## B3/S23-e

For discussion of other cellular automata.

### B3/S23-e

B3/S23-e is like Life, but much more stable. Traffic lights are also slightly less common, because only the bullet heptomino generation and onwards of the T generates the traffic light sequence. Along with that, the B-heptomino and R-pentomino generate much less forward momentum:
x = 3, y = 24, rule = B3/S23-e2o$b2o$bo18$3o$2bo$2bo$bo!

There are novel oscillators known for periods 2, 6, 9, 12, and 80:
x = 82, y = 15, rule = B3/S23-e2o7b2o9b2o6b2o13b2o$obo6bobo7bobo7bo13bo28bo$2bo2bo6bo5bo10bobo9bobo27bobo$bo3bo5bo7b2o9b2o5bo3b2o29bo$2bo2bo18b2o10bobo$obo19bo2bo9b2ob2o$2o14b3o3bobo11bobo$16bo2bo3bo13bo$19bo$18b2o33b2ob2o18b2ob2o$54bobobo18bobobo$55bob2o19bob2o$56bo22bo$57b2o21b2o$58bo22bo!

I feel like a two-p80 gun is on the horizon. I tried looking through a bunch of combinations but they didn't yield anything special besides creating and deleting a blinker, but I lost that one. It was still p80 anyway.

There's a 2c/6 ship and a (12,6)c/40 knightship:
x = 18, y = 5, rule = B3/S23-e2obo8b2ob2o$2o2bo8bo2b2o$4bo9b3o$obo12bo$3o!

Here are a couple useful two-(knight)ship puffers, as well as a three-ship rake, although a two-ship rake seems likely. I couldn't have gotten all of the ship pairings, after all:
x = 842, y = 60, rule = B3/S23-e14bo51b2o42b2o49bo51bo51bo49bo43b2o4b2o43bo56b3o45b2o44b2o3b3o48b2o3b3o37b2o3b3o41b2o3b3o40b2o$13b2o51b2o41bo3bo46b2o45b2o3b3o49b2o48bo5b2o37bo4b2obo41b2o51b2o3bob2o43bo45bo2bo2bo2bo46bo2bo2bo2bo35bo2bo2bo2bo39bo2bo2bo2bo38bo$13bo3b2o47bo3b3o35bo5bo45bo3b2o40bo2bo2bo2b2o47bo3b2o44bo5b2o37b3o3bobo40bobo50bo5bo3bo41bo4bo42bobo5b2o46bobo5b2o35bobo5b2o39bobo5b2o36bo4bo$14bo3b2o46b2o4bo37bo3bo46bo3b2o39b2o6bobo48bo3b2o44b2obo3bo37bobo2b3o34b2o5bo3b3o45b3o4b2obo35b2o5b2o3bo41bo7bo47bo7bo36bo7bo40bo7bo31b2o5b2o3bo$13bo3b2o51b3o36b2o2b2o45bo3b2o42bo5b2o48bo3b2o45bo5bo39b6o34bo2bo4b3o50bo5bo2bo35b2o10b2o48bo55bo44bo48bo31b2o10b2o$16bo51b2o40bobo50bo50b2o51bo48bo3b2o40b4o35bo2bo6b2o3bo52b2o35bo2bo5bob4o42bo4bo50bo4bo39bo4bo43bo4bo31bo2bo5bob4o$14bobo52bo40b3o48bobo46bo54bobo49b3o43bo37b2ob2o5bo95bobo6bo2b2o43b2o54b2o43b2o47b2o35bobo6bo2b2o$15bo52bo93bo47bo55bo145bo2bo91bobo7b3o231bobo7b3o$412b3o103bo81b2ob2o45b2ob2o45b2ob2o57bo$50b2ob2o195b2ob2o295b2ob2o46bo2b2o45bo2b2o45bo2b2o$2ob2o46bo2b2o195bo2b2o44b2ob2o45b2ob2o196bo2b2o46b3o47b3o47b3o$bo2b2o46b3o45b2ob2o147b3o46bo2b2o45bo2b2o94b2ob2o97b3o48bo49bo49bo$2b3o48bo47bo2b2o44b2ob2o45b2ob2o48bo48b3o47b3o96bo2b2o97bo$3bo98b3o46bo2b2o45bo2b2o97bo49bo98b3o$103bo48b3o47b3o248bo$153bo49bo196b2ob2o95b2ob2o$401bo2b2o95bo2b2o$402b3o97b3o$403bo99bo29$836b2ob2o$837bo2b2o$838b3o$839bo6$833b2ob2o$834bo2b2o$835b3o$836bo!

This pair of (knight)ships creates a tub and a loaf and deletes both:
x = 34, y = 17, rule = B3/S23-e7b2o$6bo2bo7b2o$7bo6b2o13b2o$13bo4bo8b2o2bo$12bo4bo9bo2bobo$13bobo6bo9b2o$21b2obo3bobo2bo$obo19bobo3bo3b2o$b3o19bo6b2o$2o2bo6bo$2b2o6b2o$10bo3b2o$11bo3b2o$10bo3b2o$13bo$11bobo$12bo!

Two ships combine to make a (6,3)c/20 ship:
x = 24, y = 18, rule = B3/S23-e18bo$10bo7bo$8bo2bo$8bo$3b2o2bo3b2o$2b3o6b2o$bo2bo13b6o$2o16b2o3bo$2bo17bo2bo$20b3o2$3b2o$2bo3bo$bo5bo$3bo3bo$2b2o2b2o$3bobo$3b3o!

An 11c/180 orthogonal puffer showed up in D4_+2, and it is just two very distant B-heptominoes:
x = 3, y = 33, rule = B3/S23-e3o$2bo$2bo$bo26$bo$2bo$2bo$3o! This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) B2-ac3i4a/S12 drc Posts: 1592 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: B3/S23-e drc wrote:An 11c/180 orthogonal puffer showed up in D4_+2, and it is just two very distant B-heptominoes: x = 3, y = 33, rule = B3/S23-e3o$2bo$2bo$bo26$bo$2bo$2bo$3o!

8-engine 11c/180 p180 spaceship:
x = 198, y = 150, rule = B3/S23-e155b2o6bo9b2o$155bobob2o2bo3b2o3b2o$157b2o4bo3b2o5bo$157bo4bo$158bo2bo$86bo10bo62bo$85bobo8bobo$85bo2bo7bo2bo6b3o8b3o8b3o8b3o8b3o$86b2o9b2o67b3o4$169bo$168bobo$168bobo$168b2o2$168b2o$168bobo$84b2o23bo58bobo24b2o$84b2o10b3o8b2ob2o57bo25bobo$97b2o7bo3b2o85bo$99bo6bobob2o83b3o$98b2o6bo2b2o$98bo8bo58b3o$14bo10bo10bo10bo10bo10bo10bo25bo21b3o8b3o8b3o$14bo10bo10bo10bo10bo10bo10bo26b2o79bo$14bo10bo10bo10bo10bo10bo10bo79bo27bo$158bo2bo26bo$157bo4bo$157b2o4bo3b2o$155bobob2o2bo3b2o$155b2o6bo2$123bo$122b3o$122bob2o$123bobo$123bo2bo$120b2o4bo$120b2o4bo$121b2o$123b3o8b2o9b2o$58bo10bo10bo53bobo8bobo$58bo10bo10bo26b2o11b2o13bo10bo8bo10bo10bo10bo$58bo10bo10bo25bo13b2o33bo10bo10bo10bo$98bo8bo47bo10bo10bo10bo$98b2o6bo2b2o$99bo6bobob2o$97b2o7bo3b2o$84b2o10b3o8b2ob2o83b3o$84b2o23bo87bo$195bobo$195b2o11$97bo$96bo$53b3o40b3o$53bo$54bo2$174bo$172b2o$173b2o4$58bobo$58b2o32b2o$59bo31b2o$93bo2$177b3o$177bo$178bo13$114b2o74bo$84b2o28bobo71b2ob2o$84b2o9b2o19bo70bo3b2o$94bo2bo16b3o70bobob2o$94bo3bo88bo2b2o$94bo6bo86bo$94bobobob3o84bo$96bo5bo4bo46b3o8b3o8b3o9b2o$57b3o8b3o8b3o15b2ob2o5bo27bo10bo$98bob2o5bo26bobo8bobo$99bo34b2o9b2o8$124b2o$124b3o40bo$125bo29b2o9bobo$120b2o33b2o8bo2bo$121b2o41bo2b2o$2b2o116b2o45bo$o4bo93bo20bo2bo40bo$o4bo92bob2o5bo16bo63b2o$o4bo7b3o8b3o8b3o8b3o8b3o8b3o8b3o15b2ob2o5bo13bo2bo4bo10bo10bo12bobo20bo$2b2o92bo5bo4bo14b3o4bo10bo10bo36bo$94bobobob3o26bo10bo10bo11bo23bo2b2o$94bo6bo61bo2bo20bobob2o$94bo3bo65bo3b2o17bo3b2o$94bo2bo16b3o48bo3bo18b2ob2o$84b2o9b2o19bo49b3o21bo$84b2o28bobo$114b2o6$166b3o$165bo3bo$164bo3b2o$163bo2bo$86b2o9b2o8bo10bo10bo10bo10bo11bo$85bo2bo7bo2bo7bo10bo10bo10bo10bo26bo$85bobo8bobo8bo10bo10bo10bo10bo12bobo10bo$86bo10bo79b3o$164bo$167bo$164bo2b2o$155b2o8bo2bo$155b2o9bobo$167bo! Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) : 965808 is period 336 (max = 207085118608). AbhpzTa Posts: 313 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: B3/S23-e AbhpzTa wrote:8-engine 11c/180 p180 spaceship: rle Shameless corollary snipe, but 4-engine clean quadruple rake: x = 117, y = 112, rule = B3/S23-e84b2o23bo$84b2o10b3o8b2ob2o$97b2o7bo3b2o$99bo6bobob2o$98b2o6bo2b2o$98bo8bo$14bo10bo10bo10bo10bo10bo10bo25bo$14bo10bo10bo10bo10bo10bo10bo26b2o$14bo10bo10bo10bo10bo10bo10bo16$58bo10bo10bo$58bo10bo10bo26b2o$58bo10bo10bo25bo$98bo8bo$98b2o6bo2b2o$99bo6bobob2o$97b2o7bo3b2o$84b2o10b3o8b2ob2o$84b2o23bo13$97bo$96bo$53b3o40b3o$53bo$54bo8$58bobo$58b2o32b2o$59bo31b2o$93bo17$114b2o$84b2o28bobo$84b2o9b2o19bo$94bo2bo16b3o$94bo3bo$94bo6bo$94bobobob3o$96bo5bo4bo$57b3o8b3o8b3o15b2ob2o5bo$98bob2o5bo$99bo13$2b2o$o4bo93bo$o4bo92bob2o5bo$o4bo7b3o8b3o8b3o8b3o8b3o8b3o8b3o15b2ob2o5bo$2b2o92bo5bo4bo$94bobobob3o$94bo6bo$94bo3bo$94bo2bo16b3o$84b2o9b2o19bo$84b2o28bobo$114b2o!
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: 1354
Joined: September 13th, 2014, 5:36 pm
Location: 0x-1

### Re: B3/S23-e

I noticed the B-heptomino turns around after 72 generations, and is almost a p144 oscillator, I couldn't find a way to finish it, sadly :^(
x = 16, y = 29, rule = B3/S23-e12bo$12b3o$15bo$14b2o9$8bo$9bo$9bo$7b3o$2b2o$bobo$bo$2o6$8b2o$8bo$9b3o$11bo! And then there's this 4-boat (the oscillator,not the hypothetical constellation) producing reaction: x = 8, y = 8, rule = B3/S23-e3o$3o$bo3$6b2o$5b3o$6b2o!

It leads to this 6G synth, although the cleanup glider being moved to a different side would be preferrable:
x = 25, y = 25, rule = B3/S23-eo$b2o2bo$2o4b2o$5b2o$13bo$13bobo$13b2o3$19bo$18bo$18b3o6$22bo$21b2o$21bobo3$23bo$22b2o$22bobo! A single dot spark can turn an eater into a boat-with-tail, leading to this 2G component: x = 12, y = 9, rule = B3/S23-e6bobo$6b2o$b2o4bo$obo$2bo$8b2o$8bo$9b3o$11bo! There's also this weird almost catalyst? A similar catalysis could work in Life: x = 16, y = 15, rule = B3/S23-e6b2o$6b2o6b2o$14bo$12bobo$bo10b2o$2bo$2bo$3o10b2o$13b2o2$8b2o$8b2o2b2o$12bobo$14bo$14b2o!

Wing->LoM+Junk->B using only two blocks:
x = 26, y = 29, rule = B3/S23-eHistory21.3D$21.D2.D$25.D7$.A$A.A$A2.A$.3A6$2A$2A8$19.2A$19.2A!

EDIT: 4G synth of the 11c/180 switch:
x = 13, y = 37, rule = B3/S23-eobo$b2o$bo4$10b3o$10bo$11bo22$4bo$5b2o$4b2o2$3bo$2b2o$2bobo! This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.) B2-ac3i4a/S12 drc Posts: 1592 Joined: December 3rd, 2015, 4:11 pm Location: creating useless things in OCA ### Re: B3/S23-e drc wrote:I noticed the B-heptomino turns around after 72 generations, and is almost a p144 oscillator, I couldn't find a way to finish it, sadly :^( x = 16, y = 29, rule = B3/S23-e12bo$12b3o$15bo$14b2o9$8bo$9bo$9bo$7b3o$2b2o$bobo$bo$2o6$8b2o$8bo$9b3o$11bo!

p144 oscillator using 2 Bs and catalysts:
x = 35, y = 37, rule = B3/S23-e19b2o$19b2o7$33b2o$33bo$31bobo$18bo12b2o$17b2o$16b2o$17b2o8$16b2o$17b2o$16b2o$2b2o12bo$bobo$bo$2o7$14b2o$14b2o! p144 glider gun: x = 58, y = 56, rule = B3/S23-e8bo$8b3o$11bo$10b2o7$10b3o$9bob2o$9bo3bo21bo$10b2o2bo18b3o$2o9b3o18bo$2o30b2o5$23b3o$22bo2b2o22bo$23bo3bo19b3o$24b2obo18bo$24b3o19b2o7$25b2o$25bo$26b3o$28bo$56b2o$56b2o$34bo8bob2o$33b3o7b3o$32b2obo8bo$21b2o$21b2o11$31b2o$32bo$29b3o$29bo!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
AbhpzTa

Posts: 313
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan