Margolus-neighborhood rules

[muzik]

A funny looking explosion:

Code: Select all

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

The "inverse" family of the oscillator from before isn't time symmetric:

Code: Select all

x = 17, y = 2, rule = M0,8,4,3,2,5,6,7,1,9,10,11,12,13,14,15
bobobobo2bobobobo$bobobobo2bobobobo!
[[ GRID ]]

[PHPBB12345]

Usage of @TABLE Margolus neighborhood

[unname4798]

Rule I randomly discovered:

Code: Select all

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

It produces beautiful patterns from 2x2-block of state 1 cells:

Code: Select all

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

[muzik]

Rule I randomly discovered:

Identify's period maps give interesting checkered patterns if we run this on a torus.

Code: Select all

x = 30, y = 30, rule = M0,14,13,3,11,5,6,8,7,9,10,4,12,2,1,15:T30,30
ob2o3b3obo3bo3bo3bo2bob2o$o2b3obobob3obobobo4b2ob2o$b2obob6o2bo2bo2b2o
2b5o$ob2ob3obo2b2ob3obo2bobo2bo$2obo3b2ob3o2b3o3bobo3bo$b2obob4o4b4ob
ob3obob3o$2b2ob2o3b3o6bobob7o$o2bobob3obob3ob3obo2bo2bo$2ob4o2b2ob2o4b
obob6obo$bob2obo4b4o2b4o2b4obo$o2b5o8b6ob2obo2bo$2bo2bo6b2ob2ob2ob5ob
3o$4b2o5bo5bo2bo2bob5o$2bo2b3obobo2b3o2b2obo2b2obo$bo4bo2bob3ob2obobo
2bob2ob2o$o3b2o2b2ob3obobo2bo2bobo2bo$b2o4bob2obob3o3b2ob2ob2o$ob3o4b
2obo4b3o3b2o2bo$b2obo2b4o2b3o2b4o3bobobo$b2o2bo2bob2o3b2o3bobobo4bo$b
3obo3bo2bo2b3ob4o2b2o$2o3bo4bobo4b3obob7o$2obob3ob2obob6obob2o2b2o$b2o
3b2o3b5o4bo3bob2o$ob5o2bo3bo2b2o6b3ob2o$obo2b3obob6o2bobobo3bobo$2o3b
2o7b4o2b3o2bo$ob2o2bo2bob3ob4o4b3o2b2o$o2b5ob5o4b4o4bob2o$2obobob2ob2o
b3o2b3o3b3ob2o!

[muzik]

This rule has tiny oscillators that even identify cannot currently evaluate the periods of:

Code: Select all

x = 7, y = 6, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
b3o$2bo$bob2o$3b3o$bo2b3o$bob2obo!

This is a time symmetric p364712:

Code: Select all

x = 6, y = 6, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
b3obo$2bo2bo$bob2o$3b2o$bo2bo$bob2o!

[Haycat2009]

Why are margolus rules usually reversable? Also, what is the notation for margolus rules?

[azulavoir]

Answering these in reverse order makes more sense.

what is the notation for margolus rules?

The one LifeViewer uses, at least, is M then 16 comma-separated numbers. Each of these represents one of the 16 possible arrangements of four on/off cells within the neighborhood, and their order represents which arrangement transitions into that one. So the first entry (always either 0 or 15 for well-behaved rules) dictates what a group of four empty cells becomes, the second what a single cell in the top left of the Margolus square becomes, until the final dictates the fate of a group of 4 alive cells.

Why are margolus rules usually reversable?

If every number is used exactly once, then you can reverse the rule by taking every input to output function and reversing it. So if the rule is M0,2,4,1,3... then since 1 goes to 2, 2 to 4, 3 to 1 and 4 to 3, you could reverse it by making 2 go to 1, 4 to 2, 1 to 3 and 3 to 4 - M0,3,1,4,2...

[muzik]

Even more tiny, incredibly high period objects from the rule I mentioned earlier. Challenge question: what is the smallest thing from this rule that LifeViewer cannot identify?

Code: Select all

x = 7, y = 6, rule = M0,1,2,3,4,10,6,11,8,9,5,13,12,14,7,15
$3bo$bobobo$3bo2bo$b4o$bob2o!

This is 7x8 and Identify can't find its period, maxing out at 23 seconds or so:

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$5bobo$bob3obo$5bobo$4bo!

Interested to see if this record (time, or bounding box) can be broken.

[rowett]

This is 7x8 and Identify can't find its period, maxing out at 23 seconds or so:

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$5bobo$bob3obo$5bobo$4bo!

LifeViewer Pro finds it in 157 seconds...

identifypro.png (107.97 KiB) Viewed 766 times

[muzik]

Very interesting period map:

Code: Select all

x = 5, y = 34, rule = M0,2,1,12,4,5,6,7,8,9,10,11,3,13,14,15
$bo2bo$2b2o3$bo2bo$2b2o3$bo2bo$2b2o3$bo2bo$2b2o3$bo2bo$2b2o3$bo2bo$2b
2o3$bo2bo$2b2o3$bo2bo$2b2o3$bo2bo!

LifeViewer Pro finds it in 157 seconds...

An obvious, if delayed, question arises: how do I get my hands on this?

[breaker's glider gun]

Some of the patterns packaged with MCell:

Code: Select all

x = 5, y = 36, rule = Rotations
obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obob
o$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$ob
obo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$obobo$
obobo!

Code: Select all

x = 289, y = 284, rule = M0,2,8,12,1,10,9,11,4,6,5,14,3,7,13,15
$83b2obo$86bo$86bo$84bo10$158b2obo$161bo$161bo$148bo5$144bo$151b2o$145b
o$153bo2$142bo9bo2$150bo$145bo2$146bo15bo$154bo$151bo$155bo7$157bo$152b
o$151bo2bo$154bo$147bo7bo$158bo$156bo7$151bo2$156bo$153bo$150bobo3$152b
o3$154bo3$149bo$152bo2$152bo3$147bo3$150bobo$152bo3$145bo$147bo2$151b
o$149bo2bobo$152bo4$147bo3$148bo$151bobo3bo$155bo2$155bo$153bo2$147bo
2bo5bo5$154bo$147bo2$146bo6bo$149b2o$151bo$148bo3bo$146bo4$149bo3$151b
2o$148bo2$151b2o2$149bo98bo$251bo$145bo105bo$150bo97bo2bo$144bo2bo$147b
o3$149bobo3$150bo2$280bo6bo$280bo$150b2o59bo$127bo23bo$3b2o126bo18bo18b
obo83bo26bo$bo125bo9bo5bo5bo45bo10bo73bo$5bobo49bo5b2o28bo27bo50b2o3b
o9bo13bo6b2o27b2o25bo$5bo55bo17bo23bo24bo7b2o4bo16bo7bobo13b2o9bo3b2o
3b2o4bo20bo50bo$14bo37bo13b2o18bo9bo19bo5bo7bo14bobo5bo23bo5bo9bo14bo
30bo41bo$57bo21bo14bo8bo5bo4bo16bo16bo9b2o48bo10b2o7b2o7b2o17bo3bo15b
o$32bo2b2o38b2o13bo25bo5bo15bo6bo19bobo84bo17bo2bo10bo$29bo13bo50bo8b
o11bo26bo6bo3bo4bo14bo2bo5bo13bo21bo24bo8b2o14bo3bo$14bobo23bo9bo26bo
bo4bo11bobo5bo7b2o14bo5bo3bo5b2o7bo30bo10bo9bo15bo3bo15bo28bo$31bo18b
o4bo13bobo32bobo9bo19bo8bo7bobo2bo34bo2bo13bo16bo4bo14b2o11bo9bo15bo$
51bo2bo11bo8bo22bo50bo89bo$21bo7bo16b2o104bo2bo80bo3bo7bo39bo$30bo13b
obo34b2o$22bo21bo36bo$82bo68bo$79bo$84bo$80bo$77bo71bo$146bob2obo$149b
o2bo2$152bo$146bo3$152bo2$151bobo2$151bo6$157bo$157bo$149bo$149bo4bo$
153bo$148bobo3bo$149bo4bo2$155bo3$151bo$151b2o$154bo6$150bo$153bobo$151b
o4bo$153bo$148bo2bo$153bo4bo6$154bo3$149bo4$150b3o$151bo3$150bo$157bo
4$158bo$154bo$154bo2$151bo2$157bo$155bo$157bo$151bo3bo$149bobo$156bo2$
148bobo$148bo2$151bo2$158bo$156bo2$155bo$157bo$148bo$153bo4bo2$157bo3$
147bo$149bo2bo$146bo$152bo$150bo$147bo5bo$147bo2$156bo$149bobo4$148bo
$152bo$156bo2$155bo3$148bobobo2bo$149bo3$154bo$152b2o2$153bo4$153bo!
[[ AUTOSTART STEP 10 STOP 10000 ]]

[LaundryPizza03]

This skewed Margolus emulator for an anisotropic rule was discovered by domokoa on March 6 at discord:

Code: Select all

x = 15, y = 10, rule = B01e3-ejqr6i7c/S024it
o$3bo7bo$14bo2$4bo7bo$7bo$10bo2$8bo$11bo!

They constructed a c/2d wickstretcher based on it:

Code: Select all

x = 55, y = 20, rule = B01e3-ejqr6i7c/S024it
o$3bo$6bo$9bo$12bo$15bo$18bo$21bo$24bo$27bo$30bo$33bo$36bo$39bo$42bo$
45bo8bo$48bo4bo$51bobo2$49bo!

[b-engine]

The population is conserved, but interestingly the birth plot goes at sqrt scale:

Code: Select all

x = 2, y = 2, rule = M0,4,2,3,1,5,6,7,8,9,10,11,12,13,14,15
1000o!
#C [[ GRAPH ]]

[b-engine]

(Anyone?)
Spaceships of various diagonal speeds spit out from soups, but so far only 1 orthogonal speed had occurred from mega-soups:

Code: Select all

x = 97, y = 5, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$20bo66bo$o4b2o4b3o7b2o7bo9bo10bo10b3o11bo9b3o6b2o$20bo10bo6bobo11b2o
8bo11bo2bo10bo$29b2o8bo11bo11bo11bo19b2o!

[confocaloid]

[...] but so far only 1 orthogonal speed had occurred from mega-soups: [...]

Another (p158 orthogonal c/79):

Code: Select all

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

You'll have to take my word that the following is indeed a soup:

Code: Select all

x = 111, y = 51, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
2o6bob3ob2ob7o2b2obobo4b3o4b2o5b3o2b2o3bobo2b2ob3o2b2obobo4bobobo4b2o
b4ob3obo2bo2bo$bob3o2bob5o3b5o3bobo11bo4bo2bob2obo4bo3bobob3obo2bob2o
3bobo3bob2ob2obo2b8obo2b2o$4bo2b3ob2o6b2o3b6o6b5o2bobo2bobo5bobo2b3o4b
3o4b5obobob3obo2bobo2b4o4bo2b3o$b2o2b2o2b2obo3b3o2bo4bob3ob4ob2ob3ob4o
2b2obobob3ob5ob2o3bo2b2obobo2b2obobobobobo2bo8bo$2o3b2o3bo3bo2b2obo4b
ob2o2bobo2b3o7b2o2bo2b3ob4ob3o3b2o5bo5bob4o6b4obo5bob5o$2obobobob3ob3o
2b4o2b2o2b3ob2o2b2obobobobo2b3o2b3ob3ob3ob3ob4o3bo2b4ob8ob3o2bobob2o2b
obo$b5ob5o2b2o2b3obo2bo2b8obob7o3b3o2bobo4b2o5b2obob3o2b2o2b2obobobob
2o4bo4bob2o2bo$2obo4bo4b3obo6b3ob4o2bobob2ob2ob4o2bobo2b2ob2o2b2o2bob
obo5bob2obobob6o5bo2bo2b4o2b2o$b3obo5bobob2ob2ob9ob4o5b2o3bobob2obo2b
o3b3o6b2obobob2o6bo2b3ob2o6b4o4b3obo$2b3obobo2bob3o3bobobob4obo3b2obo
b3o3b6ob2obobo2bob2o2b3obo3bo2bobob3o5bo3bo4b2o3b2obobobo$bob3obobo3b
o2bo2b2obo2b3ob2obob3ob2o2bo2b4ob2obob2o2b2obobo3bo2b3obobo4b2obo6bo2b
3o2b2o2bob2ob2o$2o3b2o2bo2bo3b2o5b3obo2bo2b3o3bob2o7b2ob2o6bobo3bo2b2o
bo3bo4bo4bo2bob2o2b3ob2ob2ob2o$obo2bob2ob3ob2o2bobo3bo2bo6b2obo2bo2bo
b2ob2ob4o2b2obobobo5bobobobo2bob2o3bo5b2ob7ob2o3b2o$2bo2b4o3b3ob2o5b4o
bo3b2obo2bob2obob4o4bo2bobo2b3ob5obobo2b2ob4ob3o7bob2o3bob2o2b4o$bo2b
2obo2bo2b2o3b2ob4o2bobobo2bob3obo2bob3ob4o3bobobo2bo2bo3bob2o3b2obobo
3b2o3bo3bo2b2o3b3o2bobo$4b3o2bobo4b3ob4ob2obobobo3bo2b6o2bo5b2obo2bo4b
8obo2bo3b2o2b4ob2ob2ob5obo4b2o$2ob2ob2o7bob5ob2o4b2o2b3o4bobo2bo2bobo
bo3b5o2b3ob2o3bobo5b2o3b5o2bo2bob2ob2ob4ob2o$obo2b2ob2o2bo4b6obob2o2b
4obo3bobo3b2o4bo2bob2ob4o2b2o3b3o5b3obob2o4b2ob2obo3b3o2b3obo$2o4bo2b
o2b3o2b2o2bo5b3o2bob3o2bo2b6o2b4ob2obo4b2o4b2o4bobob2o4b4o2bobob2o4bo
bob2o3bo$2bob3o2b2obo2b2o4bo3bobob2obob3obobo2b3o2bob4o2bob2o3bob2o2b
5obob2o2b3ob2o3bobobob4obo2b7o$bo4b2o2b4o7bo3bob2o4bo3b4ob6o3bo3bobo3b
o4bo2b3o2b2obobo2b4o2bobo2b3ob3o2b3obob2o$2bob4ob2ob3obobob2obobobo2b
4obo3b4o2b5o2bo2bo3bo4bo2bob2o8bo2bo3bo2b4o3b4o3b2o3b2o$ob5ob2o2bo2b3o
2bobo3b4o4bob3o3b2o3bo2bo3b4obob3o2bo3bo3bob2ob2o2bob2o3bobo5b3obo3bo
$3bo7bobobo2bo3bobo3bob2ob3obo2b3ob2ob4o2bo2bo2bob3ob2ob2o3b2o4b3o2bo
b2ob2o6b2ob3o2b3o$b2o2b3o2b2ob2o2b3ob2obobo3bo5b2o4bob3o2b2obo2b3o2b2o
2b2o4bob2obo2b3o3b3o3b2ob3ob6o4b4o$b2ob4o2b3o3b2obobo4b4ob2obo2bobo2b
obob2ob2ob2o2bo2b2ob2obo6bob2obo2b2o2b2o5bo2b2ob4ob2ob3o2bo$o3bo3bobo
2bobo5b5o4b3o2b2o8b2ob4obo3bobobob5ob3o6b5o2b2o2b4o2bobo2b2obob4obo$4o
b2obob3ob2ob2o6b4o2b5ob2o3bob4o2b4o5b4obo5b2o4b5o3bo4bob3ob2o3b3o2b2o
bobo$4o3bo2b2obob2ob2o5bob4obobob2obo2b3o3b2o3b5o4b2obob2o2b2o2bo5bo2b
3obob2ob2o5bob2o2bob2o$2bo3b2o2bobob3o2bo2bo4b2obobo2b2obob2ob4obobo2b
5o2bo2bobobob2obobo4bo3b3o3b3ob2o2bob2o3b4ob2o$2o3bo2bo4b2o5bob2o3bob
obo2b3obo2bo3bo3b3o3bo2b3ob2ob2o3bo2b3ob3o3b3o2bob2ob5ob2obo2bobo2bo$
o2b4o6bo6bob3ob3ob4o3bobobo3b2o2bo2bo6bob2o2b3o2bo3bo3bo3bob2ob4obob3o
2bo2b2ob3obo$2bo4bo2b6ob2ob2o2bo7bob4ob2o2bo2b2obobo2bo3bobob6o2bob2o
b2o2bobobo2b3o4bobob3ob2o3bob3o$o2bo3bo4bo2bobob2ob6ob2ob2obob2ob2o2b
3o7bobo2bobo5bobob4ob2o5bob2ob4o2b2ob5ob6o$bob4o2bob3ob2ob3o3bob2obo2b
3o3b3o2b2obo2b3o2b2obob2obo2bob2obobo2bo2bo2b2o8b3ob2o4b3o4b2o$6bob3o
4b4o4b4obo3b3obob2o2bo4b2ob2o8bo3bo2b2o2bob2o2bobo2b3o3b2obo3bo2bob2o
2b3o2bo$2b2o3b2o3b3obo3bobob2o2bo3b3o2bob2ob3o2b2obo2bob6o3bobo3b4ob2o
b4obo2b2o3b2ob3o3b3obob3obo$obobo4bobob2obo2bob2o2b6o2b3o7bob2o2bobob
obob3obobobo4bob2ob2o2bo4b2o4bob2o2b5ob3obobobo$3bo3b2o3b2o2bobob3o2b
ob2ob5o5bobo2b2o2b3o2b4o2bo2b4o2bo2b11o2bobobobobo2bo3b5obob2o$o4b2ob
ob4o2bo4b3o2b6o2b2ob2o2b2o2bo2bo4b2o4b3obobobobo4bob2obob2ob3o2b2obo5b
2ob3ob3o2bo$2o2b3o4b2obo4bob2ob2ob2ob3ob3o2b2ob4ob2o5bobob5o3b3o3bobo
b2obo2b2o5bo4bo3b2o2b2obobobo$bo2b5ob3o2b2ob2o6b2obo2bo2b3ob4ob3obo2b
2obo5bo2b2obob2ob2o5b5ob2o3bo4b3obob2o2b2o4bo$2obob4o2bo2bobo2b5obob2o
2b2o2b3o2bo4b3obobobo3bobobobobo2bo3b2o2bo3b3obob2o2b3ob2o3b2o2bobo4b
o$ob4obobobob3o2bob2o3b6ob7ob2ob2o4b2ob5o3b2ob3o2bo5bob4ob2ob2ob2o2bo
2bob4o4bobo$3o3bo2bobobobo2b2o2bo3b2obob2ob4ob3ob7o2bo3b4obob4ob2o4bo
2bo2bo4b5obobob3o3b4obob2o$bobobo2b2obobo2b3o2b2obo2b4o3b2o2bo2b3o3b2o
2bob4obo2bo2bo2bo2bo2bo3b7obob2obo2b2o4b3o2b2ob2obo$4bob9o2b2o3bo4bo5b
3obobo2bobob3o7bo2bo4b3o2b2o2b2o2b2ob3obobo2b2obob2o2bob2o5b4o$3obo3b
o2bo2bob4obobo2bob2ob2o2bobo2bo2bo4bo3b2o2b2obo4b2ob2o5bobob7obob2o2b
o3b3ob4ob2ob3o$bobo2b2obo2bob2ob4obob3ob8ob2ob2o2bobob2obo2b3o2b3o2bo
b2ob2o2b2ob2o2bo4b2obob2o2bo3b2ob2o2b2ob2o$b2o2b2ob3o2b2o3bobo2bobob2o
4b2o2b3ob3obo3bobo3b4ob2obob2obobob2o9bob3obobo3bo2b3o2bo2b4o$3b2o5b5o
3bo3bob2ob3o2b2o2b2ob4obo2b3o2b2obobobob4o3b10o2b4obo4b2o4b4o2b2o3bo!

Obviously that's not from apgsearch. That was generated in LifeViewer by selecting a region and doing random fill. The spaceship appears around T = 26000, heading north. Most likely it will be hit by a faster spaceship at some later point.

[b-engine]

[...] but so far only 1 orthogonal speed had occurred from mega-soups: [...]

Another (p158 orthogonal c/79):

Code: Select all

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

You'll have to take my word that the following is indeed a soup:

Code: Select all

Obviously that's not from apgsearch. That was generated in LifeViewer by selecting a region and doing random fill. The spaceship appears around T = 26000, heading north. Most likely it will be hit by a faster spaceship at some later point.

I've just discovered a p6420 by rotating the 2c/158:

Code: Select all

x = 4, y = 5, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$2bo$2obo2$bo!

Obviously you can draw a polyplet to discover some spaceships and oscillators.

[confocaloid]

The 8x8 seed shown below eventually settles after T = 40000. Here is the story:

• Two gliders appear around T = 1000 (a p44 diagonal c/22 heading northwest, and a p12 orthogonal c/6 heading east).
• Around T = 3500, a p368 diagonal c/184 "slowship" appears, heading southwest.
• Around T = 33000, a p48 diagonal c/24 glider is sent southwest, while the stationary part seemingly settles into p4.
• Around T = 37000, the faster southwest glider catches the "slowship". That collision evolves into four p4 dots and a
  p28 diagonal c/14 glider heading northeast.
• Around T = 40000, said glider collides with stationary junk from the initial reaction. The collision evolves into stationary p4 junk and a p28 diagonal c/14 glider heading southwest.
• Around T = 43000, said glider passes very close to four p4 dots from an earlier collision between two southwest gliders, but doesn't interact this time.

Code: Select all

#C Generated by random fill in LifeViewer
x = 9, y = 9, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
$2bobo2bo$3bobo2bo$2bo3b3o$2bobobobo$bo3b2obo$bo2bobobo$7b2o$3b5o!

EDIT: the following seed emits six gliders before settling around T = 23500:

Code: Select all

x = 8, y = 8, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
ob2obobo$ob4o$2bo2b3o$bo2b3o$2bo2b2o$6o$4b4o$4o2b2o!

Other interesting stories with glider collisions:

Code: Select all

x = 8, y = 8, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
ob3obo$bo2b3o$2b3obo$2o5bo$2b3ob2o$b4o$bo3b2o$b2o3b2o!

Code: Select all

x = 8, y = 8, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
2bo2b2o$2bobobo$2o5bo$2o5bo$b2o4bo$2bob4o$2ob2o2bo$3o2b2o!

Code: Select all

x = 8, y = 8, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
ob2o2bo$5ob2o$bobobo$o2bo2bo$ob3o$2o4b2o$o2b3o$2bobobo!

Code: Select all

x = 10, y = 10, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
ob2o4b2o$2o3bo3bo$2ob3o2b2o$bo6b2o$2b4obo$2b3o4bo$b2o2bo3bo$2bo2b5o$o
2bob3obo$5b2obo!

Code: Select all

x = 10, y = 10, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
obob3obo$6bobo$bo2b2obobo$2bo2bob2o$5b5o$3bo3b2o$ob3obo2bo$6ob2o$3o3b
2obo$o4bob3o!

[b-engine]

Maze solver:

Code: Select all

x = 93, y = 92, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
b44o4b44o$b44o4b44o$b2o88b2o$b2o88b2o$b2o88b2o$b2o88b2o$b2o4b26o4b8o4b
26o4b8o4b2o$b2o4b26o4b8o4b26o4b8o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b
2o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b2o4b2o$b2o4b2o22b2o4b2o10b2o22b
2o4b2o4b2o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b2o4b2o$b2o4b8o4b2o4b8o
4b2o4b8o4b14o4b2o4b2o4b2o4b2o$b2o4b8o4b2o4b8o4b2o4b8o4b14o4b2o4b2o4b2o
4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o10b2o4b2o4b2o10b
2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o
4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o4b2o4b2o4b2o4b
2o4b2o4b2o4b2o4b8o4b20o4b2o4b2o$b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o4b8o4b
20o4b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b2o10b2o
4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o
28b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b14o4b8o4b
2o4b8o4b2o4b26o4b2o$b2o4b14o4b8o4b2o4b8o4b2o4b26o4b2o$b2o16b2o4b2o10b
2o16b2o4b2o28b2o$b2o16b2o4b2o10b2o16b2o4b2o28b2o$b2o16b2o4b2o10b2o16b
2o4b2o28b2o$b2o16b2o4b2o10b2o16b2o4b2o28b2o$b14o4b2o4b14o4b14o4b2o4b20o
4b2o$b14o4b2o4b14o4b14o4b2o4b20o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o
16b2o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o16b2o4b2o$b2o4b2o4b2o4b2o4b
2o22b2o10b2o4b2o16b2o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o16b2o4b2o$
b2o4b2o4b8o4b8o4b2o4b8o4b2o4b2o4b2o4b2o4b8o4b2o$b2o4b2o4b8o4b8o4b2o4b
8o4b2o4b2o4b2o4b2o4b8o4b2o$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o
$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o$b2o4b2o22b2o4b2o4b2o10b2o
10b2o4b2o4b2o10b2o$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o$b2o4b26o
4b2o4b2o4b2o4b2o4b8o4b14o4b2o$b2o4b26o4b2o4b2o4b2o4b2o4b8o4b14o4b2o$b
2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o
4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b
2o22b2o4b2o$b2o4b2o4b26o4b8o4b2o4b2o4b8o4b8o4b2o$b2o4b2o4b26o4b8o4b2o
4b2o4b8o4b8o4b2o$b2o10b2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b2o34b2o
4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b
2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b14o4b14o4b8o4b2o4b8o4b2o4b2o4b8o4b2o
$b14o4b14o4b8o4b2o4b8o4b2o4b2o4b8o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o
4b2o10b2o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o4b2o10b2o4b2o$b2o16b2o10b
2o4b2o4b2o4b2o16b2o4b2o10b2o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o4b2o10b
2o4b2o$b2o4b8o4b2o4b2o4b8o4b14o4b8o4b14o4b2o$b2o4b8o4b2o4b2o4b8o4b14o
4b8o4b14o4b2o$b2o4b2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b2o10b2o
10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b
2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b20o4b2o4b14o4b8o4b8o4b8o$
b2o4b2o4b20o4b2o4b14o4b8o4b8o4b8o$b2o4b2o22b2o4b2o34b2o4b2o10b2o$b2o4b
2o22b2o4b2o34b2o4b2o10b2o$b2o4b2o22b2o4b2o34b2o4b2o10b2o$b2o4b2o22b2o
4b2o34b2o4b2o10b2o$b2o4b2o4b8o4b2o4b8o4b14o4b14o4b14o$b2o4b2o4b8o4b2o
4b8o4b14o4b14o4b14o$b2o4b2o4b2o10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o10b
2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o
10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b20o4b8o4b14o4b8o4b8o4b2o$b2o4b2o4b20o
4b8o4b14o4b8o4b8o4b2o$b2o4b2o22b2o4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b2o
4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b2o4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b
2o4b2o16b2o16b2o10b2o4b2o$b2o4b26o4b2o4b2o4b8o4b14o4b14o$b2o4b26o4b2o
4b2o4b8o4b14o4b14o$b2o34b2o4b2o16b2o28b2o$b2o34b2o4b2o16b2o28b2o$b2o34b
2o4b2o16b2o28b2o$b2o34b2o4b2o2bo13b2o28b2o$b92o$b92o!

[unname4798]

Maze solver:

Code: Select all

x = 93, y = 92, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
b44o4b44o$b44o4b44o$b2o88b2o$b2o88b2o$b2o88b2o$b2o88b2o$b2o4b26o4b8o4b
26o4b8o4b2o$b2o4b26o4b8o4b26o4b8o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b
2o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b2o4b2o$b2o4b2o22b2o4b2o10b2o22b
2o4b2o4b2o4b2o$b2o4b2o22b2o4b2o10b2o22b2o4b2o4b2o4b2o$b2o4b8o4b2o4b8o
4b2o4b8o4b14o4b2o4b2o4b2o4b2o$b2o4b8o4b2o4b8o4b2o4b8o4b14o4b2o4b2o4b2o
4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o10b2o4b2o4b2o10b
2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o
4b2o$b2o10b2o4b2o4b2o10b2o4b2o22b2o4b2o4b2o4b2o4b2o$b2o4b2o4b2o4b2o4b
2o4b2o4b2o4b2o4b8o4b20o4b2o4b2o$b2o4b2o4b2o4b2o4b2o4b2o4b2o4b2o4b8o4b
20o4b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b2o10b2o
4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o
28b2o4b2o$b2o4b2o10b2o4b2o4b2o4b2o4b2o4b2o4b2o28b2o4b2o$b2o4b14o4b8o4b
2o4b8o4b2o4b26o4b2o$b2o4b14o4b8o4b2o4b8o4b2o4b26o4b2o$b2o16b2o4b2o10b
2o16b2o4b2o28b2o$b2o16b2o4b2o10b2o16b2o4b2o28b2o$b2o16b2o4b2o10b2o16b
2o4b2o28b2o$b2o16b2o4b2o10b2o16b2o4b2o28b2o$b14o4b2o4b14o4b14o4b2o4b20o
4b2o$b14o4b2o4b14o4b14o4b2o4b20o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o
16b2o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o16b2o4b2o$b2o4b2o4b2o4b2o4b
2o22b2o10b2o4b2o16b2o4b2o$b2o4b2o4b2o4b2o4b2o22b2o10b2o4b2o16b2o4b2o$
b2o4b2o4b8o4b8o4b2o4b8o4b2o4b2o4b2o4b2o4b8o4b2o$b2o4b2o4b8o4b8o4b2o4b
8o4b2o4b2o4b2o4b2o4b8o4b2o$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o
$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o$b2o4b2o22b2o4b2o4b2o10b2o
10b2o4b2o4b2o10b2o$b2o4b2o22b2o4b2o4b2o10b2o10b2o4b2o4b2o10b2o$b2o4b26o
4b2o4b2o4b2o4b2o4b8o4b14o4b2o$b2o4b26o4b2o4b2o4b2o4b2o4b8o4b14o4b2o$b
2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o
4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b2o22b2o4b2o$b2o4b2o28b2o4b2o4b2o4b2o4b
2o22b2o4b2o$b2o4b2o4b26o4b8o4b2o4b2o4b8o4b8o4b2o$b2o4b2o4b26o4b8o4b2o
4b2o4b8o4b8o4b2o$b2o10b2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b2o34b2o
4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b2o10b
2o34b2o4b2o4b2o4b2o4b2o4b2o10b2o$b14o4b14o4b8o4b2o4b8o4b2o4b2o4b8o4b2o
$b14o4b14o4b8o4b2o4b8o4b2o4b2o4b8o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o
4b2o10b2o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o4b2o10b2o4b2o$b2o16b2o10b
2o4b2o4b2o4b2o16b2o4b2o10b2o4b2o$b2o16b2o10b2o4b2o4b2o4b2o16b2o4b2o10b
2o4b2o$b2o4b8o4b2o4b2o4b8o4b14o4b8o4b14o4b2o$b2o4b8o4b2o4b2o4b8o4b14o
4b8o4b14o4b2o$b2o4b2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b2o10b2o
10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b
2o4b2o10b2o10b2o16b2o4b2o22b2o4b2o$b2o4b2o4b20o4b2o4b14o4b8o4b8o4b8o$
b2o4b2o4b20o4b2o4b14o4b8o4b8o4b8o$b2o4b2o22b2o4b2o34b2o4b2o10b2o$b2o4b
2o22b2o4b2o34b2o4b2o10b2o$b2o4b2o22b2o4b2o34b2o4b2o10b2o$b2o4b2o22b2o
4b2o34b2o4b2o10b2o$b2o4b2o4b8o4b2o4b8o4b14o4b14o4b14o$b2o4b2o4b8o4b2o
4b8o4b14o4b14o4b14o$b2o4b2o4b2o10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o10b
2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b2o
10b2o10b2o4b2o16b2o28b2o$b2o4b2o4b20o4b8o4b14o4b8o4b8o4b2o$b2o4b2o4b20o
4b8o4b14o4b8o4b8o4b2o$b2o4b2o22b2o4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b2o
4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b2o4b2o16b2o16b2o10b2o4b2o$b2o4b2o22b
2o4b2o16b2o16b2o10b2o4b2o$b2o4b26o4b2o4b2o4b8o4b14o4b14o$b2o4b26o4b2o
4b2o4b8o4b14o4b14o$b2o34b2o4b2o16b2o28b2o$b2o34b2o4b2o16b2o28b2o$b2o34b
2o4b2o16b2o28b2o$b2o34b2o4b2o2bo13b2o28b2o$b92o$b92o!

That is not a perfect maze solver.

[b-engine]

Sawtooth (?):

Code: Select all

x = 2, y = 2, rule = M15,14,1,12,11,10,9,8,7,6,5,4,3,2,13,0
$2o!

[tommyaweosme]

This should clear things up: http://www.mirekw.com/ca/rullex_marg.html

i 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.

[NimbleRogue]

Maze solver:

What is this?

Code: Select all

x = 45, y = 44, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
b20o4b20o$b20o4b20o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b
2o$b2o16b2o4b2o16b2o$b14o4b2o4b2o4b14o$b14o4b2o4b2o4b14o$b2o16b2o4b2o
16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b8o4b8o4b
14o4b2o$b8o4b8o4b14o4b2o$b2o4b2o4b2o22b2o4b2o$b2o4b2o4b2o22b2o4b2o$b2o
4b2o4b2o22b2o4b2o$b2o4b2o4b2o22b2o4b2o$b2o4b2o4b8o4b8o4b2o4b2o$b2o4b2o
4b8o4b8o4b2o4b2o$b2o10b2o10b2o4b2o10b2o$b2o10b2o10b2o4b2o10b2o$b2o10b
2o10b2o4b2o10b2o$b2obo8b2o10b2o4b2o10b2o$b8o4b2o4b8o4b14o$b8o4b2o4b8o
4b14o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$b2o4b8o
4b8o4b8o4b2o$b2o4b8o4b8o4b8o4b2o$b2o4b2o7bo8b2o10b2o4b2o$b2o4b2o16b2o
10b2o4b2o$b2o4b2o16b2o10b2o4b2o$b2o4b2o16b2o10b2o4b2o$b2o4b2o4b8o4b2o
4b14o$b2o4b2o4b8o4b2o4b14o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$
b2o10b2o28b2o$b44o$b44o!

Code: Select all

[quote=unname4798 post_id=182593 time=1713098843 user_id=3175]
That is not a perfect maze solver.
[/quote]

As long as the reaction starts out touching the main still life (the one that makes up the outside) it will be a perfect maze solver

[TYCF]

What is this?

Code: Select all

x = 45, y = 44, rule = M0,2,8,3,1,5,6,7,4,9,10,11,12,13,14,15
b20o4b20o$b20o4b20o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b
2o$b2o16b2o4b2o16b2o$b14o4b2o4b2o4b14o$b14o4b2o4b2o4b14o$b2o16b2o4b2o
16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b2o16b2o4b2o16b2o$b8o4b8o4b
14o4b2o$b8o4b8o4b14o4b2o$b2o4b2o4b2o22b2o4b2o$b2o4b2o4b2o22b2o4b2o$b2o
4b2o4b2o22b2o4b2o$b2o4b2o4b2o22b2o4b2o$b2o4b2o4b8o4b8o4b2o4b2o$b2o4b2o
4b8o4b8o4b2o4b2o$b2o10b2o10b2o4b2o10b2o$b2o10b2o10b2o4b2o10b2o$b2o10b
2o10b2o4b2o10b2o$b2obo8b2o10b2o4b2o10b2o$b8o4b2o4b8o4b14o$b8o4b2o4b8o
4b14o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$b2o4b8o
4b8o4b8o4b2o$b2o4b8o4b8o4b8o4b2o$b2o4b2o7bo8b2o10b2o4b2o$b2o4b2o16b2o
10b2o4b2o$b2o4b2o16b2o10b2o4b2o$b2o4b2o16b2o10b2o4b2o$b2o4b2o4b8o4b2o
4b14o$b2o4b2o4b8o4b2o4b14o$b2o10b2o28b2o$b2o10b2o28b2o$b2o10b2o28b2o$
b2o10b2o28b2o$b44o$b44o!

A P25602 oscillator.

[b-engine]

Adjustable spaceship loop:

Code: Select all

x = 25, y = 25, rule = M0,2,8,3,1,5,6,11,4,9,10,14,12,7,13,15
$13bo7$8bo6bobo$9b2o5bo$8bo7bo2$bo$24bo2$9bo7bo$9bo5b2o$8bobo6bo7$12b
o!

[confocaloid]

i 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