Thread for basic questions

[muzik]

Do any oscillators exist with volatility 1 but strict volatility 0, that aren't just unions of two non-interacting 100% volatile oscillators?

Something like Trivial p6-1, except statorless? (Strict volatility 0 means the oscillator is trivial. Volatility 1 means the oscillator is statorless.)

Yes, also consider the tiny OCA example on the trivial oscillator page on the wiki.

[Haycat2009]

No offence, but recently I have seen "B0 rules have 0 still lives." Those with S8 are basically black/white reversals of rules that CAN have still lifes. A counter example would be B0/S3: The block IS a still life in that rule, but most people refuse to run it the proper way and thus eliminate all still lifes.

Now, the question: Does the method we are using to emulate B0 really work?

Why can we not:
1. Change the colour of the background to the colour of cells and back if they are further than range of alive cells
2. Run it like Black/white symmetric counterpart, but dead cells are treated as if they were alive and vice versa.

[b-engine]

Now, the question: Does the method we are using to emulate B0 really work?

Why can we not:
1. Swap colour of background and cells every generation
2. Run it like Black/white symmetric counterpart

It should works, but can cause confusion without prior notice.

1. This causes an awful flashing background, and any software will waste lot of resources just to switch the color.
2. This requires a R2 rule emulation for R1 rules. No known algorithm can convert between emulation and original.

[confocaloid]

Do any oscillators exist with volatility 1 but strict volatility 0, that aren't just unions of two non-interacting 100% volatile oscillators?

If the requirement "with volatility 1" is removed, then it is possible to engineer a high-period example in the following way:

Code: Select all

x = 279, y = 184, rule = LifeHistory
278.A$276.2A$277.2A4$269.A$267.2A$268.2A6$114.A$115.2A$114.2A$256.A$
256.A.A$256.2A8.A$264.2A$265.2A2$258.A$252.A.A3.A.A$252.2A4.2A$253.A
4$131.A$132.2A$131.2A3$20.2A2.2A5.2A3.2A3.A$17.A2.A2.A.A5.A4.A4.3A$2A
.2A3.2A3.2A.A.A.A.2A9.A3.A6.A202.A$.A.A3.A.A4.A.A.A.A2.A8.2A2.2A5.2A
201.A$A3.A2.A4.A.A2.A2.A.2A6.A2.A.A210.3A$.2A.A.A.A3.A.2A.A.A10.2A3.A
$2.A.A.A5.A.A2.A.3A12.A30.2A$.A2.A4.3A4.2A4.A11.2A24.2A4.A$.3A3.A10.
5A6.2A24.2A3.A2.3A$4.3A11.A10.2A24.2A4.A.A$3.A17.4A35.2A$3.2A5.2A8.A
3.A4.3A22.3A3.A2.A2.A$.2A7.2A7.A.3A4.A3.A7.A4.A7.A3.A2.2A.4A$2.A16.A.
A11.A4.2A.4A.2A4.A$2.A.A12.A.A2.A.2A2.A3.A7.A4.A7.A3.A4.3A$3.2A4.2A6.
2A.A.A2.A3.3A22.3A4.A2.A$8.A2.A8.A.A.2A35.3A$8.A2.A8.A.A.A4.2A24.2A$
9.2A10.A2.A4.2A24.2A6.3A$22.2A26.2A11.A2.A$51.A12.3A$38.2A10.A3.2A$
37.3A10.A.A2.A6.2A.2A$25.A11.2A9.2A2.2A8.A2.A$25.3A7.A2.A9.A3.A9.2A3.
A$9.A18.A7.A12.A4.A5.A.A3.2A$8.A.A16.2A8.A5.A4.2A3.2A3.3A2.A$8.A.A31.
A.A12.A4.2A$9.A33.A13.2A$13.2A126.A6.A$13.A.A17.2A3.A102.3A4.3A$15.A
8.2A8.2A.A.A.2A101.A6.A$15.2A2.2A4.2A2.A9.A.A2.A98.2A5.2A6.2A$18.A2.A
4.4A4.A4.A3.2A113.2A$21.A5.2A10.A$21.A5.2A.A5.A2.A$18.2A.A7.3A4.4A$
18.2A9.A.A10.A$26.2A.A8.5A42.A49.A$25.A.4A7.A44.3A47.3A$19.2A4.A.A.A.
2A7.A18.A22.A26.A22.A33.2A$19.2A3.2A.A.A4.A4.2A18.3A20.2A25.3A20.2A
31.A.A$25.A2.2A.4A27.A49.A53.A$23.A.A4.A30.2A48.2A$23.2A5.A.A$31.2A9.
A49.A48.2A$42.3A47.3A47.A$45.A49.A46.A.A$32.A11.2A11.2A35.2A11.2A34.
2A$30.3A24.2A48.2A$29.A$29.2A$14.2A$15.A168.2D$15.A.2A164.D.D$16.A2.A
23.A135.2C.D.D$17.2A24.A.A133.2C.D$32.2A9.3A36.2A48.2A48.D$32.2A11.A
23.2A11.2A35.2A11.2A48.D.D$70.A49.A62.D.D$67.3A47.3A64.2D$67.A49.A42.
2A$160.2A$40.A3.2A40.2A48.2A$39.A.A3.A41.A49.A$35.2A.A.A3.A12.2A25.3A
20.2A25.3A$35.2A.A4.A13.A26.A22.A26.A$39.5A.A12.3A47.3A$31.2A.A.2A.A
4.A.A13.A49.A$31.A.2A.A2.A.2A2.A$24.2A12.2A.A.2A$24.2A129.2A$155.A$
156.3A$158.A35$241.2A$240.2A$242.A3$127.3A$129.A$128.A123.A$251.2A$
251.A.A$124.3A$126.A$125.A$260.2A$260.A.A$260.A10$261.2A$260.2A$262.A
$109.3A$111.A$110.A$268.2A$267.2A$269.A4$277.2A$276.2A$278.A!

The transformation on the left (i.e. remove and add the block) happens every 1000 ticks.
To complete the example, you need to repeat the transformation on the right (i.e. add and remove a 14-bit island) every 1500 ticks (by repeating the 18 gliders).
What you'll get is a trivial p3000 oscillator with a p1000 part and a p1500 part where evolution of the p1500 part depends on the p1000 part.

Probably one could also engineer a trivial oscillator with two mutually dependent lower-period regions, in a similar fashion.

If both parts can be made statorless, the result would be an oscillator with volatility 1 but strict volatility 0, that isn't just an union of two non-interacting 100% volatile oscillators.

[hotdogPi]

Found one.

Code: Select all

x = 24, y = 16, rule = B3/S23
22bo$21bobo$3b3o2bo13bo$4b2obo9bo$4b3o4bo3bob2obob2o$o3bobo8bob4o$4o2b
o6bo$3o15b3o$2b3o2bo11b5o$bo4bobo3b2o8bo$o6bo2b2o2$8bo$2bo5bo$7bo$4bo
2bo!

The LCM cell is period 40, not 80.

[confocaloid]

Found one. [...]

Apparently the oscillator was added to the wiki, along with several other oscillators: https://conwaylife.com/w/index.php?diff ... did=125212
Unfortunately discovery information / sources for patterns are completely missing. "Where those patterns come from?"

[Sokwe]

Apparently the oscillator was added to the wiki, along with several other oscillators: https://conwaylife.com/w/index.php?diff ... did=125212
Unfortunately discovery information / sources for patterns are completely missing.

Those trivial oscillators were found by Keith Amling, James Pascua, and myself. See the posts starting here.

[H. H. P. M. P. Cole]

How do I find glider syntheses for some methuselah? Suppose I would like to find syntheses for this:

Code: Select all

x = 8, y = 5, rule = B3/S23
b3o$o2bo$3bob2o$3o2b3o$5b2o!

Which database should I look up?

[hotdogPi]

That would be the octo3g database, although I suspect zero matches here. I don't have octo3g, but I have octo3obj (1G seeds), which generally gives more results than octo3g, and I'm getting zero matches.

[dvgrn]

That would be the octo3g database, although I suspect zero matches here. I don't have octo3g, but I have octo3obj (1G seeds), which generally gives more results than octo3g, and I'm getting zero matches.

Yup, zero matches from octo3g. On the other hand, there are 33 matches for the left half:

Code: Select all

x = 783, y = 189, rule = B3/S23
b3o128bo77bo70bo43bo59bo75bo52bo66bo59bo68bo70bo$o2bo129bo76bobo69bo
43bo59b2o61bobo10bo52bo63b2o61b2o67bo70bo$3bo127b3o60bo15b2o68b3o41b3o
58b2o63b2o8b3o50b3o64b2o59b2o66b3o68b3o$3o192bo254bo$193b3o193bobo$
130bo149b2o39b3o2b3o60b2o70b2o51b2o194b2o69b2o$130b2o149b2o40bo4bo61bo
69b2o51b2o63bo67bo62b2o69b2o$129bobo61b2o85bo41bo4bo134bo52bo63bo67bo
63bo58bo11bo$194b2o381b3o65b3o122b2o$134b2o57bo193b3o379bobo$133b2o
252bo$135bo252bo189b2o66b2o$577b2o66b2o$579bo67bo$516b2o187b2o$515b2o
189b2o$517bo187bo7$258bo$258b2o$257bobo63$132bo63bo63bo63bo13bo50bo69b
o56bo5bo63bo57bo63bo63bo$133bo63bo6bobo54bo63bo11bo49bobo69bobo55bo5bo
63bo57bo63bo63bo$131b3o61b3o6b2o53b3o61b3o11b3o48b2o69b2o54b3o3b3o61b
3o55b3o61b3o61b3o$205bo$775b3o$132b2o62b2o64b2o62b2o196b2o62b2o56b2o
62b2o65bo$131b2o62b2o66b2o62b2o59bo63bo72b2o62b2o56b2o62b2o63bo$133bo
7bo55bo64bo63bo62bo63bo70bo63bo57bo63bo$140b2o245b3o61b3o125b3o75b3o$
140bobo438bo75bo$580bo77bo$390b2o62b2o$391b2o62b2o316bo$390bo63bo318b
2o$260b2o453b2o55bobo$259bobo453bobo$261bo453bo64$146bo46bo69bo58bo63b
obo69bobo53bo63bo70bo56bo68bo$144b2o48b2o68bo58bo63b2o69b2o55bo63bo70b
o56bo68bo$130bo14b2o46b2o4bo62b3o56b3o63bo71bo53b3o61b3o61b3o4b3o54b3o
66b3o$131bo68bo442bo$129b3o66b3o65b3o56b3o189b3o61b3o58bo$268bo58bo
191bo63bo2bo62b3o54b3o64b2o$133b3o66b3o52b2o8bo58bo10b2o179bo63bo3bobo
62bo56bo64bobo$135bo68bo53b2o76b2o248b2o62bo56bo65bo$134bo68bo53bo80bo
47bo63bo$387bo63bo318b2o$385b3o61b3o317bobo$771bo$389b3o61b3o67bo$391b
o63bo66b2o$390bo63bo67bobo4$712b3o$712bo$713bo!

-- so maybe (I haven't checked) one of those could be combined with one of the 2G traffic-light syntheses to produce a 5G recipe.

[confocaloid]

How do I find glider syntheses for some methuselah? Suppose I would like to find syntheses for this:

Code: Select all

x = 8, y = 5, rule = B3/S23
b3o$o2bo$3bob2o$3o2b3o$5b2o!

Which database should I look up?

Here is a 6-glider synthesis for the exact configuration (no extra sparks, etc.), check generation 64:

Code: Select all

#C [[ THEME Catagolue STOP 64 ]]
x = 42, y = 32, rule = B3/S23
29bo$27b2o$28b2o$39bobo$39b2o$40bo15$bo$b2o8b3o$obo10bo$12bo4$17b2o$
18b2o$17bo22b2o$39b2o$41bo!

Code: Select all

x = 42, y = 32, rule = LifeHistory
28.BA$27.2AB$26.2B2A$25.4B10.ABA$24.4B10.B2AB$23.4B10.3BA$19.B2.4B10.
4B$15.10B10.4B$12.10B3D9.4B$11.10BD2BD3.2B3.4B$11.13BD.2D3B.4B$10.11B
3D2.3D6B$9.4B.9B3.2D6B$8.4B4.7B4.6B$7.4B6.5B4.8B$6.4B7.4B6.8B$5.4B7.
4B6.8B$4.4B7.4B6.10B$3.4B7.4B8.8B$2.4B7.4B8.7B$.A3B7.4B8.9B$B2AB7.3AB
8.4B2.5B$ABA8.2BA8.4B5.4B$12.A8.4B7.4B$20.4B9.4B$19.4B11.4B$18.4B13.
4B$17.2A2B15.4B$17.B2A17.4B$17.AB19.2B2A$39.2AB$40.BA!

I looked up the two parts separately in octo3g, and picked two three-glider collisions that were compatible with each other.

In general, if the octo3g database doesn't lead to a solution, one can also check the octohash database and the octo3obj database. The latter two databases collect predecessors in the form of stationary one-glider seeds (a constellation hit by a glider). So one would need to construct the seed as well, before hitting it by a glider. (Constructing the seed should be relatively easy, since it consists of cheap well-separated objects.)

[confocaloid]

Is there a different island that can be attached to the block with a synthesis component, such that when the resulting still life is sparked as shown below, the block is restored in the same location?

Code: Select all

x = 7, y = 12, rule = LifeHistory
2E.2E$.E.E$.E.E$2.E2$6.A$3.2C$3.2C2$.4A$A3.A$2A!

[muzik]

Have any patterns been constructed such that no cell in the plane remains on permanently, yet the overall growth rate is clearly quadratic? e.g. a nonfiller whose "eating" reaction is slower than its "filling" reaction in much the same way as a growing spaceship would be?

[Bullet51]

Have any patterns been constructed such that no cell in the plane remains on permanently, yet the overall growth rate is clearly quadratic? e.g. a nonfiller whose "eating" reaction is slower than its "filling" reaction in much the same way as a growing spaceship would be?

Make a puffer whose product is the Blinker ship 1 that goes in a direction perpendicular to the puffer.

[Bullet51]

Q1: Do all oscillators whose rotors are 1 cell thick (i.e. the rotor fits in a 1xn bounding box for some n) have period 2 or 4?

Q2: What is the smallest number m such that the oscillators whose rotors are ≤m cell thick have unbounded period?

The second question may be simplified by allowing infinite oscillators and m×∞ rotors; the lightspeed fuse works for m=3.

[dvgrn]

Q1: Do all oscillators whose rotors are 1 cell thick (i.e. the rotor fits in a 1xn bounding box for some n) have period 2 or 4?

Q2: What is the smallest number m such that the oscillators whose rotors are ≤m cell thick have unbounded period?

The second question may be simplified by allowing infinite oscillators and m×∞ rotors; the lightspeed fuse works for m=3.

m=1, isn't it? The design of the unidimensional spaceship should allow for a variant that rebuilds itself in the same location.

EDIT: D'oh -- rotor. Sorry, nothing to see here...

[Bullet51]

Q1: Do all oscillators whose rotors are 1 cell thick (i.e. the rotor fits in a 1xn bounding box for some n) have period 2 or 4?

m=1, isn't it? The design of the unidimensional spaceship should allow for a variant that rebuilds itself in the same location.

Every cell outside the 1xn region should be stationary, so the unidimensional spaceship design does not work.

[confocaloid]

Q2: What is the smallest number m such that the oscillators whose rotors are ≤m cell thick have unbounded period?

An upper bound, m ≤ 63:

Code: Select all

x = 187, y = 73, rule = LifeHistory
168.2E$169.E$165.E.E6.2E$161.E2.E.6E2.E.E.2E$161.4E6.E4.E.E$165.C3EB
5.CE.E$161.2ECBC2.CB4.3B.E.2E$160.E2.2C7B2.B3CE2.E$160.2E.12BCB2.2E$
167.9BC2E$166.10B2.E$167.9B2.E.E$163.12B4.2E$161.16B$47.E113.17B7.E$
47.3E108.B2.14B2CB5.3E$50.E106.ECB.14BCBCB3.E$49.EC106.EC17BC2B.B.CE$
49.5B8.2E94.2B.23B$51.3B8.E98.21B$49.6B4.BE.E100.18B.E$49.9B.BCE102.
15B2.E.E$47.5B2C6B104.13B5.E$46.5BC2BC5B103.12B$45.7B2C6B102.14B$44.
133B$43.4B2.68B4C57B$42.4B5.66BC3BC56B$41.4B4.68BC60BCB$40.4B5.EC2.
65BC2BC55BCBCB$39.4B7.E2.6B97.4B6.11B2C4B$38.4B5.3E5.5B95.4B6.9B.8B$
37.4B6.E5.7B65.2E27.4B8.4B5.6B.BCE$36.4B11.E.2C.3B66.E.E6.E18.4B9.2B
2CB4.5B2.BE.E$14.2E19.4B10.3EB2C2.2CB2.2E62.E6.E.E16.4B12.2E5.6B4.E$
14.E19.4B10.E4.B3.E2.C2.E69.E.E15.4B18.ECB.3B5.2E$7.2B2.BE.E18.4B12.
3E.2E3.5E61.5E3.2E.3E12.4B18.E.EB2.2B$2E5.3B.BCE18.4B15.E.E69.E2.C2.E
3.B4.E10.4B19.E$.E4.6B5.2E12.4B16.E.E6.E62.2E2.B2C2.2CB3E10.4B19.2E$.
E.EB2.5B4.B2C2B9.4B18.E6.E.E66.3B.2C.E11.4B$2.ECB.6B5.4B8.4B27.2E65.
7B5.E6.4B$4.8B.9B6.4B95.5B5.3E5.4B$4.4B2C11B6.4B97.6B2.E7.4B$6.BCBC
55BC2BC65B2.CE5.4B$7.BC60BC68B4.4B$9.56BC3BC66B5.4B$9.57B4C68B2.4B$
10.133B$11.14B102.6B2C7B$12.12B103.5BC2BC5B$4.E5.13B104.6B2C5B$3.E.E
2.15B102.ECB.9B$4.E.18B100.E.EB4.6B$5.21B98.E8.3B$3.23B.2B94.2E8.5B$
3.EC.B.2BC17BCE106.CE$4.E3.BCBC14B.BCE106.E$.3E5.B2C14B2.B108.3E$.E7.
17B113.E$10.16B$6.2E4.12B$6.E.E2.9B$8.E2.10B$8.2EC9B$6.2E2.BC12B.2E$
5.E2.E3CB2.7B2C2.E$5.2E.E.3B4.BC2.CBC2E$8.E.EC5.B3EC$8.E.E4.E6.4E$7.
2E.E.E2.6E.E2.E$11.2E6.E.E$17.E$17.2E!

[squareroot12621]

Q2: What is the smallest number m such that the oscillators whose rotors are ≤m cell thick have unbounded period?

An upper bound, m ≤ 63:

Code: Select all

x = 187, y = 73, rule = LifeHistory
168.2E$169.E$165.E.E6.2E$161.E2.E.6E2.E.E.2E$161.4E6.E4.E.E$165.C3EB
5.CE.E$161.2ECBC2.CB4.3B.E.2E$160.E2.2C7B2.B3CE2.E$160.2E.12BCB2.2E$
167.9BC2E$166.10B2.E$167.9B2.E.E$163.12B4.2E$161.16B$47.E113.17B7.E$
47.3E108.B2.14B2CB5.3E$50.E106.ECB.14BCBCB3.E$49.EC106.EC17BC2B.B.CE$
49.5B8.2E94.2B.23B$51.3B8.E98.21B$49.6B4.BE.E100.18B.E$49.9B.BCE102.
15B2.E.E$47.5B2C6B104.13B5.E$46.5BC2BC5B103.12B$45.7B2C6B102.14B$44.
133B$43.4B2.68B4C57B$42.4B5.66BC3BC56B$41.4B4.68BC60BCB$40.4B5.EC2.
65BC2BC55BCBCB$39.4B7.E2.6B97.4B6.11B2C4B$38.4B5.3E5.5B95.4B6.9B.8B$
37.4B6.E5.7B65.2E27.4B8.4B5.6B.BCE$36.4B11.E.2C.3B66.E.E6.E18.4B9.2B
2CB4.5B2.BE.E$14.2E19.4B10.3EB2C2.2CB2.2E62.E6.E.E16.4B12.2E5.6B4.E$
14.E19.4B10.E4.B3.E2.C2.E69.E.E15.4B18.ECB.3B5.2E$7.2B2.BE.E18.4B12.
3E.2E3.5E61.5E3.2E.3E12.4B18.E.EB2.2B$2E5.3B.BCE18.4B15.E.E69.E2.C2.E
3.B4.E10.4B19.E$.E4.6B5.2E12.4B16.E.E6.E62.2E2.B2C2.2CB3E10.4B19.2E$.
E.EB2.5B4.B2C2B9.4B18.E6.E.E66.3B.2C.E11.4B$2.ECB.6B5.4B8.4B27.2E65.
7B5.E6.4B$4.8B.9B6.4B95.5B5.3E5.4B$4.4B2C11B6.4B97.6B2.E7.4B$6.BCBC
55BC2BC65B2.CE5.4B$7.BC60BC68B4.4B$9.56BC3BC66B5.4B$9.57B4C68B2.4B$
10.133B$11.14B102.6B2C7B$12.12B103.5BC2BC5B$4.E5.13B104.6B2C5B$3.E.E
2.15B102.ECB.9B$4.E.18B100.E.EB4.6B$5.21B98.E8.3B$3.23B.2B94.2E8.5B$
3.EC.B.2BC17BCE106.CE$4.E3.BCBC14B.BCE106.E$.3E5.B2C14B2.B108.3E$.E7.
17B113.E$10.16B$6.2E4.12B$6.E.E2.9B$8.E2.10B$8.2EC9B$6.2E2.BC12B.2E$
5.E2.E3CB2.7B2C2.E$5.2E.E.3B4.BC2.CBC2E$8.E.EC5.B3EC$8.E.E4.E6.4E$7.
2E.E.E2.6E.E2.E$11.2E6.E.E$17.E$17.2E!

I think this is m ≤ 61:

Code: Select all

x = 186, y = 72, rule = LifeHistory
167.2E$168.E$164.E.E6.2E$160.E2.E.6E2.E.E.2E$160.4E6.E4.E.E$164.C3EB5.
CE.E$160.2ECBC2.CB4.3B.E.2E$159.E2.2C7B2.B3CE2.E$159.2E.12BCB2.2E$166.
9BC2E$165.10B2.E$166.9B2.E.E$162.12B4.2E$160.16B$46.E113.17B7.E$46.3E
108.B2.14B2CB5.3E$49.E106.ECB.14BCBCB3.E$48.EC106.EC17BC2B.B.CE$48.5B
8.2E94.2B.23B$50.3B8.E98.21B$48.6B4.BE.E100.18B.E$48.9B.BCE102.15B2.E
.E$46.5B2C6B104.13B5.E$45.5BC2BC5B103.12B$44.7B2C6B102.14B$43.133B$42.
4B2.68B4C57B$41.4B5.66BC3BC56B$40.4B4.68BC60BCB$39.4B5.EC2.65BC2BC55B
CBCB$38.4B7.E2.6B97.4B6.11B2C4B$37.4B5.3E5.5B95.4B6.9B.8B$36.4B6.E5.7B
64.2E.E7.E18.4B8.4B5.6B.BCE$14.2E19.4B11.E.2C.3B65.E.2E6.E.E16.4B9.2B
2CB4.5B2.BE.E$14.E19.4B10.3EB2C2.2CB2.2E70.E.E15.4B12.2E5.6B4.E$7.2B2.
BE.E18.4B10.E4.B3.E2.C2.E61.5E3.2E.3E12.4B18.ECB.3B5.2E$2E5.3B.BCE18.
4B12.3E.2E3.5E61.E2.C2.E3.B4.E10.4B18.E.EB2.2B$.E4.6B5.2E12.4B15.E.E70.
2E2.B2C2.2CB3E10.4B19.E$.E.EB2.5B4.B2C2B9.4B16.E.E6.2E.E65.3B.2C.E11.
4B19.2E$2.ECB.6B5.4B8.4B18.E7.E.2E64.7B5.E6.4B$4.8B.9B6.4B95.5B5.3E5.
4B$4.4B2C11B6.4B97.6B2.E7.4B$6.BCBC55BC2BC65B2.CE5.4B$7.BC60BC68B4.4B
$9.56BC3BC66B5.4B$9.57B4C68B2.4B$10.133B$11.14B102.6B2C7B$12.12B103.5B
C2BC5B$4.E5.13B104.6B2C5B$3.E.E2.15B102.ECB.9B$4.E.18B100.E.EB4.6B$5.
21B98.E8.3B$3.23B.2B94.2E8.5B$3.EC.B.2BC17BCE106.CE$4.E3.BCBC14B.BCE106.
E$.3E5.B2C14B2.B108.3E$.E7.17B113.E$10.16B$6.2E4.12B$6.E.E2.9B$8.E2.10B
$8.2EC9B$6.2E2.BC12B.2E$5.E2.E3CB2.7B2C2.E$5.2E.E.3B4.BC2.CBC2E$8.E.E
C5.B3EC$8.E.E4.E6.4E$7.2E.E.E2.6E.E2.E$11.2E6.E.E$17.E$17.2E!

[dvgrn]

I think this is m ≤ 61...

m <= 39 seems to be possible. Add 46N columns between the two halves and this relay will still work:

Code: Select all

x = 181, y = 39, rule = LifeHistory
39.2A111.2A$38.B2A112.A$16.4B3.B.9B.B2.B12.A101.A.2A.2A.A$16.4B.9B2A3B
A5B8.3A102.A.A.A.2A$15.2A13B3ABAB2A2B2A6.A92.A7.3B3.AB18.2A$15.2A13B3A
4BA2B2A5.2BA91.3A4.5B.4B17.A$16.B.15BA3BAB.B4.A3BA94.A3.10B6.2A6.BA.A
$18.16B3A2B6.A2B95.AB3.9B7.A4.2A.B2A$38.2B4.2BA2B94.A3B7A5B2.BA.A3.B2A
2B$18.16B3A4B2.A5BA95.4BA10B.B2A5.4B$6.A9.B.15BA3BA5BA5BAB93.A4BABAB2A
7B5.6B$6.3A6.2A13B3A4BA5BA5BAB93.2A3BABABABA6B5.7B2A$9.A5.2A13B3ABAB2A
13B94.B.6BAB2A5B4.8B2AB$8.2A6.4B.9B2A3BA9B3A3B96.2ABA2BAB2A4B4.12B$2.
2A4.5B3.4B3.B.9B.8B2.6B3.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.B.B.B.B.B6.B15.2B4A4B5.9BA3B$3.A6.4B20.4B2.5B.81B
.B.5B.B.B.A.B.B.B.B.9B.11B3A2B4.A$2.A6.5B20.4B3.4B.92BA3BA11B3A4BABA7B
ABAB3.3A$2.2A4.7B2.B.B.B.B.B.B.B.B.B.3B.B.92B2A2BA16B3A4BA2BA6B2A3B.A
$5.2B.124B2A3BA4BA12BA8BA11BA.A$2.2A13B2A20B5A90BA2B5A20B2A13B2A$2.A.
A11BA8BA12BA4BA129B.2B$3.A.3B2A6BA2BA4B3A16BA96B.B.3B.B.B.B.B.B.B.B.B
.B.8B4.2A$3A3.BABA7BABA4B3A11BA3BA92B.4B3.4B20.5B6.A$A4.2B3A11B.9B.B.
B.B.B.A.B.B.5B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.B.
B.B.B.B.B.B.B.B.B.B.9B.5B2.4B20.4B6.A$4.3BA9B5.4B4A2B15.B82.6B2.8B.9B
.B3.4B3.5B4.2A$4.12B4.4B2ABA2BAB2A96.3B3A9BA3B2A9B.4B6.2A$4.B2A8B4.5B
2ABA6B.B94.13B2ABAB3A13B2A5.A$5.2A7B5.6BABABABA3B2A93.BA5BA5BA4B3A13B
2A6.3A$8.6B5.7B2ABABA4BA93.BA5BA5BA3BA15B.B9.A$8.4B5.2AB.10BA4B95.A5B
A2.4B3A16B$8.2B2AB3.A.AB2.5B7A3BA94.2BA2B4.2B$6.2AB.2A4.A7.9B3.BA95.2B
A6.2B3A16B$5.A.AB6.2A6.10B3.A94.A3BA4.B.BA3BA15B.B$5.A17.4B.5B4.3A91.
A2B5.2A2BA4B3A13B2A$4.2A18.BA3.3B7.A92.A6.2A2B2ABAB3A13B2A$19.2A.A.A.
A102.3A8.5BA3B2A9B.4B$19.A.2A.2A.A101.A12.B2.B.9B.B3.4B$27.A112.2AB$27.
2A111.2A!

-- Come to think of it, I should have put the p46 glider gun on the same side of the lane as the MWSS gun. There might be an m <= 31 option, or somewhere around there.

EDIT: Hmm, maybe that doesn't actually improve anything, at least not with the 180-degree-reflection geometry. This works, for example, but it's m = 42:

Code: Select all

x = 191, y = 42, rule = B3/S23
123b2o$123b2o$112bo49b2o$112b3o12b2o2bobo29bo$115bo6b2o2b3obo3bo12b2o
14bob2ob2obo$114b2o6b2ob2o6bo13b2o15bobobob2o$126bob5o18bo7bo5bo19b2o
$117b2o8b3o21b3o5bo25bo$154bo4b2o13b2o7bobo$127b3o23b2o5bobo11bo4b2o2b
2o$113b3o3b3o4bob5o26bo2bo9bobo4b2o$6bo118b2o6bo13b2o11bo2bo8b2o$6b3o
108bo8b3obo3bo12b2o5b2o4bob2o$9bo107bo9b2o2bobo20b2o4bo2b4o$8b2o107bo
40b2ob3ob2o$2b2o156b3ob3o$3bo156bo3b2o$2bo162b2o23bo$2b2o117b3o38bob3o
3bo2bo10bo3b3o$8bo35b3o69bo3b5o18b2o18b2ob5o2b3o4b2obo3bo$2b8o33b5o21b
2o44bo3b2ob3o17b2ob3o15b2o5bo2bo6bo7bo$2bo7bo6bo2bo5b2o15b3ob2o17b3ob
2o43b3o2b2o21b5o33b8o$3bo3bob2o4b3o2b5ob2o18b2o18b5o73b3o35bo$3o3bo10b
o2bo3b3obo38b3o117b2o$o23b2o162bo$25b2o3bo156bo$24b3ob3o156b2o$24b2ob
3ob2o40bo107b2o$24b4o2bo4b2o20bobo2b2o9bo107bo$27b2obo4b2o5b2o12bo3bo
b3o8bo108b3o$17b2o8bo2bo11b2o13bo6b2o118bo$10b2o4bobo9bo2bo26b5obo4b3o
3b3o$6b2o2b2o4bo11bobo5b2o23b3o$5bobo7b2o13b2o4bo$5bo25bo5b3o21b3o8b2o
$4b2o19bo5bo7bo18b5obo$19b2obobobo15b2o13bo6b2ob2o6b2o$19bob2ob2obo14b
2o12bo3bob3o2b2o6bo$27bo29bobo2b2o12b3o$27b2o49bo$66b2o$66b2o!

EDIT2: Okay, that's better -- m <= 27 (I forgot there would be four rows of stator):

Code: Select all

x = 234, y = 106, rule = B3/S23
6bo174bo$6b3o170b3o$9bo168bo$8b2o168b2o$2b2o180b2o$3bo180bo$2bo182bo$
2b2o180b2o$8bo35b3o43b3o48b3o35bo$2b8o33b5o21b2o2b3o13b5o18b3o2b2o21b
5o33b8o$2bo7bo6bo2bo5b2o15b3ob2o17b3ob2o3bo13b3ob2o17bo3b2ob3o17b2ob3o
15b2o5bo2bo6bo7bo$3bo3bob2o4b3o2b5ob2o18b2o18b5o3bo17b2o19bo3b5o18b2o
18b2ob5o2b3o4b2obo3bo$3o3bo10bo2bo3b3obo38b3o48b3o38bob3o3bo2bo10bo3b
3o$o23b2o136b2o23bo$25b2o3bo126bo3b2o$24b3ob3o126b3ob3o$24b2ob3ob2o40b
o40bo40b2ob3ob2o$24b4o2bo4b2o20bobo2b2o9bo40bo9b2o2bobo20b2o4bo2b4o$27b
2obo4b2o5b2o12bo3bob3o8bo40bo8b3obo3bo12b2o5b2o4bob2o$17b2o8bo2bo11b2o
13bo6b2o56b2o6bo13b2o11bo2bo8b2o$10b2o4bobo9bo2bo26b5obo4b3o3b3o32b3o
3b3o4bob5o26bo2bo9bobo4b2o$6b2o2b2o4bo11bobo5b2o23b3o60b3o23b2o5bobo11b
o4b2o2b2o$5bobo7b2o13b2o4bo114bo4b2o13b2o7bobo$5bo25bo5b3o21b3o8b2o40b
2o8b3o21b3o5bo25bo$4b2o19bo5bo7bo18b5obo58bob5o18bo7bo5bo19b2o$19b2ob
obobo15b2o13bo6b2ob2o6b2o34b2o6b2ob2o6bo13b2o15bobobob2o$19bob2ob2obo
14b2o12bo3bob3o2b2o6bo36bo6b2o2b3obo3bo12b2o14bob2ob2obo$27bo29bobo2b
2o12b3o30b3o12b2o2bobo29bo$27b2o49bo30bo49b2o$66b2o52b2o$66b2o52b2o45$
6bo220bo$6b3o216b3o$9bo214bo$8b2o214b2o$2b2o226b2o$3bo226bo$2bo228bo$
2b2o226b2o$8bo35b3o43b3o94b3o35bo$2b8o33b5o21b2o2b3o13b5o64b3o2b2o21b
5o33b8o$2bo7bo6bo2bo5b2o15b3ob2o17b3ob2o3bo13b3ob2o63bo3b2ob3o17b2ob3o
15b2o5bo2bo6bo7bo$3bo3bob2o4b3o2b5ob2o18b2o18b5o3bo17b2o65bo3b5o18b2o
18b2ob5o2b3o4b2obo3bo$3o3bo10bo2bo3b3obo38b3o94b3o38bob3o3bo2bo10bo3b
3o$o23b2o182b2o23bo$25b2o3bo172bo3b2o$24b3ob3o172b3ob3o$24b2ob3ob2o40b
o86bo40b2ob3ob2o$24b4o2bo4b2o20bobo2b2o9bo86bo9b2o2bobo20b2o4bo2b4o$27b
2obo4b2o5b2o12bo3bob3o8bo86bo8b3obo3bo12b2o5b2o4bob2o$17b2o8bo2bo11b2o
13bo6b2o102b2o6bo13b2o11bo2bo8b2o$10b2o4bobo9bo2bo26b5obo4b3o3b3o78b3o
3b3o4bob5o26bo2bo9bobo4b2o$6b2o2b2o4bo11bobo5b2o23b3o106b3o23b2o5bobo
11bo4b2o2b2o$5bobo7b2o13b2o4bo160bo4b2o13b2o7bobo$5bo25bo5b3o21b3o8b2o
86b2o8b3o21b3o5bo25bo$4b2o19bo5bo7bo18b5obo104bob5o18bo7bo5bo19b2o$19b
2obobobo15b2o13bo6b2ob2o6b2o80b2o6b2ob2o6bo13b2o15bobobob2o$19bob2ob2o
bo14b2o12bo3bob3o2b2o6bo82bo6b2o2b3obo3bo12b2o14bob2ob2obo$27bo29bobo
2b2o12b3o76b3o12b2o2bobo29bo$27b2o49bo76bo49b2o$66b2o98b2o$66b2o98b2o
!

Another idea: sometimes guns pointed at each other can be arranged with a phase offset of half the period, in a way that allows the two streams' collision point to travel away from one gun and toward the other one, until some kind of guard oscillator changes the parity of the collision and starts it moving the other way. Might there be any hope of something like that working for the narrow MWSS gun above, possibly saving a few more rows?

Code: Select all

#C high-period oscillator from Cambrian-Explosion.rle
x = 275, y = 266, rule = B3/S23
31bo$31b3o$34bo$33b2o6$36bo$35b3o7b2o$34bo2b2o5bo2bo$34b2ob2o4bobobo$
33b3o2bo2b3o2bo$34b2obo$35bo7b2o$35bo3bo4bo$36bobo$37bo2$40bo$39bobo$
31b2o5bo3bo$30bo2bo8bo$30bobobo5bob2o$31bo2b3o2bo2b3o$26b2o11b2ob2o24b
2o$2o23bo2bo4b2o4b2o2bo23bo2bo$bo24bobo4bo6b3o25bobo$bobo9bo8b2o3bo13b
o22b4obo$2b2o7b4o8bob2o27b3o7b2ob2o$10bob5o8bo27b2o3bo8bo$9b2o6bo7bo26b
2o2bobo$10b3obo3bo34bo5bo6bo$11b3o3bo4bo31b2o2bo5bo$16bo4bo3b3o30bo5b
o2b2o$20bo3bob3o27bo6bo5bo$13bo7bo6b2o34bobo2b2o$13bo8b5obo14bo11bo8b
o3b2o$12b2obo8b4o16bo9b2ob2o7b3o8b2o$11bo3b2o8bo16b3o8bob4o18bobo$10b
obo39bobo24bo$10bo2bo38bo2bo23b2o$11b2o40b2o4$52bo$32bo8b2o10bo$31b3o
6bo2bo7b3o$30b2o2bo4bobobo$30bo3bo3b3obo$30bobo3bo3bo$39b2o$31b2ob2o3b
2o10b2o$33bo16bo2bo$49bobobo7bo$49bobob2o7bo$47b2obo3bo5b3ob2o$36bo10b
o2bob3o9bobo$29b2o3b2ob2o5b2obobobo2bo9bo$29b2o13bo2bo5b2o$29bo3bo3bo
bo5b2o4bobo$27bob3o3bo3bo7b5obo$26bobobo4bo2b2o7bo4bo$26bo2bo6b3o9b4o
$27b2o8bo11bo$47bo25b2o$47b2o24bobo$73bo4$39b2o$39bo$40b3o$42bo39b2o$
82bobo$82bo7$91b2o$91bobo$91bo7$100b2o$100bobo$100bo7$109b2o$109bobo$
109bo7$118b2o$118bobo$118bo7$127b2o$127bobo$127bo7$136b2o$136bobo$136b
o7$145b2o$145bobo$145bo7$154b2o$154bobo$154bo7$163b2o$163bobo$163bo7$
172b2o$172bobo$172bo7$181b2o$181bobo$181bo7$190b2o$190bobo$190bo3$232b
o$232b3o$235bo$234b2o$199b2o$199bobo$199bo$236bo$226b2o8b4o$227bo12bo
$225bo11b2obo5b2o$223b4o10b2o6bo2bo$222bo4bo8bo7bobobo$208b2o11bob5o6b
4o5b3obo$208bobo10bobo4b2o8bo6bo$208bo11b2o5bo2bo2bo3b2o5b2o$220bo2bo
bobob2o3bo2b2o5b2o$220b3obo2bo7b2o$220bo3bob2o$220b2obobo$221bobobo$221b
o2bo18b2o$217b2o3b2o10b2o5b2o2bo$217bobo14b2o5b2o3bo$217bo16bo6bo$232b
ob3o5b4o$231bobobo7bo$231bo2bo6b2o$232b2o$239bo2bo$240b2o$226b2o15b2o
$226bobo11b2ob2o$220b2o4bo13b2ob2o17b2o$194b2o23bo2bo18bob2o16bo2bo$195b
o13bo10bobo18bob2o17bobo$195bobo9bo2bo5b4obo21b2o4b2ob2o4b2o3bo$196b2o
9bo3bo4b2ob2o17bo2bo2bo4b2ob2o5bob2o$201b2o3b2o3bo7bo17bo7bo3bo3b2o6b
o$202bob2obob2o21b3o2bo8b2ob2ob2o7bo$202bob2o2b3o20bo3b3o4bo5b5o$202b
o20bo13b2o2bo2bobo4bo$203b2o19bob2o8bo3bo18bo2b2o2b2o$216b3o2bo2bob4o
bo3bo22b5obob2o$216b2obobobo10bo14bo7b2ob2o$207bo7bo3b2o4b6o18bo6b2o3b
o2b4o$206b2ob2o4bo3bo5b7o3bo12b2obo5b2ob3o3bo4b2o$205bob4o5bo2bo12bo14b
o3b2o4b2ob2o9bobo$204bobo10bo15bobo5bo4bobo24bo$204bo2bo25bo6b2o4bo2b
o23b2o$205b2o27bo12b2o$230b5o3b3o2bo$230b2ob2o5bobobo$234b2o5bo2bo$230b
2ob2o7b2o$230b4o$232bo2$239bo$238b4o$230bo6b2ob2o$230b2o4b2o$237b2ob2o
$228bo2b3o3b5o$227bobobo4b2o2bo$227bo2bo5bo$228b2o7bobo$239bo$236b2ob
2o$236b2obo4$240b2o$240bo$241b3o$243bo!

[shirAko]

Is there a python script that, given a spaceship/rake synthesys, makes the corresponding gun/rake?

[dvgrn]

Is there a python script that, given a spaceship/rake synthesys, makes the corresponding gun/rake?

Not exactly. We know how to write a script like that, but without a whole lot of optimization work, the patterns will come out so un-optimized and ugly that nobody seems to want to see them.

Instead we've got some helper scripts like Goldtiger997's place-edgeshooters-automatic.py, which can be used to semi-automatically create things like spaceship guns.

[Drelectron8]

How do we calculate an equivalent Wolfram rule for any 1-range cellular automata rule?

[pifricted]

How do we calculate an equivalent Wolfram rule for any 1-range cellular automata rule?

For non-strobing rules, look up the cells.

Code: Select all

#W150
x = 1, y = 1, rule = B3/S238:T0,1
o!

For strobing rules, idk.
(e.g. B026/S1)

Code: Select all

x = 20, y = 1, rule = B026/S1
obo2b5o3b7o!

[Citation needed]

Is this the usual way for the paperclip to form?