Thread for basic questions

For general discussion about Conway's Game of Life.
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Gustone
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Re: Thread for basic questions

Post by Gustone » October 14th, 2019, 12:37 pm

Is there a spaceship that can support this tagalong

Code: Select all

x = 4, y = 5, rule = B3/S23
2b2o2$2o$2bo$2o!
My favourite oscillator of all time

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x = 15, y = 13, rule = B3/S23
7bo2$3b2o5b2o$b2o4bo4b2o$5b2ob2o$bobo7bobo$bo2bobobobo2bo$5obobob5o$o
4bo3bo4bo$b3obobobob3o$3bob2obo2bo$8bobo$8b2o!

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Hdjensofjfnen
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Re: Thread for basic questions

Post by Hdjensofjfnen » October 21st, 2019, 8:23 pm

All 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 = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!

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x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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toroidalet
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Re: Thread for basic questions

Post by toroidalet » October 21st, 2019, 8:32 pm

Hdjensofjfnen wrote:
October 21st, 2019, 8:23 pm
All 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.
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:

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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!
There's also one that systematically searches through 35-glider collisions until it finds one that cleans up all the ash and releases 1 glider, then creates that one, which is slightly more constructive.

EDIT: It would take a little more, since reflection reactions would be needed to get some of the closer gliders.
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Hdjensofjfnen
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Re: Thread for basic questions

Post by Hdjensofjfnen » November 5th, 2019, 3:13 am

Would 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!

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x = 5, y = 9, rule = B3-jqr/S01c2-in3
3bo$4bo$o2bo$2o2$2o$o2bo$4bo$3bo!

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x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Ian07
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Re: Thread for basic questions

Post by Ian07 » November 5th, 2019, 12:01 pm

Hdjensofjfnen wrote:
November 5th, 2019, 3:13 am
Would 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!
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.

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Gustone
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Re: Thread for basic questions

Post by Gustone » November 9th, 2019, 11:20 am

How are mirage flying wing and chehire cat notable
My favourite oscillator of all time

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x = 15, y = 13, rule = B3/S23
7bo2$3b2o5b2o$b2o4bo4b2o$5b2ob2o$bobo7bobo$bo2bobobobo2bo$5obobob5o$o
4bo3bo4bo$b3obobobob3o$3bob2obo2bo$8bobo$8b2o!

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Ian07
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Re: Thread for basic questions

Post by Ian07 » November 9th, 2019, 11:58 am

Gustone wrote:
November 9th, 2019, 11:20 am
How are mirage flying wing and chehire cat notable
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.

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Re: Thread for basic questions

Post by dvgrn » November 9th, 2019, 1:53 pm

Ian07 wrote:
November 9th, 2019, 11:58 am
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.

Most of the strange old irrelevant-looking stuff like Cheshire cat is in the Life Lexicon because it was in LIFELINE. And it's in the LifeWiki because Nathaniel basically started the LifeWiki by importing the 2006 version of the Life Lexicon.

It seems reasonable to leave these scattered "historical interest only" terms in place, since they do get mentioned in old articles and books about Conway's Life. But maybe it would make sense to add some kind of "This term is no longer in common use" template at the top of those articles, to help explain why it's there.

If I remember right, "flying wing" sneaked in to the LifeWiki because it got nominated for a Pattern of the Year competition, and got a few votes. So it became a case where people might stumble over the name and want to look up what it is, even if it's not a particularly notable advance in spaceship technology.

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calcyman
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Re: Thread for basic questions

Post by calcyman » November 30th, 2019, 8:20 am

Is there a universal 2-lane monophase slow-salvo toolkit?
What do you do with ill crystallographers? Take them to the mono-clinic!

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Scorbie
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Re: Thread for basic questions

Post by Scorbie » December 5th, 2019, 11:15 pm

calcyman wrote:
November 30th, 2019, 8:20 am
Is there a universal 2-lane monophase slow-salvo toolkit?
I guess the question is "basic" as in "basic research"? : )
Best wishes to you, Scorbie

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Re: Thread for basic questions

Post by GUYTU6J » December 11th, 2019, 3:34 am

How about a new database that storages the way B-heptomino displace in some Life-like isotropic non-totalistic cellular automata? This can provide insights into the behaviours of INT rules.
In my imagination the information is stored in this format:

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gen,dx,dy,orient,isorulemin,isorulemax
where gen=generations for B to reappear, dx and dy=offsets in two directions, orient=new orientation of B, isorulemin and isorulemax=range of rules for the sequence. Orientations follow the conventions for Herschel conduits:

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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 ]]
For example, B in Conway's Life evolves into some junk and a new B at gen=64:

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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!
Then it is encoded as

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64,19,1,R,B3/S23-c,B34ce8/S234c5e8
Some issues I think of:
  • The database includes no information about what actually the B is. Whether B is a oscillator, a spaceship, a replicator or merely a methuselah is not relevant to the offset. (But the new orientation does suggest behaviours.)
  • Why B-heptominos? For me, it seems more likely to be observed in soups for INT rules than R-pentominos, Herschels, buns or block&gliders. But this statement may be biased and I can't decide on other small methuselahs like bookends, pre-loaves and Pi's. There's even the isomeric B-heptaplet. Moreover, unnamed methuselahs in other rules exist. (A survey on the most common small methuselah across INT rules?)
  • The junks around the new B may interact with B so quickly that the characteristics of B is interrupted.
  • Multiple B's can occur simultaneously.
  • The B-heptomino may never appear again in the evolutionary sequence, but one of its descendants reappears and shows its features.
  • The database can be exhaustive, but it may turn out to be randomly collecting stuffs like the 5S database.
I admit that I haven't gone through the general considerations, but the crude idea is potentially powerful.
Lifequote:
Chuangtse wrote: What we love is the mystery of Life. What we hate is corruption in death. But the corruptible in its turn becomes mysterious life, and this mysterious life once more becomes corruptible.

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Ian07
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Re: Thread for basic questions

Post by Ian07 » December 11th, 2019, 5:00 pm

Does anyone have a comprehensive list of all two-spaceship collisions involving gliders, LWSSes, MWSSes, and/or HWSSes? e.g.

Code: Select all

x = 10, y = 7, rule = B3/S23
7bobo$6bo$6bo$6bo2bo$bo4b3o$2bo$3o!

pcallahan
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Re: Thread for basic questions

Post by pcallahan » December 30th, 2019, 1:48 pm

This may be very basic for someone with better linear algebra skills than mine, at least if they extend to diophantine equations. How do you characterize the class of infinite still lifes such that every 3x3 window contains exactly 4 cells? We know that this pattern is a still life because a live cell has 3 neighbors and an empty cell has 4 live neighbors. (Specifically, are they always periodic as are the examples below.)

Extrementhusiast posted this example of a 2x9 block that if repeated infinitely across a row of the plane forces the value of all other cells. (There is also no fixed-width stabilization for n of these in succession.)

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o..oo...o
..oo..oo.
Here it is repeated but not stabilized. You can see every 3x3 neighborhood contains exactly 4 live cells.

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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!
You can also take any 3x3 neighborhood containing exactly 4 cells and if you tile the plane with it, it is guaranteed to be an infinite still life. E.g. one of these three (this must be a truly ancient observation since you don't need a computer to see it).

Code: Select all

.o.....o.o....o.o
...............o.
ooo....o.o....o..
Here's a patch of the one on the right (again not stabilized):

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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!
So take this 5x5 neighborhood:

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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
We have equations such as g+h+i+l+m+n+q+r+s=4 for the center neighborhood. There is an equation for each neighborhood, but there's clearly not a unique result, so they must not all be independent. In fact, through linear combination, they can be reduced to 7 equations that constrain 9 overlapping windows (corrections welcome).

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>
Are these equations all independent? (I think so but haven't worked it out).

So what kinds of infinite life patterns satisfy these equations. You can specify 2 out of 9 cells on average, and then the rest are determined. Are all of these patterns periodic?
Last edited by pcallahan on December 31st, 2019, 3:24 pm, edited 1 time in total.

Hubi1857
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Re: Thread for basic questions

Post by Hubi1857 » December 31st, 2019, 8:15 am

pcallahan wrote:
December 30th, 2019, 1:48 pm
This may be very basic for someone with better linear algebra skills than mine, at least if they extend to diophantine equations.
This is very basic, indeed, for someone with the linear algebra skills of a theoretical physicist like me.

Linear algebra simply doesn't work for any scientific purpose whatsoever because you need complex numbers to describe and understand the world we live in, 3x3 neighborhoods, turing machines, computers and weather satellites included, since complex numbers z:=(a+ib) are binomial.

It needs the (doubtful) skills of a mathematician to construct negative numbers from positive numbers alone and the number zero=0 ad hoc from nothing but hot air.
And it needs an infinite amount of (wasted) energy to actively ignore the existence of the imaginary numbers.
(Edit: clarified wording)
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pcallahan
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Re: Thread for basic questions

Post by pcallahan » December 31st, 2019, 1:11 pm

Hubi1857 wrote:
December 31st, 2019, 8:15 am
And it needs an infinite amount of (wasted) energy to actively ignore the existence of the imaginary numbers.
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.

On the other hand, the algebraic constraints can narrow down the possibilities. Say I have a wrapped row of 6 cells a, b, c, d, e, f such that each consecutive triple adds to 2.

I.e. a+b+c=2, b+c+d=2, c+d+e=2, d+e+f=2, e+f+a=2, f+a+b=2.

In this case, it's easy to see by observation that the corresponding life cells must be "oo." repeated and shifted by 0, 1, or 2 positions. But you can also observe that c=2-a-b, d=2-c-b, e=2-d-c, etc. and use this to assign all cells having set the first two (you also can see that the first equation fails with c>1 if you assign a=0, b=0). You can also observe that a=d, b=e, c=f and derive the periodicity that way (and conclude that there is no integer solution if the row length is not a multiple of 3).

The same could be accomplished by writing a boolean formula and using that to derive the functional relation from (a, b) to c etc., but it's often easier to work with this using arithmetic equations.

Linear algebra does not provide a general means of finding satisfying solutions with integer constraints (which often leads to NP-hard problems). It can be used to rule out solutions. E.g., if I set up a system of equations and find it has no solutions even allowing negative or complex solutions, then I can conclude it is unsolvable for solutions restricted to 0 and 1. So, for example if all solutions to the above equations are periodic in the general case, then they are periodic in the restricted case of still life patterns.

There are also standard techniques such as Linear programming relaxation which
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.
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).

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Re: Thread for basic questions

Post by pcallahan » December 31st, 2019, 4:52 pm

Note that if the question had about the set of patterns in which 3x3 neighborhoods have even parity (a superset of the 4-cell neighborhood still lifes) then there would be a pure solution in terms of linear equations on GF(2). Are all of these solutions periodic? If so, then all the still lifes are. If not, then this is insufficient to resolve one way or the other, but it might give some hints.

There are some useful tools than can potentially help here, such as superposition. If you have a a set of solutions, you can XOR them together to product a new solution. E.g., in the simpler case of rows constrained by (x_(i-1) + x_i + x_(i+1)) mod 2 = 0 (which are periodic), the only solutions consist of windows 000, 110, 011, 101, repeated periodically (and you can superpose e.g. 110 + 101 to get 011). It is trivial in this case, but might be more useful to apply superposition in the 2D case.

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toroidalet
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Re: Thread for basic questions

Post by toroidalet » December 31st, 2019, 5:47 pm

Here's an example of a nonperiodic way to fulfill the parity condition (imagine the block rows extend infinitely)

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!
Or, if you prefer, this one also works:

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!
Here's a slightly less trivial example (not that it really matters):

Code: Select all

x = 24, y = 14, rule = B1357/S1357
2ob2ob2ob3ob2ob2obob2o$2ob2ob2ob3ob2ob2obob2o2$b2ob2ob2obob2ob2ob3ob2o
$b2ob2ob2obob2ob2ob3ob2o2$b2ob2ob2obob2ob2ob3ob2o$b2ob2ob2obob2ob2ob3o
b2o2$2ob2ob2ob3ob2ob2obob2o$2ob2ob2ob3ob2ob2obob2o2$b2ob2ob2obob2ob2ob
3ob2o$b2ob2ob2obob2ob2ob3ob2o!
I'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!
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pcallahan
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Re: Thread for basic questions

Post by pcallahan » December 31st, 2019, 6:23 pm

toroidalet wrote:
December 31st, 2019, 5:47 pm
I'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!
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.

(Actually, all the examples I can think of can be shifted like this, including Extrementhusiast's. Even the still life consisting of closely packed blocks can be shifted on the columns that contain live cells.)

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Re: Thread for basic questions

Post by Hubi1857 » January 1st, 2020, 8:51 am

pcallahan wrote:
December 31st, 2019, 1:11 pm
Hubi1857 wrote:
December 31st, 2019, 8:15 am
And it needs an infinite amount of (wasted) energy to actively ignore the existence of the imaginary numbers.
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.
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?

And you simply cannot calculate neither the age of the universe, nor the height of Olympus Mons on planet Mars, not even the average temperature on planet Earth a hundred years from now, using nothing but the arbitrary set {0,1} of numbers and the most sophisticated digital number cruncher imaginable.
Michael Ernst Hubi homo homunculus Hubertz
artist - composer - phantastrophysicist @ExtinctionRebellion

Lou Reed about time, Turing tapes and data streams:
"First thing you learn is that you always got to wait"

pcallahan
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Re: Thread for basic questions

Post by pcallahan » January 1st, 2020, 3:40 pm

toroidalet wrote:
December 31st, 2019, 5:47 pm
I've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following:
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).

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!
The idea is a little like a sliding puzzle. Any row or column can be moved freely without breaking constraints as long as it has periodicity 3. You can slide the columns to create a slidable row. Then when you displace this row by one position, you have aperiodicity in both directions. Can we create all such still life patterns by applying this operation to a series of rows and columns (e.g. starting with the packed-block pattern)?

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Ian07
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Re: Thread for basic questions

Post by Ian07 » January 1st, 2020, 8:15 pm

Why wasn't the first p20 oscillator (145P20) discovered until 1995 when both components of mold on fumarole were known by 1988? 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?

*A term I borrowed from Tropylium
Last edited by Ian07 on January 1st, 2020, 10:28 pm, edited 3 times in total.

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Re: Thread for basic questions

Post by Sokwe » January 1st, 2020, 9:51 pm

Ian07 wrote:
January 1st, 2020, 8:15 pm
Why 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?
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.

Here is an excerpt from an email sent on September 13, 1994 (referring to the p26 pre-pulsar shuttle, not toad flippers):
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.)
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.
-Matthias Merzenich

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Re: Thread for basic questions

Post by Ian07 » January 1st, 2020, 10:17 pm

Sokwe wrote:
January 1st, 2020, 9:51 pm
They did consider such oscillators. In fact, that entry in the oscillator table is almost certainly incorrect.
Thanks. Here are the other examples of this I noticed, if we're going to be correcting the table: Even where the discovery dates are certain, I'm not entirely sure all of these were explicitly constructed at the time, or if that should really matter.

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Re: Thread for basic questions

Post by Hubi1857 » January 2nd, 2020, 9:43 am

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...
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.

That Game-of-Life-enthusiasts all over the world measure the speed of their very special spaceships relative to what they call "the speed c of light" doesn't establish any reasonable connection to Einstein's general relativity since cellular automata depend heavily on the flat earth model of Euklidean geometry.
Michael Ernst Hubi homo homunculus Hubertz
artist - composer - phantastrophysicist @ExtinctionRebellion

Lou Reed about time, Turing tapes and data streams:
"First thing you learn is that you always got to wait"

pcallahan
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Re: Thread for basic questions

Post by pcallahan » January 2nd, 2020, 3:09 pm

toroidalet wrote:
December 31st, 2019, 5:47 pm
I've only been able to find answers to the original question that are aperiodic in 1 direction, such as the following:
Another idea that may provide a big simplification. Take this 4x4 neighborhood:

Code: Select all

a ? ? b
? ? ? ?
? ? ? ?
c ? ? d
From the original neighborhood constraints, it is easy to derive the equations:

Code: Select all

a - c = b - d
a - b = c - d
This limits the 0-1 solutions to:

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
(Did I miss any cases?)

When a pair of corresponding cells are unequal, they must be repeated periodically across their rows or columns. When they are equal, all such pairs must be equal across the pair of rows or columns.

These fall into 9 non-overlapping subsets of the grid, so they can be treated independently. However, they do eventually need to add up to 4 within 3x3 neighborhoods.

Update

Code: Select all

a ? ? a
? ? ? ?
? ? ? ?
b ? ? b
a≠b is incompatible with

Code: Select all

c ? ? d
? ? ? ?
? ? ? ?
c ? ? d
c≠d for the same grid coordinates (i,j) mod 3 because the a/b pattern forces horizontal stripes and the c/d pattern forces conflicting vertical stripes. So any perceived aperiodicity is the union of striped patterns.

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