.
Example soup:

Code: Select all

x = 64, y = 64, rule = M0,4,0,10,8,7,14,15,6,7,2,15,10,3,12,7
2o2b2ob3ob2o2b3o2bobob3ob2o2bob4ob2obo3b2o2b2ob4o3bo2bo$7o2b3ob4obob2o
bob2ob2o3b2o2bo2b2o3bo3b2o2b2o2b3o2bo$bo2b3ob2ob3o4bob2o4b2o4b3o2bob5o
4b2ob9o2bo$2b2ob2o2bo2bobobob3ob5o2b3o2bobob2o2b4obo4b3o2bo3b2o$o6b2o
2b3o2b3o4bobo3b3o2b2o2bob4o2bo2b3o2bo3bo3b2o$8bobob3o2bob5obo3b3o3bob
2ob3o3bo2bob2ob4o2bob2o$3o2bo2bo2b2o4bo10b2ob3obo2bo6b5obo4b3obo$3bob
4ob7o7bobobo3b3ob2ob2obo2b2ob2ob2o2b3obob2o$2bo3b4o2bobobo3b8obo2bo2b
o2bobo3bo2bo2b3ob2ob4obo$6ob4o2bob2ob2obo2b3ob3o4b2o2bo2b4obob3ob9obo
$11ob2o2b4obo2b2o2b2obo4b2obob2o6b7o3bob3o$2o5b2ob4o2b2obo4b6ob2o2bo3b
o2b7o8bob5o$2b4obobobob5o5bob4o4bo2bo2bob3ob7ob4o$2b3o2b2ob2o3b2ob2o3b
3ob10o3bob3o3bo3b7o2bobo$b2ob2ob3o4bob2o2bo2bo2bo6b2ob3o3b7ob2o5bo5bo
$ob3ob4o3b2o3b2o3b3ob5o3bobo6bo6bo2bobo2b4o$5b2o5bo5b2o3bob2ob2ob2o3b
2o2bo2b2o4bo3b2ob2o3b3o$bo4bobob3o6b11o3bob2o4bo2b2o3b3o3bo2bob3o$2o2b
o2b4o3b5o2b2ob2obo3bo4bob4obob2o3bob2ob3o$b2o2b2obob2o3bo2b3obo3b4ob4o
2bobo3bobo2b2o5b4obo$2o3b2ob2ob2o2bo5bo3bo3b5o5bob2obo4b2o2b2obo6bo$o
b3obobo2b2ob5obo2b4ob2o4bob3obo5b2obo3b2ob3o2bo$3b2ob3o2bobo2bob2o2bo
b2ob2o4bo4bob2o4b9obob2ob3o$o2b5obobo2b2o2b2ob4o2b4obo2b3obo2b4obo2bo
b3o3bobo$bobo2b5ob4o6bobo2b4ob3o3bob3o4b2o2bobob3ob5o$5bobo2bo2bob2ob
2obo2bobob3obo8bo2bob3ob2obobo3b2obo$b3o2b2o2b2obo3bobob2ob2o2bob2o9b
4o2bo2b5o2bo3bo$2bobo3b5ob4o3b2o6b2o2b2o4bob3o2b5ob2obobo3b3o$o2b3o2b
o3bo2b2ob5ob2ob4o3b3o3bo6b4o2b4o3b2obo$bo2bob2obob2o2b3ob2o2b2o2b4ob2o
b2o2b4o4bob2o2bobob4o2bo$2b2obo2bob3o4b2obobob2o6b2ob2obo5bo6b2o3bo2b
obobo$2bobobo5b2o2bo2b3o2bo2bo2b3o3bobobob3o2b2obobo7b2o$2bobob3obob2o
bob5ob3o5bo6b2o5bob2o2bo4bobo4bo$b3o7b5ob5o2bo3bobobo3bo2bobo4bobo2b2o
b3ob6o$bo2bo3bo2b3o5bob2o2b5o2bo2b2obobob5o2b2ob2obo2bo$b2o2b2ob2obob
o3bob2ob3o2b2o2bobo2b2o3bo2bobo2bo2bo3b3o3b2o$obo5bob4o2b2o7bo4b2obob
3o5bobob3ob7ob2o2bo$obobob4obob2obo2b2ob3o4b2ob3ob4ob3ob2o3b3o2bo7bo$
ob2ob3o2bo8bob6o4bo5b2o2b3o4b2obo2bo3b3o2bo$ob2o2bo3bo4b2ob3o2bo2bo3b
2o2bob5o3bo4bo4b3ob2ob2o$2obob4o3b2o2b2o4b2obob2o2bob2obo2b2obobo2bo3b
obo2bo2b3o$3b2o3b3o3bo2b2ob3o2bo2bo8b4o2b5o2b2obobobobob3o$2ob3ob2o4b
o3b2ob5obob2ob3obo4b2ob4ob2o2bo2bob3ob3o$2b3o3b3obobob2o2b2obobo2bo3b
ob2o2b2o2bo4bo2bo2b2o4bo$2bo5bo3b3o2b2obobobobo2bo4bo2bo5b2o6bobobo2b
o3bo$bobo2bob5o3b5o2b2obo2b3obo6b5obob3ob2o6bob2o$ob2o5b2ob2ob2o2b2o2b
2o2b4o8bo3bob3o3bob4ob2o2b2o$o2b2o5b2ob2ob2o3b3obob3obo3b3o2bobo2b2ob
2o2bo3b5o2bo$ob4o2b3o3bo5b2o5bo5b4o2b6obo2bobob5ob3o$bo3bobobob4obob3o
b2o3b3o2b2o3b2ob2obobo2b2o5bobob2o2bo$b2o2bo3b3o2bo2b3o2bo2bo2bob3obo
3b4ob2o4b4o2b2o2b2o2bo$b4ob2obo4b2o3bobobo2bobo3bobo3b3o4bo11b5o$bob2o
bo3b2o2bo3bob2obo4bobo2bo2bo2b2o2bo2bo2bo7b2obob2o$b5o2b2o2bobo2b3o2b
ob2ob2o4bobob2o7b2ob2o2b5o2b4o$4bo3bo2bo6bob6ob2o4b3obo6b2o2bo6bobob3o
bo$o4bobo2bob3o3bo2b2o2bob3obobo3b2obob2ob2ob4obobo7bo$7o2bob2o2bo2bo
2b5ob2o2b4ob4ob2ob3ob2ob3obo5bo$2bo3b4o2b2o2bo7b2ob3obo2bob2o4bob2obo
4bo2b2obobo$obo2bo2b3obobo5bo3bobobobob3o2bobo3b2o2b2obo5b2ob3o$b3obo
b2ob2o2bobobo3bo2b2o3b4ob2ob6obo2b2o4b3o3bo$8bo2b3o2b3obo2bob2o3bo2bo
2b2ob2obo2b2o2b4obo2bob2ob2o$4obob2o2bo2b2obobo2b2obo2b2o2bobob2obobo
b8o3b5ob4o$2obo8b4ob2o2bobo5bobob3o3bob2o3b2ob4o2bo2b2o2bo$b2ob4o2bob
o2bo3bo2b2ob3o3bo6b2ob2o2bo3b2ob3o3bob2o!

CARuler · Post by **CARuler** » August 14th, 2024, 11:57 am

a LOT of BCA rules
M0,2,8,12,1,10,6,13,4,9,5,7,3,14,11,15|BBM
M0,8,4,15,2,15,0,6,1,0,15,9,15,9,6,15
M0,8,4,15,2,15,0,6,1,0,15,9,15,9,6,15|Sand
M0,8,4,15,2,15,0,6,1,0,15,9,15,9,6,15|MargSingRot
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|BounceGas
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|Rotations
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|StringThing
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|BBM
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|MargSingRot
M0,8,4,0,2,0,15,15,1,15,0,15,0,15,15,15|M0,8,4,15,2,15,0,6,1,0,15,9,15,9,6,15
M0,2,8,15,1,15,0,9,4,0,15,6,15,6,9,15
M0,2,8,15,1,15,0,9,4,0,15,6,15,6,9,15|BBM
M0,2,8,15,1,15,0,9,4,0,15,6,15,6,9,15|Rotations
M0,2,8,15,1,15,0,9,4,0,15,6,15,6,9,15|MargSingRot
M0,2,8,15,1,15,0,9,4,0,15,6,15,6,9,15|M0,8,4,0,2,0,15,6,1,15,0,9,0,9,6,15
M0,2,8,11,1,7,9,5,4,6,14,3,13,12,10,15|Rotations
M0,2,8,11,1,7,9,5,4,6,14,3,13,12,10,15|M0,8,4,0,2,0,15,0,1,15,0,0,0,0,0,15
M15,7,11,3,13,5,9,8,14,6,10,4,12,2,1,0
M15,14,13,3,11,5,9,1,7,6,10,2,12,4,8,0
M15,8,4,3,2,5,9,14,1,6,10,13,12,11,7,0
M15,1,2,12,4,10,9,7,8,6,5,11,3,13,14,0
M15,14,13,3,11,5,9,8,7,6,10,4,12,2,1,0
M15,11,14,3,7,5,9,1,13,6,10,2,12,4,8,0

confocaloid · Post by **confocaloid** » August 14th, 2024, 1:10 pm

CARuler wrote: August 14th, 2024, 11:57 am a LOT of BCA rules
(long badly formatted list)

Known. If you are going to post a long list of rulestrings, please search first, to check whether they are already listed somewhere else. If posting a list, please format it better, so that it's easy to navigate for readers.

confocaloid wrote: April 15th, 2024, 12:03 pm
tommyaweosme wrote: April 14th, 2024, 3:09 pmi dont know what the numbers mean either, but i dont have access to many sites. thats why i was reluctant to go to the catagolue in january and february, because i didnt have access to it yet.
Margolus CA are two-state, and use the square tiling partitioned into 2x2 blocks. The vertical and horizontal lines partitioning the grid into 2x2 blocks are shifted diagonally by one cell after every tick. That means there are two different partitions (one used on even generations, another used on odd generations).

The 16 numbers refer to the 16 possible configurations in a 2x2 block:
Code: Select all
 0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15 | Index
---------------------------------------------------------------+-------------
00  10  01  11  00  10  01  11  00  10  01  11  00  10  01  11 | Configuration
00  00  00  00  10  10  10  10  01  01  01  01  11  11  11  11 |
---------------------------------------------------------------+-------------
In Margolus CA, current states of cells in the 2x2 neighbourhood determine the future states of the same four cells. To make a rulestring, for every numbered configuration above, write down the index of the configuration it should evolve into.

For example, Single Rotation Rule can be defined 'M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15'
That means configuration #1 evolves into #2 which evolves into #8 which evolves into #4 which evolves into #1, while every other 2x2 configuration remains unchanged.
A more intuitive way to explain this CA is to say that every 2x2 block with exactly one alive cell rotates clockwise, and nothing else happens:
Code: Select all
x = 7, y = 3, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
o3b3o$3o2bo$bo!
Code: Select all
x = 7, y = 3, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15:T80,60
o3b3o$3o2bo$bo!
Here is an incomplete list of explored and/or named CA:

M0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 Everybody Dies

M15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15 Everybody Lives

M0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 Nothing Happens

M15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 Awful Strobe

M0,8,4,3,2,5,9,7,1,6,10,11,12,13,14,15 Billiard Ball Machine

M0,8,4,3,2,5,9,14,1,6,10,13,12,11,7,15 BounceGas

M0,8,4,12,2,10,9,7,1,6,5,11,3,13,14,15 BounceGasII

M15,14,13,3,11,5,6,1,7,9,10,2,12,4,8,0 Critters

M0,8,4,12,2,10,9,14,1,6,5,13,3,11,7,15 HPP Gas

M0,2,8,12,1,10,9,11,4,6,5,14,3,7,13,15 Rotations

M0,2,8,12,1,10,9,13,4,6,5,7,3,14,11,15 RotationsII

M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15 RotationsIII

M0,4,1,12,8,10,6,14,2,9,5,13,3,11,7,15 RotationsIV

M0,4,8,12,4,12,12,13,8,12,12,14,12,13,14,15 Sand

M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15 Single Rotation Rule

M0,1,2,12,4,10,9,7,8,6,5,11,3,13,14,15 StringThing

M0,1,2,12,4,10,6,7,8,9,5,11,3,13,14,15 StringThingII

M0,8,4,12,2,10,6,14,1,9,5,13,3,11,7,15 SwapOnDiag

M15,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0 Tron

ababa11e · Post by **ababa11e** » August 24th, 2024, 8:19 am

this rule, M0,1,0,15,12,12,7,12,12,2,13,15,0,14,15,7, makes right triangles out of dot agar that slowly decay, with decaying lines drifting through them.
example soup [128x128, lasts 78k gens]

Code: Select all

x = 128, y = 128, rule = M0,1,0,15,12,12,7,12,12,2,13,15,0,14,15,7
2obob3ob2obobobo2bobobo4b3o2bo2b4obob2ob6o2b2o3b2o2b2o2bob3o2bo4bobob
2obobo2b4o5bo2b2o2bobo6b3o2b5o$obo3b2obob2o3b3ob2ob2ob2obo2b4o3b2o2b2o
bo2b2o2bo3b2o2bo3b3o2b3o2b5o7b5obo3b2o2bobo3bo2b2o2bobobo2b2o$2b6ob2o
2bob3o7b2o4bob4ob3o2b4o10bo2b2ob3o4b4obo5b2o2b2o3b2o3b2o3bob4o2bo3b2o
3b2o3b2obo$b2obo2b2obo2bo2b2o2bo7bobo5b4o2b4obobo3bo2bob2o2bo3b2o4b3o
6bobo2bo3b2o2b2obo2b2o2b3ob3obob6obobob2o$obob5ob4o3b2obo3b5obo2bobob
obob4o2bob3obo5b2ob5o4bo2b2o3bob3ob4obobob2obob3o3b4obo2b2o2bobobo4b2o
$5bob3ob4ob3ob2obo2bobo6bobo4bo2b3o2bobobob4ob2obo2b2obo3b3o3bob3obo2b
3o2bo2b3o7bobob2obob2o2b4o3bo$2b2obo5bo2bob3o4bo2b2o2bob3ob3o6b2obob2o
b4ob2obo4b2o2b2o3b2ob3o2b2ob2o3bobo2bo2bo3b2ob3o2b3o3bo2bo6bo$2ob2o2b
o2b6o2b3o4bo2bo2bo2bobo2bob2o5b6ob2o2b5o4bob6o2b2o4b2obo3b2o2b2o5b3ob
obob2o4b2o2b4ob3o$3bo2b7ob2obo2bobob2o2bob3ob2o3bo2b4o2b2o2bo2bobo3bo
b2o2b3ob4o5bob2o4bo2bo2bob2obob4o2bo2bobobobo4b3ob2o$o3bobob3obo5bob2o
bob2o2b9ob4o3b3obob2ob2obob4o4bobobobobobob3ob4o2b4o2b2ob3o2b8ob7obob
2obo$2bobobobo3b3ob3o5b2ob2ob7obo3bob4o2bo2b4o2bobo6b2o2b5o3b8ob3ob2o
2b5ob5o4b2ob3ob4obo2bo$b2obo4b3o2bo3b8o2bobobo2b4ob2o2bo3b2ob2obob2o5b
3o2bo2bobobobob2obob2ob5ob3obob2ob3o4b3o3b4o3bobo2bo$b4o4bob3ob2o2b7o
2b6o3bo4bo2bo3bo2b2o2bo2b2obo5b5o5b7obo2b2o2b2o6bobobo2bo2b4obo2bo2b2o
2b2o$obob2o3b3obo2b2obo3b2ob4ob2o2bob4obo3b4o2b2o7b5o2bo2bob2o2b2obob
o3bob2o3bo2b5ob2obo2bob2o3b2o2bo2bo4bo$2b2o3b3o2b2ob4o2b3o2b3ob2o2b2o
2bobob3ob2ob2o3b2o3b2ob4ob4ob4obob2ob3o5bobo2bo5b2ob2obobo2bo2b2ob3o3b
3o$2b3obo3bob2obo2b5o3b2obob2o2bo3bo2bo2b5obo7bo2b2ob2ob3o3b2obob2obo
bo2bo2bo6b2o2bo5b2obo4bob2obob5o$bo2bo8b2obo2b2o3bobo6bo3b2ob3obob6ob
6obo3bo2b2o4b3o4bobobob3o2b3obobob2ob2ob2obob7o4bob5o$o2bobobo2bobobo
2bo2b3o3b5ob2obo2bob2o4bob4o2bo2bo2b4o5bobo2bobobo6bobobob2o4bobob2ob
4o2bobobob5ob2obo$2o2bo2bobo2b2ob2o3bo3b5ob2ob2o2b5o2b3o4bob2o2b2o2bo
bo4bo3bob3obo2b5obo11b2o2bob4o2bob4o4bob3obo$b2ob2o2b10o4b5obobo3b4ob
obobo2b3o2b2o3b3ob4obobo2b2o2bobo2bob2obo6b3obobobo2bob5ob9obobo$2obo
b2obo4b2ob2obo2bobobo4bobo3b3ob2obo3b2o2bob6ob2ob4ob2obo5bo3b2obo3b2o
2bo3bob2o2bo4b3ob4o$o2b5o3bo3b4o2b4o4b3o3bobo2b2o4b5o2bo2bo5b2ob2ob3o
4bo2b2o4b2o2b3obobob6o2bob5o2bob2obo2bo3b2o$4obo2bo2b2o2bobob4o2bo2b2o
bobob2o2b2o2bo2b4obobobo2b2o4bobob4ob2o3bo3bo2bobo4bob3o2bo3bo2bobo2b
2o2b5obobobobo$bob3o2bobo2b3o2b2o4bobob2o6bo2bobob2obo3b2obo2bo3bobo2b
o2bo3bo2bo2bob3o2b3o4b2obob5obo4b3o2b3obob4o$2o2b2obob2ob4o4b3obo4b3o
bob3ob2ob6ob2o2b5o5b5obo2bo2bo2b3ob2o6b2o5bob2obo2b3ob4obob3o3bob4o$b
2obob2o2bobob2o2bo3bo3bobobob2o4b2o2b2o2b2ob3ob3o3bobo2bo2b8o2bo3bo2b
2o2bo2b3o3bob2ob2o3bo4b2o3bo3bo$3o2b2ob2o5bo3bo4bob4o4bo2bobo2b2o3bo5b
2obo7bobob4o2b2obobo2bob2obo3bob3o2b2o3bo3bobobob2o2bob2o2b2o2bo$2bob
2obo2bobob5o11b2ob3o6b2o3bobo2bo2b3ob2obobobo9bobobobob2o2b4obobo5b5o
4bob2obo3bo3b2o2bo$bo2b3ob2obo6b2obo3bob3o3bobo2b3o4bo2b5o2b3o4b2o2b2o
3b5o7bo3b2o2bob3obob4ob3o2b2o4b5ob2obob2o$2b2o2b3ob2o4b2o2b2o2b2o2bo3b
obo4b2ob5obo4bo2b2o2b4o3b2o2b2ob5o5bo3bo2b2o3bo2b4o6b3ob4o2b2obo2b2o$
2bo4b2o4b5ob3obo3bo3b4obo2b3o2b2ob3o5b2o2bob2obobo3b2o7b5obob2o2bo3b3o
6bob3ob2o2b2o2b3o3bo$obo2b2ob5ob4ob6o2b2obo3bob2o4bobob4o3b5o3bo3bo2b
2ob2obo2bo2b3o2bo3bo2bobo2bo2bo2b2ob3ob7o2bo3b2obo$o2bob4o3b3ob4o3bo6b
o2b2o3bo2b2o2b3ob2o2b2o2b2o2b4ob4obo7bob4ob3obo2b3o3b6o2b2o2b3ob2ob2o
2b6o$o2bobo4b2o2bob2obobo2b4o3b7o2b6o2bobo2bob2o3bo4bo2bo2b3obo3bobo3b
3o2b3obo2bobob3o3bo4b2o2b2o4bo2b2o$b4obo2b4o3b2o3b2o2b2o2bob3ob3ob2o2b
ob2ob3o7bo2b2obob2ob2ob2o2bob7o7b3o3b5o5b8o2bobobob2o$3o3b3o3bo2b3obo
2b3o3b2o2b5obo2bo2b2o3bobo2b7obo4bobo2b2obobo2b2o2b2o4b4ob5o4b3obob2o
2bob3obo2bo2bo$2b2o3bo3b4ob2ob2o2bo2bo5bob2o2b2o3b8o2b5obobob4obob2ob
4ob3o3b2ob2obob2o2b2o4bo5bob4obob2o2bo5bo$2ob2o3b3o2bob4o2bobobob4o8b
o3b2ob4o2b3obob2ob2ob2o3bo6b2o5bobo3b2ob2o4b6ob2obo2bo3bo2bo3bo3bo$o2b
2obo2bo4bob4o2bob6obo2b2o2b2ob3ob4o2bobo4b6ob2ob3obobobobobo5b2o2b2o2b
obo4bo2bo2b4ob2o2b2o2b2o2bob2o$3o3b2obobo2b3o3bobob2ob6o2b2o2bo3bo2b2o
3bo2bo3bo2bo2b4obo2bob2o4bob5o4b3obobob4o2bo2bo6b2o3b2o2bobo$3b3ob2o3b
o4bobo3bob6o3b5o2bob2o3b2obob2obobo3bob3obo3b2o2bo2bo5bo3bobo2bo2bob3o
bobobo2b2o5b2o3b2obobo$o2b3o3b4o3b4obo2bo3b4ob2o2b7obo2b2o3bo2bo4bo2b
4ob9o5bo7bob2o3b2o5b2obo4b4obo4bob3o$o2b2o2b3obo2bobob2obobob2ob2obob
5o2b3ob2ob2obo5b2o3b2o5bobobobobo6bo2bob2o4bobobo2b9ob2obob6o5bo$bob4o
bo2bob4o2bo2bobobob4ob2o11b4ob3o2b3o3bo4bo4b3ob3o3bobob3o8b4o2bobobob
ob5o4bob2o2bo$obo4b2o3b2ob3o3bo3bob2ob2o3bo4bo4bobob4ob2ob2o4b2o3b2o2b
obob2o5bo2b2o2bob5obo3bo3bo2bob2ob3o4b2o2bo$obo2b2ob5ob3ob2o2b2o2b2ob
o2bo2bob5o2bobo2bob2o2b2ob3ob4o2bo3bo2b5o3bob3o2bob5o9bo2b4o4b2ob2o3b
3o$b2obobo2b3obobobo4b2obo2bo2b3o2bob3ob2o4b2obobo3bo4b4o5bo2b2o3b2o3b
obob5o2bo3b2o12b2o2b3o4b4o$obobob2obobobo3b4o3bobob3obo6bobo2b3obob2o
b4ob8o2bo3b2o2b4o2bobobo2bo2bo3b5ob2o2bo5bob2o2bo3b2o3bo$4o6bobobob2o
2bo2bob2o2bo2b10o2b3ob4o2bo4bobob2o2bo4bob2obob2o4bobo4bo3b2o2b2ob7ob
3o5bobobob3o$4o2b2o3b2ob4o2b8o4bo4b7o2b3o2bo5bo2bobo2bo3bo4bo2bob3o6b
ob2obo2b4obob5o2b3o4b3o3b3obo$b4o4bo4bob2obob3obobobob3ob3o2bo2b7obo2b
ob3obobob2o4b3o3b3o2b3obo2bobo2bobobob2obo3bobobo3bobob3o3bo2bo$o5bo4b
2o2bo5b7ob3ob3obobo6bo3bo2bo2bobobob4obo4bo3bo4b2o2b2ob3o4b4o2bo2b7ob
o5bobobob2o$2ob2obob2obo2bob5ob3obo2bo6bo2b6o2bobobob2o5bo3bob2obobob
2ob3ob3o3bo3bob2o2bobo2b2obobob2o2bob2ob2o3bo4bo$obo2b2ob2o4b5obob4ob
3o2bo2bobob3obo2b3o5b2o2b3obobob4ob3o3b3obo2bob3o2bo2bo3bo2bo2b4o2bob
obo6bo$2b4o3b3o2bob2obo3bob5o2bob4obo3bo2b3obo2bo4b3o2b2ob2o3b3obo2bo
bob2o2b2o3bo4bob2obob2obobob2obo2bo2bo2bo2b3o$2o3b4ob4o2b7o2bo4bo2bo2b
o3b3obobob2obo3b2o2bobo2b3o4b2o2bo2bob2obob3o4bo3b2o3bo2b3o3b4obo2b2o
2bo2bobo$b2obo2bobo3bo3b2o2bob3o7b2ob4o3b2obobob2o5b4ob2o4b3o5bobo2bo
bobob5o5b2obob2obobob3o2bo2b2ob2ob4o$b2obob2obobob2o3bobo2bo3bobo3bo5b
obob2o10b5o2bo3bobo2b2obo2bob5obo3b4o3b2o2b3o3bo2bob2o2b2o4b3obo$obob
3obo4bo3b2o4bo2bo2bo2b4obobob3o2b3obo2bo2b4o2b4o5b5obobobo5b2ob2o2b2o
b3ob2o2b5ob2o2b2ob3obob3o$b5o2bobo2b2o2bob2o2bob2o2b5ob2obobob3obo2b2o
bob11ob2obo2b4ob4ob3ob3o6bo3b2o3b2o3b2obobo4bob2o3bo$2obo3bo7bobo2bob
2o3bo2bo2bo4bob2ob5obo2b2o2b4o2bob3o2b2ob2o3b3o5b2o4b2obob2obo2b4obob
o2b2ob2o3b3o2bobo$4b3o2b2ob3o3b3o2b2o2b7o2bob2o2bo8b7obo2bob2ob3o2bob
6o3bo2b7o2bob2obob4o4b2ob2obob5o4bo$4o4bobo2b2obobo5bob2o2bobob3o6bob
obo3bo3bob2obob5obo2b2ob2o2b2obob2o2b3o2b2o2b2obo4b2o2bo5b2obobob2o4b
o$b3obobo4bobo3bo2b2o2bo5b2o3bo4bo2bobob5o6b5obobo2bob2obo3b2obo2b4o3b
o2bo4bo4bo6b3ob3ob2obo2bo$3ob2ob7o5b5ob2obo3bo2b5obobob9obo2bob2obo3b
o2b2o8b3ob3ob4o4b3o2bo2b2ob2o2b7ob2o5b2o$3obob5ob5obobo3bobobo4b3o2bo
bo4b3obobo5b3o7b4ob2o2bobo4b2o3b3o3bob3o2bo4bo3bob2o3bo2b3obobo$3ob2o
b4o3b3ob2obo3bo3bobo5b6obo3bob2ob2o2b4obob5o2b2o2bo2b3o2b2ob5obobo2b4o
b2o2bob4obo2b3obobob3o$4bo2bo6bo2bob2o2b5ob3o2bob3ob4o3b2obo2b2o2b2ob
obo3bob3o9bo2bo2bobob6obo3bo3b2obo4b2obob3ob2ob3o$2o2bo3bobobob3obob2o
2bob5o2bobo4b2obo4b3ob2o2b2obobob2obo3bo3b2obo2b3o3bo3bo3bobo3bobob2o
2bobob2o2b3o2bo2b4o$3o4b2o3bo3bobo2b2obobob3obob5o3bo2b2o2b2o2bobob4o
b3o7bob3obob4ob2o7bob2o2b2o2bo2bo2bo6bob4o3b2o$2o3b3o2bobo2bo2bob2ob2o
2b2obob3ob2o5b2o3b2ob6o2b5o5b2o4b4o2bobob3o3b2ob3ob2o6bo2b4ob3o2b2o3b
obo$4obobo5bob4ob2o4bobo2b3o2b3ob2o2b2o2b4ob2ob2obobobob2o3bobob4o2b3o
2b2o2b4obob2o3b3obo7b2obo6b3obo$obo2bo2bo2bob2ob2o4b5obobobobob2ob3ob
o2bo2b3o5b5obob3obo2bobobo6bo2bobo7bobo2b4o3bob3o2b2o2bob3obo$b3o2b2o
2b3obobo2bo4b2o2b2obobo5bo2b2obobo2b4obobo3b5o3b6ob2obob2o2bo2b2o2bo2b
2o8b2ob2o2bobobo4b3ob2o$bobo2b5ob2o2b2ob2ob3ob2ob2ob2o4b4obobo2bobo2b
o2bo2b2obob7o4b5ob2o2bob3ob4o2bob2o4b5o3bo3b3ob6o$3b3o3b2obo3b2o3b4o2b
o2bo2b5obo2bobo2bobo2bo2b5obobo7b2obob2o3b2obobo2b2o4bo2bob2o3bob3o4b
o2b5ob2o$o5bo5bo2bo7bo2b2obo2b4obobobobo2b2ob2o3bo2bo3bo3b2o3bob2o2bo
7b2obo2bo3b3ob2o2b2o2bob3obob2ob2ob2ob3obo$2bo2bob3o4b2ob3obob3obob3o
2b4obobo3b2o3b3o2b2o5bobo2bo2bo3b4obo2bob2o3b5o5bo2bobob2o2b2o2b3o3b4o
$b2o3bobo2b2ob3ob4o3b3ob4obo5b2o4bobo2b2obo5b7o3b2obo2b2obo2bo4b3o4bo
b2ob5ob6o6bobo2bo3bo$bo2bob2ob3o2b3ob2obo3b2o2b4ob2o2b2ob2o2b4o6b2o2b
o2b2obobob2o5bob4o3b2obo2b2o3bob2o3bo2b3obobob3o2b4o2bobo$bob3obo3b4o
b3ob2ob2obob2o2bobo2b4obobo2bo2b2o4bo4b3ob2ob2o4b3obobo2bo5bo3b2ob3o2b
3o3b2o3bo2bob7ob2o$2ob2o2b4o7bob2o2b2o2bobo2bo2bobob2ob2obo4b2obo3b2o
bo2b4o2b2ob2ob4ob5ob3o2b2obob2o3bobobob4ob3obobob2ob3o$o3b2obo2b2obob
ob2ob3o3b2o3b2o4b2o3b2ob3o2b2o8bo2bo2b3o3bo3b3ob4ob2ob3obob4ob2o3b3o2b
ob2ob4o5b4o$bob2obobobob7ob2o2b3ob2obo2bo3b3o2b2o2b2o3bobob3o2bo2b2o2b
3obo9b3obo2b4o2bo4b2o2b2ob3ob3o2bo2b7obo$b2ob4o2b3obob2o3b2ob4o9bob2o
b2ob8o3bobob4ob2o2bo2bo3b2o2b2ob3ob4o2bo5b2o4b3obo2b4obobob4obo$3obo2b
5o2b2o2b3o2bo2bobo2b4ob3obobo2bo3bobobob2o3b3ob5o2bob2obob4o2b2o2bob3o
2b5obo2b2o2bob3o2bobo2b2o2b3o$ob2o9b2ob2o2bo7bo3b2obo4b3o2b3obob6ob4o
2bob3o3bob2o2bob2o2bob2o2bo2b2o2b2ob2obo2b2o4b5obob2o3bobo$o5b4o4bo7b
ob4o4bob2obo2b2ob2obo2b3obobo3b3o5b3ob4obobo2b2o6bo4b2o2bob4o5b2ob3ob
2o4bo3b2o$2b2ob2ob2o2bo3bob6ob3ob2o2bo2b7o4b2o2b4obobo2bobob2obob2obo
5bo3b2ob5o2bobo2bo3bob3ob3o2b2o5b2o3bo$b2o2b2o3bo2b2ob7ob4ob3ob2obobo
3bob3obobo6bo2bob2obo2b3o3b2o4bo2bo5bo3bob2o3b4o6bobo3b3o3bo3bo$2bob3o
2bob2o3bo3b4o4bob5ob2o5b2obo3b2obobo3bo3bo2b3ob5o3bo2b5ob2o2bo2b2o4bo
b3ob2ob2o3bobob2o4bobo$3obob2obob8o3b4ob5obob6o5b2o3bo3b2o3bob3obobo2b
5o2bo4b2obobobobo2b3ob2ob4o2b4obob2obobo3bob2o$2ob6obobo2b4o2bob4ob2o
bo2bo2bob3ob2ob4o2b5ob2obo3bo2b2o4b2ob7o2b5o2bob2o2bo2bobo3b2obo2bo2b
2ob2ob3obo$4obobo2b2o6bo2bob3ob2o2bo4bobo2bo3b2o3bob2o2b4obob2o5bo3b2o
5bo2b4o4bo3bo2bob3obob4o2b4ob2ob2ob3o$b2obo4bob4obob5obo4b2obob2obo2b
o2b2obo3bo2b2o4b6o7b3obob2ob6o2b2o2b3obo5b2o2b3obobob8o2b3o$3b3ob3ob2o
3b2o3bob3ob3o3bobob2o2bobobobo3bo2b2o4bo2b8o4bo4bob2ob2o4b2o2bobo4b2o
bo3b2o2bo3b2o3bob4o$o3bobo2bo2bobobo2bob2obob3obo2bo6bobo3bo3b4o3bo4b
2o3bobo3bo2b2ob2ob2ob2o2b4o2bo2bobob4obobo2b2o5b4ob2o$3obobo2bobo2bo3b
o2b4ob2ob2o3b3ob2obo2b2o3bob3o5bob2o4b6ob3o3bob2o4b4obobo5b4o2b5ob2o3b
o2bobob3o$bo2b2o2bobo6bo3b3o3bob2obo2b3obo4b2o2b2o5b2o3bobo2bob2ob3o2b
5o2b5o3b2obob2ob2ob2obob4obo3bo2b3o3b3o$o5b3obo7bo2b2obo2bob5o4b2obob
3o3b2ob4o3b3o3bobo2b4o3b2obo2bob5o2bo3b7obo2bo2b4ob2ob3o2bobo$2obob2o
b2obob3o3bob3o2b2ob4o3b2obo2b5o2bobo2b3o2b2ob2obo2bobo2bob2o2bo2b2o3b
obob2obobo4b2o2bo2b2o2b2o2b2ob4obo$5o2b6o3bo2b2o2b3obob2o2b3o2bobob2o
2b2ob4o2bo6bob3o2bo2bo2b2o2bob2ob5obo2bobo3b2o2bo2bobo6bobo2bob4obo$2o
5bobobo2bob2o5bo2bobob5ob3obobob2ob6o2b2o2bobob4o2b2ob2o2b2obo3bobob3o
bobobobo2bo2bob2o3b3o3bobo3bobobo$ob4o2b2o3bob6ob4o2bob2o2b2obob2o4bo
2b2ob3ob5o2bo3bo5b4o3b2o2bo3bo2b3o2b2o4b3o2bo3b2o3b3ob2o3bobo$bo3bobo
2bob3o2b2o3b4o4b6obo4bo2b3ob3o4b3obobobobo3bobo5b2obo8bob3o2b2ob2o3bo
4bob2o2bob2obo4b2o$3bo2bobo2b5o2bobo3bo2bobob2o2bo2b5o2b2ob2obo2bob3o
b5ob3o6b3o2bo2b8o3b3ob2ob2obo7bobo5b3obobo$bo2bob2ob3o2b8obo4b2o6b2o2b
2ob4o2b3o3bobo2b4o2bobobo5bo2bo2b3o2bo3bob2o5bobob2ob2ob2ob3obo2b2o3b
2o$2bo3bo2b3o4bo3bobobobob3ob2ob3o2bo3b3obo5bob2o2b2o2b2o2bobo2bo2b2o
b2ob3o3b2o3bo2b2o6bo2b5o2bobob3o2b5o$bobo4bo4b2o2b2o2b2o3bobo3b2o2bob
3o2bo9b4ob4ob2ob2obobobob2o2b2o2bo5bo3b2o2b2o4b2o2bo3bobo2bo2b2ob2obo
$o4b2ob2o2bo3bobo2b5obo4b2o2bo2b7o3b8o10bobo6b2ob5o3bobo3bo4b2obob3ob
2obob2o2b5o2bo3bo$2o2bob2ob2obobo2bob4ob3o8bobob5obo5bo3b4ob3ob3obobo
2bo2b3obo2bobo4b5ob3o7b2ob2o5b2o3b2o4bo$3b3obob4o2bo2b5ob4ob2o2bo3bob
2o6bobobob4o5b4o3bob2ob2obobob2obo3b11obo4b4obobo3b2obo4bob2o$2b3o2bo
3b2ob2o2bobo2bo5bobobo5bo6b2ob3obob2o2b2o2bobob5o2b3ob4o4b4ob2o3b2o2b
ob3o5bob3ob2obobob2o$2bo3bob3obobo2b5ob4ob4obo2bobobobo3b2obob2obo5b2o
b2obo3bo3bob3obo5b2o2bobobo2b3o2bobo5b3ob3o6bo2bo$2o2b2ob2obob2obo2b6o
bobob3o4b3o2bobob7ob4o2bob5o2bobobo3bo2bo2b2o2bobobob4ob2obob3ob4obo3b
o2bobob3ob2o$2o2bob2o3b2ob3obob3obo2bo2bo2bob3obo2b2o3bobobobo3bobobo
bob7o3bobo2b2o2bobo2b2o2bo5b2ob2ob3obobo2bobob5o2bo$bo5bo3bo2bobo2bo2b
2ob2o8b4ob7obobobobo2bob2ob2ob5obob3o2bo6bo2bo2bo4bob4ob2obo2bob3o3b3o
2bo3b2o$2b3obo3b2o3bo2b3o2bob2ob2o2bobo3bo2b6ob10o7b2o2b2ob7obo4b3ob2o
2b2obo2bob8obob3o3b2obo4b2o$ob2obo2bob2obo3bo4bobo2bo4bo3bob2ob2obobo
3b6obo2b5obobob4obobo2bobobob2ob2o4b2o5b2o3bo2b2o7bo3bo2b2o$obob4ob2o
3b2o2bo3b2ob4o2bo3b3o2b2ob2obobo2bo5b3ob8o3bobo2bo2bo3bob3ob3obob2o3b
3o2bob2o3b2o2bobobo$o2b2o2b7o3b3o2b2o3bo3b3o2b2o3b3obo3b5o2bo2b2obobo
b4ob4obo3bobobob6o2bob7ob4o5bob2obo4b2ob2o$o3b2o2bo2b2ob3obo3bo4b2o3b
2o6b3obo2bob5o5b2obobo2bo4b2ob3ob7o5bo4bob3o2bob3obo5b3o2bo3b2o$bo2bo
2b2obo4b2o2bob4obobo2bobobobob3obo2b2o2bo2bo2bobob3o2b2ob3o3b3o4bo2bo
b2obobo2bo3b2obob3ob3obo4bobobob2ob2o$b3o4bob2obo3b3obo3bo2bo4b2ob5ob
2o2b2obo2b3ob2ob2o2bob4o3b4obobo6b3obob2ob2o3bo2b2obo3b2obobob2ob2o2b
2o$obobo4bob3obo2b3o2bobo6b3o2b4ob3ob3o3b3ob2obobobo2b2obobobob2obo2b
obobobobobobo5b3ob2o5b2ob2o3bo2bobob3o$b2o2bo2b2o2b2o3b2obobo2b3ob3o6b
2ob3o2bobob4obobo2bo4bo2bo3bob3o2bobo2bobo2b2ob4o2bobo2bo2b2ob6obob2o
b2o2b3o$o3bob2o2b2o4bobob2o2bo2b3obo2b2obo2b2obo2b6ob2o3bob2obobob3ob
2obobo3b4o2b2ob3o3b3o2b2o3bob4o2b3o2b2ob2obo2bo$2ob3ob5obob2o2bobo3bo
3b2o2bo4b2o2b2o6b2ob6o6bob5ob3ob4o5bobo4bobobobo2b2o3bob2obob3o4bo2b2o
bo!

CARuler · Post by **CARuler** » August 24th, 2024, 11:25 pm

confocaloid wrote: August 14th, 2024, 1:10 pm
CARuler wrote: August 14th, 2024, 11:57 am a LOT of BCA rules
(long badly formatted list)
Known.

none of them are on that list

b-engine · Post by **b-engine** » February 19th, 2025, 6:31 am

I don't know the period of this oscillator:

Code: Select all

x = 29, y = 3, rule = M0,2,1,3,8,5,6,7,4,9,10,11,12,13,14,15
10bo16b2o$2o3bo17bo3b2o$2o3bo4bo12bo!

"Gas particles" escaping from a box:

Code: Select all

x = 50, y = 51, rule = M0,2,4,3,8,5,6,7,1,9,10,11,12,13,14,15
$50o$50o$2o46b2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o
2bobobobobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobo
bobobobobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobob
obobobobob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bo
bobobobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobob
obobobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobo
bobobob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobob
obobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobobobo
bobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobobob
obob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobobobo
bobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobobobobob
obobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobobobobo
b2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobobobobob
obobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobobobobobobo
bobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobobobobob2o
$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobobobobobobo
bobobobobobobobobobobobobobobo$2obobobobobobobobobobobobobobobobobobo
bobobobo$2o2bobobobobobobobobobobobobobobobobobobobobobo$2obobobobobo
bobobobobobobobobobobobobobobobobo$2o2bobobobobobobobobobobobobobobob
obobobobobobob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o
2bobobobobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobo
bobobobobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobob
obobobobob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bo
bobobobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobob
obobobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobo
bobobob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobob
obobobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobobobo
bobobobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobobob
obob2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobobobo
bobobobobobobobobobobobobobobobobobob2o$2obobobobobobobobobobobobobob
obobobobobobobobo2b2o$2o2bobobobobobobobobobobobobobobobobobobobobobo
b2o$2obobobobobobobobobobobobobobobobobobobobobobo2b2o$2o2bobobobobob
obobobobobobobobobobobobobobobobob2o$2o46b2o$50o$50o!

Post by **rowett** » February 19th, 2025, 8:02 am

b-engine wrote: February 19th, 2025, 6:31 am I don't know the period of this oscillator:
Code: Select all
x = 29, y = 3, rule = M0,2,1,3,8,5,6,7,4,9,10,11,12,13,14,15
10bo16b2o$2o3bo17bo3b2o$2o3bo4bo12bo!

Code: Select all

Identify:
Cells		14
Active		77 | 8 | 85
Bounding	29 x 3 = 87
Period		5915496
Mod		5915496
Heat		2 | 12 | 9.8
Temperature	0.12 | 0.13
Volatility	0.91 | 0.91

muzik · Post by **muzik** » February 21st, 2025, 3:40 pm

Insanely high period:

Code: Select all

x = 166, y = 108, rule = M0,0,0,15,0,15,0,0,0,0,15,0,15,0,0,15
42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o
$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o!
[[ SHADER Neighbour ]]

unname4798 · Post by **unname4798** » February 21st, 2025, 3:44 pm

Can also be described as an OT rule:

Code: Select all

x = 166, y = 108, rule = B3/S58
42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o
$42b82o$42b82o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o
$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$166o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b82o$42b
82o$42b82o!
[[ SHADER NEIGHBOR ]]

confocaloid · Post by **confocaloid** » February 21st, 2025, 3:52 pm

muzik wrote: February 21st, 2025, 3:40 pm Insanely high period: [...]

Since you know the period is "insanely high", presumably you can add the information to the post to tell what is the actual period? The period is a basic property of an oscillator and it is reasonable to expect it available immediately in the description, without every reader having to re-identify the oscillator (if that's possible at all).

The forum rule 5b says: "Readers of your post should have a rough idea of what to expect when they open your RLE in LifeViewer or copy it into another program. Outside of the Sandbox forum, at least briefly describe (or quote another post that describes) what pattern(s) you're posting. Descriptions also make it much easier to find patterns by searching the forums." viewtopic.php?f=3&t=2092

muzik · Post by **muzik** » February 21st, 2025, 3:53 pm

confocaloid wrote: February 21st, 2025, 3:52 pm
muzik wrote: February 21st, 2025, 3:40 pm Insanely high period: [...]
Since you know the period is "insanely high", presumably you can add the information to the post to tell what is the actual period? The period is a basic property of an oscillator and it is reasonable to expect it available immediately in the description, without every reader having to re-identify the oscillator (if that's possible at all).

It considerably exceeds what is even achievable via LifeViewer Pro, otherwise I obviously would have included this information.

b-engine · Post by **b-engine** » February 22nd, 2025, 12:34 am

Soups dissipate like gases, and dense soups would dissipate slower than less dense ones:

Code: Select all

x = 0, y = 0, rule = M0,8,4,3,2,5,6,14,1,9,10,13,12,11,7,15
!
[[ RANDOMIZE ]]

muzik · Post by **muzik** » March 10th, 2025, 9:24 am

Interestingly the frequency map of this oscillator is rotationally symmetric. Does this gain a higher symmetry at some generation before playing out in reverse again, perhaps with some transformation?

Code: Select all

x = 8, y = 7, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
5bo$5b2o$4bo2bo$5bobo$bob3o$5bo$4bo!

unname4798 · Post by **unname4798** » March 10th, 2025, 9:30 am

Code: Select all

#R M0,1,2,3,4,5,6,13,8,9,10,7,12,14,11,15
!
[[ RANDOMIZE RANDWIDTH 8 RANDHEIGHT 8 RANDFILL 75 ]]

muzik · Post by **muzik** » March 15th, 2025, 8:39 am

Gems-like dynamics:

Code: Select all

x = 17, y = 16, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
8b2o$8bo$7bob2o$5b2obob3o$4b4o3b3o$3bob4o2bob2o$2b4ob3o3bobo$bobob3ob
2o2bo2bo$bobob3ob2o2bo2bo$2b4ob3o3bobo$3bob4o2bob2o$4b4o3b3o$5b2obob3o
$7bob2o$8bo$8b2o!
[[ SHADER Neighbour ]]

b-engine · Post by **b-engine** » March 25th, 2025, 1:44 am

"MargAllRot":

Code: Select all

x = 1, y = 1, rule = M0,2,8,10,1,3,6,11,4,9,12,14,5,7,13,15
!
[[ RANDOMIZE ]]

muzik · Post by **muzik** » June 29th, 2025, 2:36 pm

Even small objects tend to have extremely high periods:

Code: Select all

x = 9, y = 12, rule = M0,2,8,10,1,3,6,11,4,9,12,14,5,7,13,15
3b2ob2o$2b2o2b2o$b2o4b2o$2bo$3bob4o$bob2obo$bo2bob3o$b3o$b2o2b4o$3bo$
bobobo2bo$b3ob4o!
[[ SHADER Neighbour ]]

muzik · Post by **muzik** » September 1st, 2025, 11:50 am

Why is it that oscillators in reversible rules that have C4 temporal symmetry tend to have an envelope, period map and (perhaps most importantly) frequency map which is D8 symmetric, rather than the more common C4 symmetry of the rules we're more used to? Is there some deeper, higher symmetry being enforced in such a way that's required for reversibility?

Code: Select all

x = 5, y = 6, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
bo2bo$2bo3$o$2bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 7, y = 5, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
$bo$3bo$2bo3bo$bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 6, y = 7, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
5bo$bo2bo$bo2bo4$bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 7, y = 8, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
$6bo2$4bo2$bo3bo$4bo$4bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 7, y = 6, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
$2bo$5b2o$2bo$bo4bo$3bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 8, y = 15, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
4bo$o2bo$5bo$2bo2$2bo2$4bo7$7bo!
[[ AUTOIDENTIFY ]]

Indeed, C2 temporal symmetry in oscillators tends to lead to D4 symmetric maps:

Code: Select all

x = 9, y = 8, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
$3bo$5bo$4bo3bo$3bo3$bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 7, y = 4, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
5b2o$2bo$bo4bo$3bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 5, y = 6, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
3bo$o3bo2$bo$4bo$3bo!
[[ AUTOIDENTIFY ]]

Code: Select all

x = 6, y = 5, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
4b2o$o2$4bo$3bo!
[[ AUTOIDENTIFY ]]

Likewise, this is time asymmetric yet has a very clearly diagonally mirror symmetric map. I wonder if this is for the same reason as this previously-discussed oscillator?

Code: Select all

x = 12, y = 7, rule = M0,4,1,10,8,3,9,11,2,6,12,14,5,7,13,15
5bo$bo2bo$bo2bo4$bo9bo!
[[ AUTOIDENTIFY ]]

muzik · Post by **muzik** » March 7th, 2026, 10:50 am

Moosey wrote: September 1st, 2019, 11:14 am1D 1-direction stretcher
Code: Select all
x=1, y=1, rule = M15,2,13,12,11,10,9,8,7,6,5,4,3,14,1,0
o!

I think this technically counts as one of those Lorentz-shifted replicators:

Code: Select all

x = 1, y = 1, rule = M15,2,13,12,11,10,9,8,7,6,5,4,3,14,1,0
!
[[ PASTET EVERY 1 PASTEDELTA 4 0 PASTE o! -4089 -4089 AUTOFIT ]]

muzik · Post by **muzik** » July 28th, 2026, 7:21 am

Are there any pattern collections for rules such as Rotations that include known high-period oscillators and spaceships?

unname4798 · Post by **unname4798** » July 28th, 2026, 9:19 am

b-engine wrote: March 25th, 2025, 1:44 am "MargAllRot":
Code: Select all
x = 1, y = 1, rule = M0,2,8,10,1,3,6,11,4,9,12,14,5,7,13,15
!
[[ RANDOMIZE ]]

Real MargAllRot:

Code: Select all

#R M0,2,8,10,1,3,9,11,4,6,12,14,5,7,13,15
!
[[ RANDOMIZE ]]

1and0nlycordershippr · July 28th, 2026, 9:48 am

unname4798 wrote: July 28th, 2026, 9:19 am
b-engine wrote: March 25th, 2025, 1:44 am "MargAllRot":
Code: Select all
x = 1, y = 1, rule = M0,2,8,10,1,3,6,11,4,9,12,14,5,7,13,15
!
[[ RANDOMIZE ]]
Real MargAllRot:
Code: Select all
#R M0,2,8,10,1,3,9,11,4,6,12,14,5,7,13,15
!
[[ RANDOMIZE ]]

B-Engine's version is less boring.

unname4798 · Post by **unname4798** » August 16th, 2026, 11:34 am

In my rule, every pattern rotates itself back every 4 generations, so I'm the winner here.
Explosive rule that has an orthogonal spaceship, a gun, a p2 oscillator and an infinite family of still lifes:

Code: Select all

#R M0,7,11,3,13,5,9,1,14,6,10,2,12,4,8,15
!
[[ RANDOMIZE ]]

Code: Select all

x = 37, y = 8, rule = M0,7,11,3,13,5,9,1,14,6,10,2,12,4,8,15
12bo12b2o2b2o$12b2o11b2o2b2o$b2o8bobo5b2o4b6o$4o7b2o6b2o4b6o4b2o$o2bo
8bo14b2o6b2o$27b2o$27b4o$27b4o!

CARuler · Post by **CARuler** » August 16th, 2026, 7:18 pm

trippy effect

Code: Select all

x = 3, y = 3, rule = M0,14,13,0,11,0,0,0,7,0,0,0,0,0,0,0
$b2o$b2o!

edit:
turns into ships

Code: Select all

x = 66, y = 39, rule = M15,1,2,3,4,5,0,0,8,0,10,0,12,0,0,0
$bo2b7o10b3o4b2obo2b3o3bo4b2obobo2bo3b3o3b3o$bobo3b2obo4bo2b8o2b2ob5o
2b2ob2obob3obo2b3o3b3ob2o$2b3o2bob2ob2ob2o2bo2b2o3b2ob4ob4o4bo2b3o2bo
2bobob3ob4o$bobob2o4bo2bob2o2bobo2b2o2bobob3o2bobo4bo2bobo2b2o3b5obo$
3bobo6b2o4bo4b3o3b5o3bobob2o2b2o4b5obo3b2o$b2o3bobo3b3obo3bob6o2bo3b2o
bo3bobobobob6o2b4obo2bo$4bo2bo7bo5b2o4b3o2bobo2bob2o2b2obob2o2bo2b2ob
3ob3o$b4ob2ob2ob2obo2bob2ob4ob4ob3ob3ob7obob3obo3bo$3bo2b4o6b3o3bo3b3o
bo3bo2b2ob4obo3bobobobobo2bobobo$bob2ob6o5b3o3bo2bo3b6obo3b3o5bobobob
3obo2bo2bo$4b2o2b3ob3o5b3o4bobob3obo3b2o3b2obob2o3bob2o2b5o$bo6bobo2b
ob2obo3b3obo2b5o2b5ob2obo2bo2bob3obo3bobo$bob2ob2o4bo7b2ob4o3b3o2b4o2b
2obo2bo4bob3o2b5o$bo2bobo2bobob4obob2ob5o2b2o2b2o2bo3bo2b3o2bo3b6obo2b
o$bo2bob3ob4o2bobo2b2obo3bob3o7bo4b2ob2o3b2obob3o$b2ob3ob3o2b6o4b5obo
2b2o4b2ob4o3bo4b2ob2o3b2o$2bo6bo4b2o2b4ob2obo4bobo3b6o2bobo2bobobo3bo
b4o$b5o2b8o3bo2bob2ob5o6bo2bo5b4o2b2o3bo2b3obo$bobo2bob5obob3o2bobo5b
obo2b2obo3b5obob2o5bob4obo$bo4b2ob3o4bo3b2obo3bo4bo3b2o2b2obobob3ob2o
2bo2b2o2b4o$3bo2b2ob2o2b2ob2obob3o2b2o3b4o5bob2ob2obo3bobo2bo4b2obo$5b
o2bob2ob5o6bo4b2obob3o2bo2bo2b3o3bobobob2ob2ob3o$4bobob4ob4o2b6ob4obo
3b2obob2o6bo2bo2b2o2bobobo$3bob2obob2o2b2o6b6ob2o2bobob2ob2o4b2o3b2ob
3o3bobo$2b2o2b2o5b2o4bobo2b5obo6b2obo2b2o4bobo3bob2o2bob3o$3b5ob2o3b2o
bo2bo2b2ob3o2bobo8b2o3b3obo4b4o2b3o$b4ob6obo3b2obob2obob4ob5obo2b10o4b
ob9o$2b2o2b2o2bo2b2obo3bo2bo3b2o3bob2o3bob2ob2obo2b4o2b7o$3b3o2bo4b2o
bo2b2ob4o2bob4obo3bobob3o2b2o4b3o3b3ob2o$2b2obobobob3o4b4o3bo3b2obo3b
2obo2bo3bobob2o3b2o2b3obobo$6bobo3bo4bobob5o2b2o5b3ob2o5b4o2bob2ob2ob
4o$4bob2ob2o3b2ob3o3bo3b2obobo5bob4o5b3o2bo2bob2obo2bo$b2obobo4bo2bob
4ob3o2bo2b5o2b3ob3o2bo2bo2b3o4bobo2b2o$2bo2bo3b2ob5o3b2obo2b2o3b4o2bo
bobo2bobo3b2obo4b2obob2o$bo2b2o2b4o2b3o3b4ob6ob2o6b6o2b4o2b2ob3o2b2o$
4bob4ob4obobo4b2ob3o2b2o3b3ob3obo3b2o2b2ob4o2b3o$5b2o4b2obo2b2ob4obo6b
5o2b2obob2ob3o6bob3o3b2o$5bo5bob3o3bobob2obo2b3ob2o6bobobo2b4o4bo8bo!

edit2:
good rule to play around in

Code: Select all

x = 66, y = 39, rule = M15,9,6,3,6,5,0,0,9,0,10,0,12,0,0,0
$bo2b7o10b3o4b2obo2b3o3bo4b2obobo2bo3b3o3b3o$bobo3b2obo4bo2b8o2b2ob5o
2b2ob2obob3obo2b3o3b3ob2o$2b3o2bob2ob2ob2o2bo2b2o3b2ob4ob4o4bo2b3o2bo
2bobob3ob4o$bobob2o4bo2bob2o2bobo2b2o2bobob3o2bobo4bo2bobo2b2o3b5obo$
3bobo6b2o4bo4b3o3b5o3bobob2o2b2o4b5obo3b2o$b2o3bobo3b3obo3bob6o2bo3b2o
bo3bobobobob6o2b4obo2bo$4bo2bo7bo5b2o4b3o2bobo2bob2o2b2obob2o2bo2b2ob
3ob3o$b4ob2ob2ob2obo2bob2ob4ob4ob3ob3ob7obob3obo3bo$3bo2b4o6b3o3bo3b3o
bo3bo2b2ob4obo3bobobobobo2bobobo$bob2ob6o5b3o3bo2bo3b6obo3b3o5bobobob
3obo2bo2bo$4b2o2b3ob3o5b3o4bobob3obo3b2o3b2obob2o3bob2o2b5o$bo6bobo2b
ob2obo3b3obo2b5o2b5ob2obo2bo2bob3obo3bobo$bob2ob2o4bo7b2ob4o3b3o2b4o2b
2obo2bo4bob3o2b5o$bo2bobo2bobob4obob2ob5o2b2o2b2o2bo3bo2b3o2bo3b6obo2b
o$bo2bob3ob4o2bobo2b2obo3bob3o7bo4b2ob2o3b2obob3o$b2ob3ob3o2b6o4b5obo
2b2o4b2ob4o3bo4b2ob2o3b2o$2bo6bo4b2o2b4ob2obo4bobo3b6o2bobo2bobobo3bo
b4o$b5o2b8o3bo2bob2ob5o6bo2bo5b4o2b2o3bo2b3obo$bobo2bob5obob3o2bobo5b
obo2b2obo3b5obob2o5bob4obo$bo4b2ob3o4bo3b2obo3bo4bo3b2o2b2obobob3ob2o
2bo2b2o2b4o$3bo2b2ob2o2b2ob2obob3o2b2o3b4o5bob2ob2obo3bobo2bo4b2obo$5b
o2bob2ob5o6bo4b2obob3o2bo2bo2b3o3bobobob2ob2ob3o$4bobob4ob4o2b6ob4obo
3b2obob2o6bo2bo2b2o2bobobo$3bob2obob2o2b2o6b6ob2o2bobob2ob2o4b2o3b2ob
3o3bobo$2b2o2b2o5b2o4bobo2b5obo6b2obo2b2o4bobo3bob2o2bob3o$3b5ob2o3b2o
bo2bo2b2ob3o2bobo8b2o3b3obo4b4o2b3o$b4ob6obo3b2obob2obob4ob5obo2b10o4b
ob9o$2b2o2b2o2bo2b2obo3bo2bo3b2o3bob2o3bob2ob2obo2b4o2b7o$3b3o2bo4b2o
bo2b2ob4o2bob4obo3bobob3o2b2o4b3o3b3ob2o$2b2obobobob3o4b4o3bo3b2obo3b
2obo2bo3bobob2o3b2o2b3obobo$6bobo3bo4bobob5o2b2o5b3ob2o5b4o2bob2ob2ob
4o$4bob2ob2o3b2ob3o3bo3b2obobo5bob4o5b3o2bo2bob2obo2bo$b2obobo4bo2bob
4ob3o2bo2b5o2b3ob3o2bo2bo2b3o4bobo2b2o$2bo2bo3b2ob5o3b2obo2b2o3b4o2bo
bobo2bobo3b2obo4b2obob2o$bo2b2o2b4o2b3o3b4ob6ob2o6b6o2b4o2b2ob3o2b2o$
4bob4ob4obobo4b2ob3o2b2o3b3ob3obo3b2o2b2ob4o2b3o$5b2o4b2obo2b2ob4obo6b
5o2b2obob2ob3o6bob3o3b2o$5bo5bob3o3bobob2obo2b3ob2o6bobobo2b4o4bo8bo!

edit3: wried rule

Code: Select all

x = 140, y = 114, rule = M15,6,9,15,9,15,0,0,6,0,15,0,15,0,0,0
$b4ob3ob2obobobobo2b4obo3bo2bobo2bobo2bobob2o2b4ob2obob6obo2b2ob2o2bo
2b2ob2o3b10o4b2obobo4b2ob2ob2ob2ob4ob7o$2b2o4bob2o2bo4bob2obob4o2b3o3b
o2b3ob6obo2b2obobo5b4o5b2ob3o2b2o4bobo4b3o4b4o2bob2o2bo6b9o2b2o$b2obo
3bobob5o7b3o2bobo7b4obo4bobob3ob5o2b2o3bo2b2o2b3obo3b2o2b3o3bobo2bo5b
obobo2bo2b3o2bobo2b3o3b3obo2bo$bo4bobo3bo6bo2b6ob3ob3obob4o3bob4o2bo4b
3o2bo2bob2o8bobo2bo3bo2b2obo2b3o2b4ob3o2bobob3o4bob6obobob4o$b2ob2o4b
3ob3ob3ob2obob2o5bob2o2bo2b2obo4b3ob2o2bob2o4bo2bob2o3bo2b6ob2o2bo3bo
2b3o3b3obo2b2o2bob4ob5ob3o2bo2bo2bo$bobob2o5b5ob2ob4obo6bob3o2bo6bob4o
5b2ob2o3b8ob2o3bob3obob4obobo2bobo3bo4bob2o2bobob6o2bo3bobo2b2o$bobo2b
obob5o4bo3b8o4bob3o2b2o2bobob2obo3bobo3b3o2bo3bobo3bob3o4bo3b2o2bob8o
3b4obo2b3ob4o2b3o3bo4b2o$b2o3bob2o5b2o2bob2ob2o2b2obobobobo2bo2bo5b6o
2bo2bob3o2bo2b2o3b6obob2o4b7obobob2ob2ob2o4bo5b5o2bo4b2o3b2o$3b3obo2b
5o2b2ob2ob3obo3b3o3b2obob4o3b6obobo2b2obob3o2b2ob2obo3bo4bobo2b2o2b3o
bobo2bo5b2o2b3obobobob3o4b4o$2bobo2bobo4b3o2b2obo7b3ob7o4bob3ob2obo2b
4obo2bo2b2ob2o4b5o2bo3b2obo3bo2bob6o6b2ob3obo6b3o2bo$3b2o2bob2ob6o2b4o
2bo4b2o3b3obobo4bobo2b2obob5ob2ob4o2bobob4o3bob5o4bobobob4ob4ob5o3b4o
2bob2ob2obo2b2o$3b2o2b2obobo2b2ob3o2b2obobobo2b9ob3o3bobo5b3obo2bo2bo
bobob2ob2o2b4obob3o4bo4b4o2bob3o3bo4bo2b3ob2o4b3obo$2bobob2o5b2obo3b2o
b4o2bo4bo2bo2bobo2bo2b2o2bob3o3b2o2bobo2b4obo3bob4o3b5ob3obobobob3ob4o
b2o3b2o2b2o2b2obo2bob3ob2o$2b2o4b3ob2obob3o5bo2bobo2bob2obo3b3obobobo
2bo2bo4bob3obo3b2obo2bo3bo3bo2bobo3b2obobob3o2bobo2b8o2b2ob6o2b2o2bob
o$bo4b2ob3o3bobobob3o2bob3ob3o2bobob2ob2ob2o2b4o2b5ob6o2bo4b2ob2o2bob
obo2bo3b2obob3o2bo2bob2obob2o4b5o2b2o2b2o2b2o2bo$4b2o5b5o3b4obo3b2obo
4b2ob2o4b3o3bob3o3b2ob2o4bobob3o4bo2b4o4b2obobob2o3b3o4b2o6bo2bobo2b3o
4b4ob3o$bobobo3b3o4b2obob2o2b2o3bob3obob2o2b2o3b2o7b3o8b2ob2o2bob3o2b
o7bo2bo4b3o3bo2bob4o3bo2bob3o2bobob2ob2o2b2obo$bo3bobob2o6b5ob2o4b4o2b
2o6b2o3b3o2b2o2b2ob2obo2bobobo2bo4bo2bob2ob3obo2bo5bo3bobo3bob2o2bo2b
2o3b2o3b4o2b2o$2bo6bobo4bo2bo4bo2bo2bob2o2bo2bobobobob2ob2o2bob4obobo
4b2ob2ob2ob7o4bo2b2obobobob3o2bo3bo2b2o3b3o2b2ob2o4b2o2bo2b2o$b2o3bob
2obo4b4o3b2o2b2o2b2o3b3ob3obo3b2o2bobobobo3bob2obo3bob4obob3obo2bo2bo
3b3ob2ob2o2b2o7b3obo2b3o2b6obobobobo$bo2bob2o2b2o2b4o5b3ob3o2b2o5b6o2b
2o4b2o2bo4bo2bo3bob2o2b2o4b4o3bobo2b2obobob2obob2o2b2ob3o2b2o3b5ob4ob
obobo$5bobo2bo2bob2ob2obo2b5o2bobo2bob2obob3ob2o5bob2o3b2ob4o2bo4bob3o
b2ob4ob2o2b6obo4bo2b2ob2o4b2o2bobob2o3b3o6bo$b2o2bo3b2o2b3o2bobobobob
3obo2bob2obo2b2obo7b2o2b4obo2b3o4b3obob2ob3ob3ob2ob4ob2obobo3bobo2b2o
2b2o2b2obo2bo3b4ob2o2b3o$b2ob3obo5bob8ob4ob5o2b3o3bobob2o3b2o4b3o6bob
14obob2ob2ob2ob2o2b3o3b2o2b3o2b10o3bobo2bo4bobo$bobo2bo3b2ob5ob2obob3o
b3obobo2bo2b2obob3o5bo2b2o3b3obob4ob2o2b2o3b3o4bob5obob3ob2obobobo2b2o
bobobobobo4bo7b2o$b3ob6o2b2obobobobob4obo2b3obo5b3obo4bobobob2ob2o4bo
bob2ob2o2bobob2obob2o6b2o2bob2o4b3o3bob3obobo3bo2b2o4b2obo$bo4b2ob3o4b
2ob2o2b2obo2bob2o4bob3ob2ob6o4bo2bob4obobob2ob3o7bo2bob3ob3o2b2ob2ob2o
bobo3bob3ob5ob4ob2obob6o$9bob4ob3o2b2ob5obo2bobo2bobo2bob3obo9bo3bobo
bob9obob2ob2ob2ob3ob3o2bobob5o2b4obobo5b2ob3o2b3o2b2o$2bo2bo8bo7b2ob2o
6b2obo3bob2o2b3o2bob2o4bo2bo2b2ob3o2bobo2b2o4b3o3b4obo5b3obo2b3o3bo2b
o2b2ob2o2b2o2b3obob2o$3b3obo2bobob3obo2b2o2b3obo3b4o4b2o3bob3o2bo6b2o
5b4o3bo4b2obobo4b3ob5obo7bo2b2o5bob2o3b2obobo3b2obo$2bob4o3bo2b3ob4o2b
5obob3o4b7ob3ob2o2bo2b4obo2b2o7b5ob3o2b5o4b2ob3obo3bob3o3b2o2b2obob6o
bobo2b4o$2b2o2b4obobob4o2bob4o2b5obo3b3o4bobo5bob11ob3o3b2o3bo4b3o2bo
2b2o2bo3b2obob3o2b2obob3o2bob2ob2o4b2o3b2obo$bo3b3ob5o2bo4b3ob2ob5o2b
5o2b2o4b2o2bobo3b2o2bob4o4b2obo4bo3b3obobo2b3ob3o4bobo2b6obo6bob3o4b2o
bobo$2bo2bo2b3obo3bobo3b3o4bo2bo2bob3o6bo3b2o3bo2bo2bo2bo2bo3bob6o3bo
2bobobo2bobo2bo4b2ob2ob3o4b2o2bobo5bo2b3o4b2o$bobo7b7o2bobo2b2o4b2obo
bob5o2b3ob2o3bo3b3o2bob5o5b3obo2bo4bo3bo2bob4obobobo3bob4obo2b2o2bo4b
obob3o2bo$bo2bobob2obobo2b2obobobob3obo2b2obo6bob2obo4bobob3o4b5o6bob
obobo3b2o3bo3b4ob3o3b2obob2obob2obobob2o3b2o5b2ob3o$b3ob2o3b2ob5ob2ob
o3bobobo2b3o3bo4bo2b4obo2bo4b3obob2obo2bobob2o3b2obobob2o3b2o3bo2bo2b
o3bo2b2o6b4o3bo4b3ob2o$bo2bo2bo4b3obo3bobobo2b2o3b3o2b2obobobobob9o6b
ob2ob3o3b5obo3bo2b6ob4o2bo2bobo2bobobob2ob3ob2o2b2obo2b2o3bobo$b2ob3o
2bo3bobo3b2o5bo3b2obobo4b2ob5ob3o2b3ob3ob2o3b7o2bob2ob2o4b2obo2b2o3b2o
b2obo4b2o3b3ob2o3bob3ob4o2b2o$bobobob2ob5obobo2bob2ob4ob4o2b2o4bo4b2o
5b2ob4ob2o3bo3bobo4bo3b3o2b2o2bo3bob2ob2ob2o3bobo2b3ob2o2b2obob2ob3o3b
4o$bo5bo2bo6b2ob2o3bob2obobobo7bob3ob2ob3o3bobo2b2ob6obobo6bob3o6bobo
2bob2obob2o2bo5bo4bobobob4o6b2o$2b2obob6o4bo3b13o3bobobob5obobo2bobob
obob2ob7o7b6ob3o2b2ob2o3bobo2b2o3bo2b2obo2bobobo2b2o2bob2ob3obo$4b5o4b
3ob2o4bob3o3bob5obo3bo3bob2o2b2ob2o3bobo2bo2b2o3bob2obobo3bob2o2b3obo
3bo2b2o3b2ob2o2b5obobo2bo2bob6o3bo$6b4o4b4o2bo3bo2b2ob2ob5o3bobo3b3ob
2obo2b4o2b3obo2bobo2bo4b2o2b9o2b4o2b3ob2o3b2o2bo2bo3b2ob4o2bo2bobob2o
$4b4o2b2o2bob3obob2obobo2b4ob4ob2o4bo2b3o6bo2b3obo3b2ob2o4bobo2bob3o2b
o3bobo3b4o2b4o3b3obo5b4ob2obo4b2obo$bob2o3bob3o9b2o2bo2bo3bo4b3obo3b4o
4b3o2bo3bo2b3obob2ob2ob3o2bob2obobob4obobob2o2bobo2bob2o3bobobo2bob2o
2bob2o$bo3bo2b2o2b3obobo2b2ob3o2bo3bo9b2o3bo2b7ob2ob5o4b3ob2ob2o4bo3b
2obo2b2o3bobob2o2bo4b4o6b2o3bob2o2bob2o$2b4o2bob4ob3ob2obobob2obo2b2o
2bob4o3bo2bo2b6ob5o4bob5obo4bob2o2b3ob2ob2ob4obo2b3obob3o2bob4ob3o2bo
b11o$2b4obob3o3b4o5b2o3bob2obo5bobobobo4bobo3b2obobo2bo7b2obob3ob2o3b
5o2b2o2b2ob2ob2o2bob2o4b4obob3o2b3o5bobo$b6obobobo2bob2o2bo3b2o7bo3bo
bo5bob2ob3ob3ob3o3b3ob2obob3ob2o2bobo3b2o3bo2bo2bob2o8bob2ob2o3b4o4bo
bobobo$b4o3b2o3b2ob2ob2obo2b2obo3bo2bo2bobo2b4o3b2ob2o3b2ob4o3b7obob4o
2b3o3bob4ob3o3bo5b3ob2ob4ob2obo2b2o2b5o$bo2bob3ob2o4b2o4bob3ob2ob2o2b
2o3b3ob3o2b4obob2obobo2bob3obo2b5ob3obo3bo5bobobobobob3o2bo2b2o5bob3o
2b2ob2obobob2o2bo$bo2bo2bob3obob2o2bo5b2o3b2o2b2ob2obob3obobo4bob2o2b
ob2o4bobo2bob5o2bob2o3b2ob3obobo2bob3obob2o2bob3ob2ob3ob2o2b3obobobo$
b4ob2o2bo2b4ob2obobob2o2bob4o2b2o2b2o5bobobo3b3o2bob3ob3o3bobobobob6o
b4o2b4o2bo2b2o3b3obob3obob4ob2obo2b4o4bo$2b3o3b3ob3o2b2ob3ob3ob2obobo
2bo2bob3o2bo3b2obobobob3o2bobobobo2b2ob2obo2bobo3b3o2b3o2b2obo6b4o2bo
b2o2b3obo2bo2b2o2b2o$b2o2b2obob3obo2b2ob4o2bo2bobobobo3bobo2b2o7bo2bo
2b2obobo3b2ob4obo2b2o2b2o4b4ob2o2b3o2bo2b2o3b6obobo2b8obo2bob3o$2bo2b
2obo3bo3b6o11b4ob2obobobo2bobobobo2bob3ob2o3b4obo2bo2b3o3bo5b6o2bo5b3o
3bobo3bo4bo4bob2o4bo$3bob3ob2obob2o2b3obo2bo3bob4ob2ob3o2bobo2bo2bo2b
2o2b5o2bo2bob2o3bobobo2b3obo2bobo3bo2bo2b4o4bob3ob3o3b2ob3o5bob2obo$b
ob4obob2obobobo8b3obobo2b2o3b4ob4obo3bob2o4b3ob3obo2bo2bobo3b4o2b2o2b
2obo4bob3o2bobo2bo5b3o2b2obobo4b7o$bob2ob6o2bob5obo3bo3bobobob3o4bo2b
2ob2o2bob2obobo5bobobo2bobo3bo5b3o2bo4bobo3b4o2b5o3b2o2bobobo4b5ob2ob
2o$2bobo3b4o2bo8bob4o3bobob2obo2b2o2bob2o2bob2ob2o2b2ob3o3b2ob2ob2o3b
obobobob2o6b3o2b2o2bo2b2ob3ob4o2b3o2b7obob3o$b2obob4o2b4obob5o2bo3bob
o2b2ob2ob4ob2o4b5obo4bobo2b7o2b2obob3ob3o6b3o2bo3b2obob3obo3bobob2o3b
2ob2obo4bobo$2b2o8bob2ob4obo2b2o2b11o3bo2b4ob2ob2ob4o2bob3ob2o3bo3b2o
bo2b2obo2bo2b4ob3obo2b2o2bobob2ob3obo3b2o2bob2ob4o2bo$6bo2b2o2bo4bobo
b2o3bo5b2obo4b3o5b9o4b2o3b2o2bobob2ob5o3bo2b2o3bobo4b4obob6ob4ob2ob3o
2b2o2b2obob3o$bo3bobo2b6obob2obob2o2b4o3b3ob4obobo3bo2bob3obo2b9o7b2o
6bob4o2bo7bob2o5bob2ob4o4bobo3bob5obo$3bo2bo5bo5bo6b2obo2bob3obob2ob3o
b2ob2ob2o5b2ob3obo6bo3b3o3bobo3bo3b2obob3o2b7o2bob2ob4o3bobobobobobo2b
2o$2b2obo3bo5b2o2b2ob4ob4o2b4o2bo2b3o2b4o5bo4bob2ob2obobo3bo2bo4bob2o
3bo5bobobo6bobo2bobob2ob2obob2obo3b2o4bo$4b6ob3ob6ob3obobobob2ob2o3bo
bobo2b2obobob2o3bo3b2o2b6o5bo2bobobo6b3ob3obob3obo3b2obo6bo6bo2b2obo2b
4o$3b5obob2o5b3o3b2obobobob4o2b2obo3bo2bob2o4b2obobob3obo2b2o2bo2b6ob
4obo2bobo2bo3b2o2b4obo4b2ob3ob9ob2o4bo$b3o3b3o2bo3bob2o2bobo6b6ob2obo
2b2ob4o4b3ob4ob2obobo4b2o3bobo4bo3b3obob2obo2b2obo4bo2b2o3bo2b3o3b2ob
obo3b3o$b3obob7obobob3o4bobo2b2ob2ob2o3b2o2bob3obo4bob2ob6ob3ob3ob2o2b
3o4b4o3bo2b4ob6obo3bo2bo5bo3bo2b2o4bob2o$b5o3b2obo5b2o3bo2b3o2b2o2b2o
2b2ob3ob2obo2b2o2bobobo2bo2bob3o2bobobobobobo5bo2b3obob2o3bo2b2ob3ob2o
3b3o5b3obobo3bo2bo$3b2obo5b2o2bob2o4bob2o4bo2b3o3b2ob2ob3o5bobo7b3o6b
o2b2o5b2obobobo2bo6bob2obo2b3ob2o2b2o2bo4b4o2bo5bo$bo5bo5bobob2obo2b3o
b5o4bobob2obob2obobob5obob2o2b4o3b3obo5bobo4bo4bobo2b2ob2o4b2obob4o2b
3obo2bo2b4obobob2o$5bob3obobobo5bo2bobob2ob2o2bobo2b2o4b2ob2o3b2o2b3o
b4ob2o2bobobo6bo6bo2b3o2bo2b4o2bo2b2obobo3bo3bo3b5ob2o4b2o$2b3o5bobo2b
2o6b4o4b7o2b3obobob4ob3o6bo2b3ob2o4bob3o4bob2o2b6o2b2o7b2o4bobobo4b3o
bo3bo4bob2o$2bob2o2bob2ob9o4b2obo3b2obob5o5bob2o2bo8b3o3bo2bo3bo2b2o3b
o6bob3o2bo4bo6b2ob6o4bob6obo2bo2b2o$b2o2b6o6bobo2bo2b2o2b2obo3bo2bobo
3b4obo2b5o4b2o2bo3bobo3b11ob2obo4bo5b2obo9bo3bob3o2bob6o2b2obo$bob3o5b
2o3b2ob4obo3b2o3b3obobob3ob5o3bobobobobo6bob3o4b3obo4bobobo3b5o2b3obo
bo2bo2bo2bo2bob2o2b3ob3ob2o4bo$b4o5b2obo2bob2o3bobo6b2o6bo2b3o2b4o5b5o
b2ob3ob4o2b2obob2ob2ob2obo6b3o3b3o2bo5bo2b2o2b2ob2o4bo3b3ob2o$9bobo2b
3o4b2ob3o4bo3b3ob2o4bo2bo2bo3bo3bobo2bo6b4o2b2o2b2o2b4o2b2ob2o3b4ob3o
4bo5b2o2b2obo2bo4b3o3b2o$b2obo3bo3b5ob3obob2o2b2o3bo2b4ob2obob2ob2o2b
4ob2o2b7o3bo3bo4bobo2b3o3b2o2bobo2bob2obo2b2o3bo6b3ob4obo5b4o$2bo4b5o
2bo2bob2ob3o10bo2bo2b3obobobo3bobo3b2o2b2ob4o2b3ob2o2bo3bo2b2o6bo2bob
ob2o4b5obo3bo2b2ob2o4bobobo$bob2obo2bo2b2ob5o2bo2bobob2ob2o2b2o2b3obo
4b2obob4ob2o4b2o2bobob2ob2o2b2o3bo2bob2ob3ob4ob4ob5o2bo2b5o3b2obo2bo2b
2o3bo$bobob2obob3obobob3ob2obo4b2obo2bo2b2o2b3obobobo4b2o2bo2bo2bo3bo
b2o2b2obob7o2bo2bo4b3o2bo5bob2ob5ob2ob4obo4bo2bo2bo$b3o2bo2bob2o3bobo
bobob4obobobo4b2o3b3obobo2b2ob3o2bo2b3o4b4obo2b3o2bobo2bo6bobo3b2ob2o
b2ob3ob2obob2obobo2b2ob4ob3obo$bob2o4b2o5b2ob2o2bob3ob3o2bo2bob2o2bob
ob2o2b4obo2b3ob2obo4bobobo3b2ob2ob4obo4b3o2bo4b2o12bob2o2b2obo2bob2ob
obo$b2ob2o3bo3b5ob2obo2bobo2b2ob2o4bo5bob2o3bob2o2bo2bo2bo2bob2ob3obo
b4obob2o2bo2b4ob2obob2obob4ob2o3bo4b2o3b3o3bo$bobobo2bobobo2bo2b6o3bo
b5obo3bobo2b2obo2bo2bo3b5obo3b4o2bob3o2b2ob2o4bo4b2o2bob6o2bo2b2ob9o3b
o4bo2bob2o$b2o2b2o2bo9bo2b6o3bo2bobo3b3obobobo3b3o4bo2b7o2bo2b3o2bo5b
o4bobo9bo7b3o3b8o2bo2b2o3b2obobo$bob4o2b5obo2b3obo2b2ob2o2b2ob2o2bobo
b7obobo4bo2b2obob5ob3ob7ob2o2b5obobob3o2bo5bob6obo2b2ob2ob3o3bo2bobo$
3bo2bobob10o2bo4bob2o2b2o2bo2bob2ob2o2bo2b2o11bo3b2o4bo5bo2b2obo2b4ob
3o3bo2b2o2b4o7b3o3bob3o2bo2bo2b2o$bo3b2ob3ob2obob2obobo2bo3bob2obobo4b
o2b2o2b2o2b2o3b3o2bo5bobob4o2bob3o2b3ob4o3bobo3b2o2bo4bo2b2o2b5obo4bo
2b2obo$5b2o2b3obo3b2o2b4o4bobo3bob2obob2obo2bo4b2o2b3obob2ob4obob2obo
b3o5bobob4obo3bobo3b4obob2ob3o3bob2o2b3ob2o2bo$bob3o2bo2b2o2b6obo2b2o
4b6o4bob2o2b2o3bo3b4o5b2obo2b2o2bobob2ob4o3bo2bob4o5b3ob7obo6b2ob2o2b
3o2b3ob2o$b2obobo2b4o2bob3o5bobo7bob4o2b3ob2o2b2o2bob3o2b2obobo3b3obo
2b2obobobo2b7ob2o2b4o5bob2obo3b3o2b2o3bobob2o3b2o$bo3b2o2b4ob3o3b2o2b
2o3b2o3bobo2b2o2bob7o4b5obo3b2o6b2o4b2obo3bobob2obo2bo3bo3b2o3b3obobo
b6o2b5o3b2obo$4b2ob6o3b3o3bob4ob4ob2o7bo6bo3b2ob3o2bo3bo2bo6b3o3bob9o
2b2o3b2o8b2ob2o2b3o2b4o4b3o2bobobo$bo5bob6ob2o2bo2bobobo2b9ob2ob2o2bo
7b2o2b3o8bo2bo2bob2o3bo2bob6ob2o2b2o2bobobobobob3o2bo3bobob2o2b3o2b3o
bo$bob2o2bo3bo2b4ob2obob2obob4obobo2b3obo2bobobo2bobob3o2bo3b3o2bobo4b
3ob4o5b3o2b3ob2ob3o3bo2b2o2bobobo2b2o2bo4b3ob2obo$4b5o2bobo2bobo3bobo
3b2o2b6o3bob3o3bob5o2b2ob2o2bobob2o4bo2b2o2b3ob7obo2bob2o3bo2b3o2b3o3b
2ob3ob2o2bob3obob3o$2b2ob2o2b2o2bob2obo2bobob4ob3ob10ob2obob3obo2bobo
3bobo2bo2bob2o3bo2b3ob2ob8o2b2ob2ob2o2b2o3b2ob2o2bobobob2ob2obo3b3o$b
o2bobob6obobo2bo3b3o2bob6o3b5o3b3ob3o2b4ob3ob3o2bo2bobo3bob9o2b3o2b2o
4bo4b2obo3bob3o3b3obob2o3bo2b2o$bo3bob2ob4o3b2ob3obob2obo10b3o2bo3bob
2ob3o2bo4b2obo2bob3o2b4ob4o12bob3obo2b2obobo2bo5b4obob2obo6bo$2bo3bo3b
o3b10ob2o5bobob5o2bo2bo2b2o3bob3o2bo9b2o5b4o2bo2bo3bobo3bobobo4b3ob4o
b2ob5o2b2o4b2ob5o$4bo2bo5bo2bo2bob2obobo2bo2b3o4bob2obob4obobo2bob2ob
o2b4obo3b2ob2o3b2obo2b5ob2ob3obob4o4b2obo2b2obob5ob2o2b2o3b2obo$2bo2b
2o3b2ob6o6b2obobobo2b3obobob3obo3b3o6b3obo3bo2b3o2b4o6b4obo2bob2o4b2o
bobo2bob8obo3b2obob3obobo2bo$2b2ob3obobo2bo4b2ob2o3bo3bobob2o2b2obo4b
o2bobobobobobo4bobo3b2o3bo2b4obo2bo2b2o2bobo4bo5b2o3bobobob2ob2o3bob2o
bo5bo$bo2b7ob2ob2ob2ob2ob4obo2bo3bo3bo2b2obob3ob3o3bob2o2b2ob4o2bo3b2o
2b3o3b2o4bo2b2o2b2obo3bo3bo2b3o2bo2b6ob2o4b2o$2bo5bobob2ob2o2bobo2bob
obo3bo3bob2obo2b4o4bo2bo2b2o2bo2b5o3b3o2bo2bo3b3obobob3obob3o2b5ob3o2b
2o4bo2b5ob2o4b2o$bo4bo3b3o3b4obobobo2b2obob2o2bobo2bob2ob4obo3bobo2b3o
b14o2bobo2bo3bob3obo2b2o3bo6bo5b2o2bobo2b5ob3ob2obo$4b2ob3o5b3o3b3o2b
ob2o2bo5bobo5b2ob2o5b2obo3b2o3b4o2b4o3b2obob2obo3bobob3obob4o3b2ob3ob
3obobo2bo6bobo$b6ob3o2b7ob3o2bobobob3ob4o4b3o4bobob2ob5ob5obo2bo2bo4b
o3bo2b3ob4o3b4ob2obobo4bo2b2ob2o2b2o4b5ob2o!

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Re: Margolus-neighborhood rules