## Thread for basic non-CGOL questions

For discussion of other cellular automata.

### Re: Thread for basic non-CGOL questions

Does there exist a (totalistic or non-totalistic) rule where all oscillators must have a prime period?
Last edited by muzik on August 3rd, 2017, 3:18 pm, edited 1 time in total.
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### Re: Thread for basic non-CGOL questions

muzik wrote:Dies there exist a (totalistic or non-totalistic) rule where all oscillators must have a prime period?

B012345678/S

and any other rule where only p2 oscillators can exist
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### Re: Thread for basic non-CGOL questions

I was more meaning rules where every prime number is possible as a period.
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### Re: Thread for basic non-CGOL questions

muzik wrote:Does there exist a (totalistic or non-totalistic) rule where all oscillators must have a prime period?
...
I was more meaning rules where every prime number is possible as a period.

Your question doesn't seem to exclude trivial oscillators. If even two different prime oscillators are available, then apparently the answer is "no".

If you add a non-triviality clause, then the answer is "arrgh, probably not, in the absence of some utterly strange unknown mathematical CA phenomenon that could theoretically be used for primality testing."

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### Re: Thread for basic non-CGOL questions

toroidalet wrote:
muzik wrote:Are these oscillators or spaceships in any rules?

The first one's trivial:
x = 4, y = 5, rule = B7e/S0123456-i78bo$4o$bo$4o$bo!

p3:
x = 4, y = 5, rule = B3ak5i/S1c2ac3i6ibo$4o$2bo$4o$bo!

p5:
x = 4, y = 5, rule = B3j4ij5ceiy8/S12ae3-ckqr4aijq5qr6ibo$4o$2bo$4o$bo!

p7:
x = 4, y = 5, rule = B2ek3aiy4akry5eiy/S12ce3jkqr4j5iybo$4o$2bo$4o$bo!

And as a spaceship -
2c/4:
x = 4, y = 5, rule = B2ce3er4aei6ik7e/S12ak3ci4nt6ibo$4o$2bo$4o$bo!

8c/16:
x = 4, y = 5, rule = B2cen3y/S2an3ibo$4o$2bo$4o$bo!

c/3:
x = 4, y = 5, rule = B2e3ij4a5iy/S2ak3j4jbo$4o$2bo$4o$bo!

c/4:
x = 4, y = 5, rule = B2c3aejr4aeirtw5i/S2a3e4ey6ibo$4o$2bo$4o$bo!

5c/55:
x = 4, y = 5, rule = B2cek3-cik4ejkqrty5acjk6aei78/S02ac3ejnry4ekrw5-einr6ck7e8bo$4o$2bo$4o$bo!
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### Re: Thread for basic non-CGOL questions

Are oscillators possible in rules without B0, B1, B2, B3, and no survival conditions?
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### Re: Thread for basic non-CGOL questions

No.

Proof:

1. In order for a finite oscillator to exist, it needs to have a perimeter, e.g. a line so that all live cells in all generations lie within it.

2. How could such a perimeter look like, in particular, how does it behave in regards to edges? 90-degree edges are impossible because of the octagonal bounding box, thus, a corner can only have one shape:
x = 4, y = 9, rule = B45678SHistory3.D$2.D$.D$B$D$D$D$D$D!

3. In this shape, the cell marked in blue has to be on in at least one generation of the cycle. Otherwise:
x = 4, y = 9, rule = B45678SHistory3.D$2.D$.D$AF$.F$2A$D$D$D!

Just use the cell below it in the picture.

4. How does this cell become alive? Well, considering it lies on one corner of perimeter, there is only one option, that one being that all its inside neighbours are ON in the generation before:
x = 4, y = 9, rule = B45678SHistory3.D$2.D$.E$BC$EC$D$D$D$D!

5. Consider the cell in yellow directly below the corner cell. How does it become ON? It can't always be ON, as there are no survival conditions, so it needs to have been born in this generation. How though?
x = 4, y = 9, rule = B45678SHistory3.D$2.D$.D$AF$.F$2A$D$D$D!

Our cell only had three neighbours that aren't also dead at the same time (remember, to be alive, they need to be dead the generation before), so the cell cannot have possibly been on in generation -1, preventing the corner cell from being born, preventing the oscillator from working.
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### Re: Thread for basic non-CGOL questions

Certain classes of patterns can be ruled out as potentially being a ship in any isotropic rule. The obvious example is the set of all patterns which have C2 symmetry (rotation by 180 deg). My question is whether this is the only class of such patterns. I believe there are other patterns which can not possibly be a ship in any 2-state isotropic rule but I can't work out what characteristics can be used to identify them. For example, patterns composed of two isolated dominoes such as this one:

x = 5, y = 2, rule = B3/S232o2bo$4bo! Neglecting B0 for the moment, either B2a or B1e is required for there to be any births in generation 1 (excluding B1c which rules out any pattern from being a ship). With B2a one side of each domino will expand indefinitely in different directions and with B1e one end of each domino will expand indefinitely in different directions. Does "two isolated dominoes" describe all patterns which can't possibly be a ship for this reason? Are there other such classes of patterns - either without B0 (probably yes), or with B0 (maybe not). wildmyron Posts: 753 Joined: August 9th, 2013, 12:45 am ### Re: Thread for basic non-CGOL questions Is a breeder that breeds itself considered a replicator? Proud owner and founder of Sakagolue x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

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### Re: Thread for basic non-CGOL questions

Using a similar concept to the "all orthogonal speeds" rule, are there any (range-1 isotropic totalistic or nontotalistic) rules where at least one of these is possible:

- both an infinite series of true-period c/odd and c/even exist within the same rule?

- an infinite series of true-period 2c/n spaceships exists?

- an infinite series of c/n diagonal spaceships exists?

- an infinite series of directions exists?

Here's a post that contains a backend that could help in proving the second item in the list:
http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1971&p=47381#p47381

EDIT: another potentially useful backend:
x = 3, y = 10, rule = B2c3aj4nrt5i6c78/S01c23enr4aet5-iq67obo$bo$bo$bo$bo$bo$bo$bo$bo$3o! 2c/n spaceships project Current priorities: see here muzik Posts: 2727 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Thread for basic non-CGOL questions Would this be considered a replicator, or just a double wickstretcher? x = 1, y = 2, rule = B2a4i/So$o!

It seems to follow Wolfram Rule 50:
x = 1, y = 1, rule = W50o!
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### Re: Thread for basic non-CGOL questions

Does this stabilize? 6M+ and it's still going:
x = 60, y = 60, rule = B3-ky4iw5cy/S2-n3-eky4t30b2o$29b4o$28b2o2bo$29b2o2bo$30b4o22$3bo$o2bo$b3o3$56b3o$56bo2bo$56bo23$26b3o$28bo$28bo$27bo!
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Current rule interest: B2ce3-ir4a5y/S2-c3-y

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### Re: Thread for basic non-CGOL questions

Are there any known 1D replicators where the central replicator stays alive after every replication cycle, resembling a one-dimensional version of the Fredkin rule and simulating Wolfram rule 150?
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### Re: Thread for basic non-CGOL questions

drc wrote:Does this stabilize? 6M+ and it's still going:
x = 60, y = 60, rule = B3-ky4iw5cy/S2-n3-eky4t30b2o$29b4o$28b2o2bo$29b2o2bo$30b4o22$3bo$o2bo$b3o3$56b3o$56bo2bo$56bo23$26b3o$28bo$28bo$27bo!

I would assume it's some sort of growing logic gate...

EDIT: No, since it's made out of rakes.
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Pattern of the month (September 2017):
#C [[ AUTOFIT ]]x = 7, y = 9, rule = B34tw/S232o$2o$4b2o$6bo$3bo2bo$6bo$4b2o$2o$2o!

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### Re: Thread for basic non-CGOL questions

muzik wrote:Are there any known 1D replicators where the central replicator stays alive after every replication cycle, resembling a one-dimensional version of the Fredkin rule and simulating Wolfram rule 150?

p2:
x = 2, y = 1, rule = B1e/S1e2i2o!
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### Re: Thread for basic non-CGOL questions

That's not particularly what I had in mind, since if you built the equivalent of a sierpinski generator for it the stream of replicators would look like this:

x = 1, y = 1, rule = W254o!

x = 1, y = 1, rule = W150o!
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### Re: Thread for basic non-CGOL questions

Here's a potential approach to adjustable-speed spaceship rules I've had on mind for quite a while now:

1. A small spaceship (T in this case) collides with a stationary object.

x = 5, y = 22, rule = bs012345678History.2E$.2E6$2.C$.3C$C.C.C$2.C$2.C$2.C3$2.A$.3A4$.2E$.2E! 2. The stationary object is translated by a slope (m,n) (in this case (1,0)), whilst the spaceship is reflected back the way it came and translated by a slope of (m,0) (in this case also (1,0)). x = 5, y = 22, rule = bs012345678History2.2E$2.2E3$.3A$2.A3$2.C$2.C$2.C$C.C.C$.3C$2.C7$.2E$.2E!

3. The spaceship then collides with another stationary object, translated in a direction parallel to the previous object (again (1,0)) and also producing a reflected copy of the spaceship, repeating this cycle infinitely.

x = 5, y = 22, rule = bs012345678History.2E$.2E6$2.C$.3C$C.C.C$2.C$2.C$2.C3$2.A$.3A4$.2E$.2E! I'm pretty sure this is the way I've seen most non-Life-like "adjustable speeds" rules done (using one-cell photons and one-cell still lifes), as well as a bold oversimplification of Life's geminoid technology, but I'm pretty interested as to if there exists such a family of spaceships in a one-state isotropic rule which could be built easily by hand. 2c/n spaceships project Current priorities: see here muzik Posts: 2727 Joined: January 28th, 2016, 2:47 pm Location: Scotland ### Re: Thread for basic non-CGOL questions muzik wrote:Here's a potential approach to adjustable-speed spaceship rules I've had on mind for quite a while now: <snip> This is certainly a viable approach but there are a few things to consider: • If the two SL are identical then they need to be moved twice the distance of the small ship at each reaction to keep up. • A lower period (and faster) small ship will give you more flexibility in the allowed speeds of the resulting larger ship. • The majority of analogous ships use a push and a pull reaction - push at the front and pull at the back - rather than a slide reaction as you've shown. That's probably harder to search for though because you need two compatible reactions (probably with different SL) rather than one which is compatible with itself. • Searching for this by presuming what the small ship and the SL are from the start is probably a needle in a haystack kind of search. I suspect you'd have more luck restricting the search to a rule (or set of rules) with an extremely common small ship, several extremely common small SL and which is productive but settles down fairly quickly - i.e. dynamics akin to JustFriends but with an orthogonal small ship. wildmyron Posts: 753 Joined: August 9th, 2013, 12:45 am ### Re: Thread for basic non-CGOL questions wildmyron wrote:Searching for this by presuming what the small ship and the SL are from the start is probably a needle in a haystack kind of search. I suspect you'd have more luck restricting the search to a rule (or set of rules) with an extremely common small ship, several extremely common small SL and which is productive but settles down fairly quickly - i.e. dynamics akin to JustFriends but with an orthogonal small ship. About the last bit: If you use a diagonal ship instead and search for diagonal offsets for the SL, you can use JustFriends almost as-is with the actual diagonal glider that already exists. This has the advantage that the SL (probably a domino) may be translated a single diagonal while still keeping the ship glide-reflective, potentially allowing perfect speeds, whereas an orthogonal variation would require semiperfect speeds or other pseudo-period speeds. All in all, it seems very likely that there is a rule in which a particular collision between a JustFriends glider (or c/4 equivalent without S2k) and a domino translates the domino laterally by (1,1) and reflects the glider 180 degrees onto a lane 1hd from its input in the same direction as the domino's translation. The non-totalistic rulespace is huge. x₁=ηx V ⃰_η=c²√(Λη) K=(Λu²)/2 Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt) $$x_1=\eta x$$ $$V^*_\eta=c^2\sqrt{\Lambda\eta}$$ $$K=\frac{\Lambda u^2}2$$ $$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$ http://conwaylife.com/wiki/A_for_all Aidan F. Pierce A for awesome Posts: 1611 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Thread for basic non-CGOL questions What would this be called? x = 13, y = 5, rule = B3-y4q5a/S23-e5bo4b2o$5bobobo2bo$b2o2b2o3b2o$o2bo$b2o! Would it be called some arcane term like "Empty space unary counting shuttle™" or is there a simpler term for it? I have the best signature ever. toroidalet Posts: 858 Joined: August 7th, 2016, 1:48 pm Location: Somewhere on a planet called "Earth" ### Re: Thread for basic non-CGOL questions wildmyron wrote: muzik wrote:Here's a potential approach to adjustable-speed spaceship rules I've had on mind for quite a while now: <snip> • Searching for this by presuming what the small ship and the SL are from the start is probably a needle in a haystack kind of search. <snip> Well, there's nothing like proving yourself wrong... A for awesome wrote:About the last bit: If you use a diagonal ship instead and search for diagonal offsets for the SL, you can use JustFriends almost as-is with the actual diagonal glider that already exists. This has the advantage that the SL (probably a domino) may be translated a single diagonal while still keeping the ship glide-reflective, potentially allowing perfect speeds, whereas an orthogonal variation would require semiperfect speeds or other pseudo-period speeds. All in all, it seems very likely that there is a rule in which a particular collision between a JustFriends glider (or c/4 equivalent without S2k) and a domino translates the domino laterally by (1,1) and reflects the glider 180 degrees onto a lane 1hd from its input in the same direction as the domino's translation. The non-totalistic rulespace is huge. That turned out to be a good idea. In this case the domino moves (2,2) with each reflection, which is probably down to me not setting up the initial pattern correctly. wildmyron Posts: 753 Joined: August 9th, 2013, 12:45 am ### Re: Thread for basic non-CGOL questions Has anybody tried to make a WLS/Gfind/Zfind-ish spaceship search program for LTL rules? Proud owner and founder of Sakagolue x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

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### Re: Thread for basic non-CGOL questions

Is there a pattern other than the dot, domino or other symmetric patterns that can't be a spaceship in any non-totalistic rule?
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### Re: Thread for basic non-CGOL questions

Any pattern can be a spaceship in some non-isotropic rules, which are non-totalistic.
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### Re: Thread for basic non-CGOL questions

muzik wrote:Any pattern can be a spaceship in some non-isotropic rules, which are non-totalistic.

x = 93, y = 81, rule = B/S0123467876bo$76bo55$o24$91b2o! Proud owner and founder of Sakagolue x = 17, y = 10, rule = B3/S23b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5bo2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)

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