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## Day & Night (B3678/S34678)

For discussion of other cellular automata.

### Re: Day & Night (B3678/S34678)

Is this non-monotonic 123 cell c/6 cell ship known? I did not find it here or on related pages.
x = 17, y = 18, rule = B3678/S346783bob5obo$5b5o$3obo2bo2bob3o$2bo9bo$bob4ob4obo$3bob5obo$4b7o$4b7o$3b9o$4b7o$15o$b6ob6o$b4o5b4o$bobobo3bobobo$2bobo5bobo$3bo7bo$o3bo5bo3bo$2bo9bo! It is slightly larger (1 cell) than the smallest currently known c/6 ship. 2718281828 Posts: 738 Joined: August 8th, 2017, 5:38 pm ### Re: Day & Night (B3678/S34678) 2718281828 wrote:Is this non-monotonic 123 cell c/6 cell ship known? I did not find it here or on related pages. I don't think it is, nice find! That's also kind of hilarious that it is one cell above the best known. I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### Re: Day & Night (B3678/S34678) AforAmpere wrote:That's also kind of hilarious that it is one cell above the best known. Yes. But this c/6: x = 15, y = 16, rule = B3678/S346787bo$6bobo$6b3o$6bobo4$6b3o$6b3o$4bo2bo2bo$3bob5obo$3b9o$4ob5ob4o$2obob5obob2o$b2o4bo4b2o$7bo! is substantially smaller, 63 cells. 2718281828 Posts: 738 Joined: August 8th, 2017, 5:38 pm ### Re: Day & Night (B3678/S34678) Awesome find! I'll update the wiki. I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule - Finish a rule with ships with period >= f_e_0(n) (in progress) AforAmpere Posts: 1047 Joined: July 1st, 2016, 3:58 pm ### Re: Day & Night (B3678/S34678) A slightly smaller 2c/5, 254 cells: x = 23, y = 30, rule = B3678/S346783bob2o9b2obo$2b4o11b4o$3b3o11b3o$bo2bo13bo2bo$obobo13bobobo$2b2o3bo7bo3b2o$2b8o3b8o$4b5o5b5o$2b8o3b8o$3b7o3b7o$5b3o7b3o$3b6o5b6o$3b3obobo3bobob3o$4bo2bobo3bobo2bo$2b2ob4o5b4ob2o$2b3o4bo3bo4b3o$3bo5bo3bo5bo$6bob2o3b2obo$6bo9bo$3bo2bo3bobo3bo2bo$2b8obob8o$2b2o3bo3bo3bo3b2o$bo2bo2bobobobobo2bo2bo$b4o5b3o5b4o$10b3o$2b2ob3o7b3ob2o$3bo2b2o2bobo2b2o2bo$4b2o3b5o3b2o$5bob2obobob2obo$6b4o3b4o!

2718281828

Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Day & Night (B3678/S34678)

Nice. Which program are you using for these? ntzfind, gfind, or something else?
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)
AforAmpere

Posts: 1047
Joined: July 1st, 2016, 3:58 pm

### Re: Day & Night (B3678/S34678)

AforAmpere wrote:Nice. Which program are you using for these? ntzfind, gfind, or something else?

Nothing else than the mentioned ones. Gfind and ntzfind. Ntzfind for the c/6 ship (with restricted length), for the 2c/5 gfind.

Maybe for the record: Another 2c/5 and a relatively small asymmetric c/3 (still a bit larger than the symmetric record holder).
x = 51, y = 53, rule = B3678/S346789$7b3o$5b7o22bo$4b2ob3ob2o20bobo$4bo3bo4bo18b5o$3b3o2bo2b2o18b2obob2o$5b2o2bob2o16b2o2bobo2b2o$4b3o2bobobo14b2ob3ob3ob2o$5bobo5b2o13b2o2b2ob2o2b2o$6b2o19b3o2bobobo2b3o$5bo21b2ob2obobob2ob2o$26bobo4b3o4bobo$25b3obobo2bo2bobob3o$29b5ob5o$24bob3ob9ob3obo$25bo3b11o3bo$24b2o2b13o2b2o$26bob13obo$26bo2b11o2bo$28b13o$26b2obob7obob2o$27bob11obo$31bob3obo$34bo$30b3obob3o$29bob3ob3obo$30b9o$30b9o$27b2o2b7o2b2o$26b3o3b5o3b3o$26bob2obob3obob2obo$25bo2b3o2b3o2b3o2bo$26b2ob2o2b3o2b2ob2o$25b6o7b6o$27bo2bo7bo2bo$27b2o2bo5bo2b2o$27bob2o7b2obo$26b2obo9bob2o$26b4o9b4o$26bo15bo! I think, a plausible speed where we might find a ship is 2c/7 diagonal. 2718281828 Posts: 738 Joined: August 8th, 2017, 5:38 pm ### Re: Day & Night (B3678/S34678) 2718281828 wrote:I think, a plausible speed where we might find a ship is 2c/7 diagonal. Funnily enough, I've already been running a width-19 bilaterally symmetric 2c/7d gfind search for a few CPU hours now (but I started it well before you posted). I'll post if it finds anything, but I'd imagine ships probably don't exist until width 21 or 23. EDIT: I was correct in my guess — there are no bilaterally-symmetric ships at width 19. Gfind output: ./gfind B3678/S34678/L140/D7/N2/Ugfind 4.6, D. Eppstein, 10 February 2001Rule: B3678/S34678/L140/D7/N2/USearching for speed 2c/7, width 19, diagonal, bilateral symmetry.Queue full, depth 5, deepening 7, 524k/531k -> 34k/36kQueue full, depth 5, deepening 14, 524k/533k -> 19k/23kQueue full, depth 6, deepening 20, 524k/535k -> 8.1k/11kQueue full, depth 7, deepening 26, 524k/535k -> 4.9k/8.4kQueue full, depth 8, deepening 32, 524k/547k -> 1.9k/5.6kQueue full, depth 10, deepening 37, 524k/566k -> 888/3.9kQueue full, depth 13, deepening 41, 524k/618k -> 534/3.1kQueue full, depth 15, deepening 46, 524k/565k -> 282/2.2kQueue full, depth 19, deepening 49, 524k/672k -> 188/1.9kQueue full, depth 23, deepening 52, 524k/641k -> 107/1.4kQueue full, depth 28, deepening 54, 524k/602k -> 69/1.0kQueue full, depth 32, deepening 57, 524k/572k -> 51/854Queue full, depth 37, deepening 59, 524k/634k -> 44/881Queue full, depth 41, deepening 62, 524k/597k -> 32/670Queue full, depth 48, deepening 62, 524k/1.0M -> 24/634Queue full, depth 56, deepening 61, 524k/994k -> 14/420Queue full, depth 66, deepening 58, 524k/1.2M -> 19/469Queue full, depth 72, deepening 59, 524k/958k -> 17/432Queue full, depth 77, deepening 61, 524k/556k -> 10/371Queue full, depth 82, deepening 63, 524k/628k -> 7/241Queue full, depth 93, deepening 59, 524k/1.6M -> 4/261Queue full, depth 119, deepening 40, 524k/3.0M -> 5/384Queue full, depth 140, deepening 26, 524k/1.7M -> 53/445Queue full, depth 145, deepening 28, 524k/648k -> 83/480Queue full, depth 154, deepening 26, 524k/1.2M -> 97/809Queue full, depth 163, deepening 24, 524k/1.1M -> 342/1.6kQueue full, depth 169, deepening 25, 524k/939k -> 313/1.7kQueue full, depth 174, deepening 27, 524k/827k -> 105/903Queue full, depth 181, deepening 27, 524k/943k -> 33/511Queue full, depth 195, deepening 20, 524k/1.5M -> 59/627Queue full, depth 204, deepening 18, 524k/1.1M -> 55/590Queue full, depth 218, deepening 11, 524k/2.3M -> 516/2.0kQueue full, depth 224, deepening 12, 524k/1.0M -> 36/483 Unfortunately, I did not think to keep the longest partial. If anyone else wants to run the width-21 and/or 23 searches, feel free — it seems like they might be worthwhile, but I don't have the patience or the CPU time to spare at the moment. 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: 1880 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 ### Re: Day & Night (B3678/S34678) New smallest 2c/5 with 164 cells: x = 26, y = 20, rule = B3678/S346785b3o10b3o$3b3ob3o6b3ob3o$2b3o2b4ob2ob4o2b3o$3b2o2b3ob4ob3o2b2o$2bob3o2bob4obo2b3obo$2b3o5b6o5b3o$2bo7bo4bo7bo$2o2bo6b4o6bo2b2o$3bobo5bo2bo5bobo$3b2o16b2o$2bo2b3o10b3o2bo$5b2obo8bob2o$b8o8b8o$2bob4o10b4obo$2b2ob4o8b4ob2o$4bo2bo10bo2bo$6bo12bo$8bo8bo$7b2o8b2o$8bo8bo!

2718281828

Posts: 738
Joined: August 8th, 2017, 5:38 pm

### Re: Day & Night (B3678/S34678)

velcrorex wrote:Found this pattern and I'm not sure quite how to classify it. It's like a wickstretcher, except the wick is "noisy".
x = 40, y = 13, rule = B3678/S34678bboo13bo$boo12b6o$5o8boob3o$b3obo7b6obboo6bobbo3boo$bbo3bob3obbobb4obbo4b5ob5o$3bobboo3bobob11oboobb8o$4b10obbob7o3boobb6obo$3bobboo3bobob11oboobb8o$bbo3bob3obbobb4obbo4b5ob5o$b3obo7b6obboo6bobbo3boo$5o8boob3o$boo12b6o$bboo13bo!

Just call it a "wickpuffer".
I will call it a "wickpuffer", since I can`t find a pattern of the oscillating "noise", which might be simulating a dirty puffer in a 1dimensional CA (i dunno)
Can anyone prove that this is aperiodic or not?
CollinGao

Posts: 4
Joined: July 31st, 2019, 7:42 am

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