Code: Select all
x = 4, y = 5, rule = B3/S23
2b2o2$2o$2bo$2o!
Code: Select all
x = 4, y = 5, rule = B3/S23
2b2o2$2o$2bo$2o!
Code: Select all
x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!
Code: Select all
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
Colliding 35 pairs of Sir Robins like this can create any 35-glider synthesis, and one of these syntheses sends salvos of gliders in just the right way to destroy all the ash and release an extra glider:Hdjensofjfnen wrote: ↑October 21st, 2019, 8:23 pmAll the buzz has been about colliding gliders to cleanly make a Sir Robin. But is it possible for a finite amount of Sir Robins to cleanly make a single glider? After all, the knightship's so big it's hard to clean any reaction up.
Code: Select all
x = 89, y = 81, rule = B3/S23
62b2o$62bo2bo$25b2o35bo3bo$23bo2bo37b3o$22bo3bo33b2o6b4o$22b3o35bob2o
4b4o$17b4o6b2o30bo4bo6b3o$17b4o4b2obo31b4o4b2o3bo$15b3o6bo4bo28bo9b2o$
15bo3b2o4b4o30bo3bo$19b2o9bo33b3o2b2o2bo$25bo3bo30b2o7bo4bo$15bo2b2o2b
3o46bob2o$14bo4bo7b2o39b2o6bo$14b2obo51b2ob3obo$12bo6b2o47b2o3bo2bo$
12bob3ob2o48bobo2b2o$12bo2bo3b2o47bo2bobobo$14b2o2bobo47b3o6bo$13bobob
o2bo48bobobo3bo$11bo6b3o51b2obobo$11bo3bobobo49bo6b3o$11bobob2o$10b3o
6bo49bo9bo$69bo3bo6bo$9bo9bo50bo5b5o$8bo6bo3bo50b3o$8b5o5bo55b2o$16b3o
52b3o2bo$13b2o54bob3obo$12bo2b3o50bo3bo2bo$13bob3obo49bo4b2ob3o$13bo2b
o3bo50b4obo4b2o$9b3ob2o4bo51bob4o4b2o$6b2o4bob4o59bo$6b2o4b4obo60bo2b
2o$11bo66b2o$6b2o2bo68b5o$9b2o72b2o$5b5o67b3o6bo$4b2o72bobo3bobo$2bo6b
3o65bo3bo3bo$2bobo3bobo66bo3b2o$3bo3bo3bo64bo6bob3o$6b2o3bo65b2o3bo3b
2o$b3obo6bo65b4o2bo2bo$b2o3bo3b2o68b2o3bo$bo2bo2b4o68bo$3bo3b2o70b2obo
$9bo68bo$6bob2o67b5o$10bo66bo4bo$7b5o64b3ob3o$6bo4bo64bob5o$6b3ob3o63b
o$6b5obo65bo$12bo61bo4b4o$10bo67b4ob2o$6b4o4bo60b3o4bo$4b2ob4o71bobo$
6bo4b3o72bo$4bobo75bo2b2o$2bo80b3o$2b2o2bo73b2o$3b3o73b3o5bo$7b2o73b2o
2bobo$bo5b3o69bo2b3obobo$obo2b2o73b2obo2bo$obob3o2bo72bobo2b2o$2bo2bob
2o75b2o$2o2bobo73b3o4bo$3b2o75b3o4bo$bo4b3o72b2o3b3o$bo4b3o73b2ob2o$3o
3b2o75b2o$2b2ob2o76bo$4b2o$5bo76b2o$84bo$5b2o$4bo!
Code: Select all
x = 17, y = 13, rule = B3/S23
10bo$8b2o$bo7b2o$2bo$3o2$7b2o$7b2o6bo$14b2o$14bobo$7b2o$6b2o$8bo!
Code: Select all
x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!
Code: Select all
x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!
I don't think so; since every cell in the block dies at some point in the reaction it can't really be used in any other situation.Hdjensofjfnen wrote: ↑November 5th, 2019, 3:13 amWould this be known as a component, because it adds a 13-cell induction coil onto a block? (Known, by the way.)Code: Select all
x = 17, y = 13, rule = B3/S23 10bo$8b2o$bo7b2o$2bo$3o2$7b2o$7b2o6bo$14b2o$14bobo$7b2o$6b2o$8bo!
Mirage and Flying wing were both tagged for unclear notability at one point, but the tags were later removed because it had been judged that the consensus was to keep them. As for cheshire cat, it seems to be one of the many patterns and general terms taken from the Life Lexicon. In fact, it appears that every term in the Lexicon (even the most obscure ones like LWTDS) has been added to LifeWiki. I'm not sure I personally agree with these decisions, but that's what been decided.
The LWTDS entry is a fairly unusual case -- deleted at one point because it's a term that no longer gets much use (if it ever did), but then brought back on general principles because it was in the Life Lexicon.
Code: Select all
gen,dx,dy,orient,isorulemin,isorulemax
Code: Select all
x = 73, y = 37, rule = LifeHistory
4D36.3D$D24.D14.D2.D21.D$D14.2A9.D2.2A9.D2.D11.2A9.D2.2A.A$4D12.CA.7D
.D2.CA8.3D13.CA.7D.D2.ACA$D14.2A9.D2.2A9.2D13.2A9.D4.A$D14.A9.D3.A10.
D.D12.A9.D$D39.D2.D4$4D36.3D$D24.D14.D2.D21.D$D4.D3.D5.2A9.D2.A10.D2.
D.D3.D5.2A9.D2.A.2A$4D2.D.D7.CA.7D.D.2A9.3D3.D.D7.CA.7D.D.ACA$D6.D7.
2A9.D3.CA8.2D5.D7.2A9.D3.A$D5.D.D6.A9.D3.2A9.D.D3.D.D6.A9.D$D4.D3.D
30.D2.D.D3.D4$3D37.D$D2.D21.D14.D24.D$D2.D11.2A9.D4.A8.D14.2A9.D3.A$
3D13.CA.7D.D2.2A8.D15.CA.7D.D.ACA$D2.D11.2A9.D2.AC9.D14.2A9.D2.A.2A$D
2.D11.A9.D4.2A8.D14.A9.D$3D37.4D4$3D37.D$D2.D21.D14.D24.D$D2.D.D3.D5.
2A9.D3.2A8.D4.D3.D5.2A9.D4.A$3D3.D.D7.CA.7D.D.AC9.D5.D.D7.CA.7D.D2.AC
A$D2.D3.D7.2A9.D3.2A8.D6.D7.2A9.D2.2A.A$D2.D2.D.D6.A9.D5.A8.D5.D.D6.A
9.D$3D2.D3.D30.4D.D3.D!
#C [[ THUMBNAIL THUMBSIZE 3 ]]
Code: Select all
x = 28, y = 15, rule = LifeHistory
14.4B$13.2A5B3.3A$13.2A3BA3B.A2BA$14.3BABA3BA3BA$13.4BABA7BA$11.13BA
3B$4.2B2.16BAB2A$3.24B$.2B2D13B.7B$2A2B2D12B2.B2ABAB$2AB2D13B4.3A$.2B
D13B6.A$2.3B.BA2B$5.2A2B$6.2A!
Code: Select all
64,19,1,R,B3/S23-c,B34ce8/S234c5e8
Code: Select all
x = 10, y = 7, rule = B3/S23
7bobo$6bo$6bo$6bo2bo$bo4b3o$2bo$3o!
Code: Select all
o..oo...o
..oo..oo.
Code: Select all
x = 18, y = 18, rule = B3/S23
2o2b2o3b2o2b2o$3b2o2b2o3b2o2b2o$b2o3b2o2b2o3b2o$2o2b2o3b2o2b2o$3b2o2b
2o3b2o2b2o$b2o3b2o2b2o3b2o$2o2b2o3b2o2b2o$3b2o2b2o3b2o2b2o$b2o3b2o2b2o
3b2o$2o2b2o3b2o2b2o$3b2o2b2o3b2o2b2o$b2o3b2o2b2o3b2o$2o2b2o3b2o2b2o$3b
2o2b2o3b2o2b2o$b2o3b2o2b2o3b2o$2o2b2o3b2o2b2o$3b2o2b2o3b2o2b2o$b2o3b2o
2b2o3b2o!
Code: Select all
.o.....o.o....o.o
...............o.
ooo....o.o....o..
Code: Select all
x = 24, y = 24, rule = Life
ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo2bo2b
o$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo2bo
2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo2bo
2bo2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo2bo
2bo2bo2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo2bo
2bo2bo2bo2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo2bo
2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o2bo
2bo2bo2bo2bo2bo2bo$ob2ob2ob2ob2ob2ob2ob2obo$bo2bo2bo2bo2bo2bo2bo2bo$o
2bo2bo2bo2bo2bo2bo2bo!
Code: Select all
a b c d e
f g h i j
k l m n o
p q r s t
u v w x y
Code: Select all
g+h+i+l+m+m+q+r+s = 4
f+k+q = i+n+s
g+l+q = j+o+t
h+m+r = <sum of three cells to the right of j,o,t>
b+c+d = q+r+s
g+h+i = v+w+x
l+m+n = <sum of three cells below v,w,x>
This is very basic, indeed, for someone with the linear algebra skills of a theoretical physicist like me.
I'm not quite sure what you're getting at, but linear algebra is often sufficient to prove the non-existence of solutions in cases like this. It's true that if you find a solution, it might fail on other constraints. For instance, assigning a value of 4/9 to each cell satisfies the constraint on the sum of neighborhoods, but is not a CGOL pattern, which must consist of 0s and 1s.
But forget about all that for a second. Is there any aperiodic solution to the original constraints including negative, non-integer (or complex, though I doubt it would help much).transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.
Code: Select all
x = 68, y = 71, rule = B1357/S1357
34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o
$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b
2o2$34b2o$34b2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2obob3ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o
2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b
2o$34b2o2$34b2o$34b2o!
Code: Select all
x = 71, y = 71, rule = B1357/S1357
36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o
$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o4b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o4b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$
36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o$36b2o2$36b2o
$36b2o2$36b2o$36b2o!
Code: Select all
x = 24, y = 14, rule = B1357/S1357
2ob2ob2ob3ob2ob2obob2o$2ob2ob2ob3ob2ob2obob2o2$b2ob2ob2obob2ob2ob3ob2o
$b2ob2ob2obob2ob2ob3ob2o2$b2ob2ob2obob2ob2ob3ob2o$b2ob2ob2obob2ob2ob3o
b2o2$2ob2ob2ob3ob2ob2obob2o$2ob2ob2ob3ob2ob2obob2o2$b2ob2ob2obob2ob2ob
3ob2o$b2ob2ob2obob2ob2ob3ob2o!
Code: Select all
x = 24, y = 20, rule = B1235678/S3
3bo2bo2bo5bo5bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$
o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2b
o2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o
2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob
5ob5o!
I see. Every third column has a count of 2 cells in each 3x1 vertical window, and the other columns have counts of 1. So each column can be shifted up and down freely. I wonder if periodicity in one dimension is required. The fact that each column has to have vertical window counts equal to the column shifted 2 cells away seems like a pretty significant constraint. The reason your solution works is that the columns can be shifted without changing the 1D cell counts because they are all the same.toroidalet wrote: ↑December 31st, 2019, 5:47 pmI've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following:Code: Select all
x = 24, y = 20, rule = B1235678/S3 3bo2bo2bo5bo5bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$ o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2b o2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o 2bo2bo2bo2bo2bo2bo2bo$b11ob5ob5o$o11bo5bo$o2bo2bo2bo2bo2bo2bo2bo$b11ob 5ob5o!
Well, linear algebra is, always has been and always will be insufficient to prove neither the existence nor the non-existence of Schrödinger's cat, or is it?
The idea of sliding (spatially) period-3 columns up or down by a cell can be applied to create both aperiodic rows and columns in the same pattern, as this example shows (the surroundings can be filled in periodically to stabilize the whole pattern).toroidalet wrote: ↑December 31st, 2019, 5:47 pmI've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following:
Code: Select all
x = 21, y = 21, rule = B1235678/S3
2ob2o4bo2b2o$b2ob2ob2ob2ob2ob2ob2o$6b2o2bo4b2ob2o$2ob2o4bo2b2o$b2ob2o
b2ob2ob2ob2ob2o$6b2o2bo4b2ob2o$2ob2o4bo2b2o$b2ob2ob2ob2ob2ob2ob2o$6b2o
2bo4b2ob2o$2ob2o4bo2b2o$2ob2ob2ob2ob2ob2ob2o$6b2o2bo4b2ob2o$2ob2o4bo2b
2o$b2ob2ob2ob2ob2ob2ob2o$6b2o2bo4b2ob2o$2ob2o4bo2b2o$b2ob2ob2ob2ob2ob
2ob2o$6b2o2bo4b2ob2o$2ob2o4bo2b2o$b2ob2ob2ob2ob2ob2ob2o$6b2o2bo4b2ob2o!
They did consider such oscillators. In fact, that entry in the oscillator table is almost certainly incorrect. The issue also applies to the p24 toad flipper (found in 1994), and I recalled reading a comment by Bill Gosper describing it as the first "non-boring" p24 oscillator.Ian07 wrote: ↑January 1st, 2020, 8:15 pmWhy wasn't the first p20 oscillator (145P20) discovered until 1995 when both components of mold on fumarole were known by 1989? Did no one consider the possibility of spark-coupled oscillators* back then, or did they just consider them to be trivial for all intents and purposes?
The p24 toad flipper was found over a month later. Gosper asked if it was the first "nonboring" p24 to which Dean Hickerson replied "yes, I think the p24 toad-flipper is the first nontrivial p24." This may be where the confusion came from. I'm not sure when the "non-trivial" terminology for oscillator periods was standardized.Bill Gosper wrote: Also, Buckingham's p26 implies a toroidal p24, a period for which we still lack a non-boring example. (Boring := the only p24 cells are an lcm spark.)
Thanks. Here are the other examples of this I noticed, if we're going to be correcting the table:
Well, matter of fact is that you forgot the proof that the so called "spaceships" of the majority of cellular automata discovered so far never exceed the speed of c/2.Saka wrote: ↑February 15th, 2016, 6:27 am
Sorry, it has been proven that spaceships cannot exceed c2 (_WSS Speed)
Though I forgot the proof.
A rule must contain b2 or b0 to get to C (or the speed of light)
At that state, time would slow down to you but not to the observer, therefore, you would look like you are speeding, but to you, you are just still, floating,this is due to Einstein's general relativity...
Another idea that may provide a big simplification. Take this 4x4 neighborhood:toroidalet wrote: ↑December 31st, 2019, 5:47 pmI've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following:
Code: Select all
a ? ? b
? ? ? ?
? ? ? ?
c ? ? d
Code: Select all
a - c = b - d
a - b = c - d
Code: Select all
0 ? ? 0
? ? ? ?
? ? ? ?
0 ? ? 0
1 ? ? 1
? ? ? ?
? ? ? ?
1 ? ? 1
0 ? ? 1
? ? ? ?
? ? ? ?
0 ? ? 1
0 ? ? 0
? ? ? ?
? ? ? ?
1 ? ? 1
1 ? ? 0
? ? ? ?
? ? ? ?
1 ? ? 0
1 ? ? 1
? ? ? ?
? ? ? ?
0 ? ? 0
Code: Select all
a ? ? a
? ? ? ?
? ? ? ?
b ? ? b
Code: Select all
c ? ? d
? ? ? ?
? ? ? ?
c ? ? d