B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8

[MathAndCode]

Moosey rulegolfed this rule after I provided B2ci3ai4c8/S1e2aei3-cnry4eiz5air6i7e8. The rule probably is omniperiodic; all periods below twenty already have known oscillators.
Here are the oscillators that I have found myself:

Code: Select all

x = 279, y = 1426, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
83b2o$53bo6bo22b2o2b2o41b2o$53bo6bo24bo2bo21b2o18bo2bo$27bo2bo24bo2bo
26bo27bo15b2ob2o$4b2o21bo2bo23b2o2b2o22bo2bo26b2obo2b2o$5bo19bobo2bob
o22bo2bo23b2o2b2o28bo$2bo22bo6bo20bo6bo25b2o28b2o$2b2o49bo6bo17$5b2o3b
2o47bo3bo$59bo3bo$3bo3b3o3bo47bo$3bo4bo4bo42b2o3bo3b2o$5bo5bo49bo$5b2o
3b2o46b3ob3o59b2o2bo$5bo5bo49bo62bo2b2o$3bo4bo4bo42b2o3bo3b2o56b2o$3b
o3b3o3bo47bo$59bo3bo$5b2o3b2o47bo3bo14$41b2o31b2o3b2o$74b2o3bo$39b3o30b
2o3bo4bo22b2o$35bo36b2o2b3o2b2o22b2o2b2o$6bo4bo23bobo5bo32b3o30b2o$3b
2obo4bob2o22bo5bo32b3o27bo$6bo4bo25bo5bobo30b3o25b2o$45bo26b2o2b3o2b2o
21b2o3bo$39b3o30bo4bo3b2o25b2o$75bo3b2o$38b2o34b2o3b2o11$2bo4b2o$2bob
o$4bo$4bo$7b2o13$93b2o$93b2o4$3bo10bo28bo5bo42b3o$3bo10bo28bo5bo42b3o
$5bo6bo32bo39b2o3b2o3b2o51bo$5bo6bo32bo2bo36b2o3b2o3b2o3b2o41b2o3b2ob
2o$5bo6bo32bo44b2o3b2o3b2o42bo3bo2bo$3bo10bo28bo5bo42b3o46b2o4bo5b2o$
3bo10bo28bo5bo42b3o4$92b2o$92b2o12$5b2o3b2o3$2bo5bo5bo$2bo5bo5bo$8bo$
5b3ob3o$8bo$2bo5bo5bo$2bo5bo5bo3$5b2o3b2o16$70bo$70bo11bo$5bo66bo9bo26b
o4bo$5bo2bo4bo20b2o2b2o31b3o6bo28bo4bo$7b2o4b2o19b2o2b2o4b2o26bo6b3o29b
o$8bo4bo2bo21b2o4b2o24bo9bo29b2o$16bo53bo11bo28bo$82bo26bo4bo$109bo4b
o11$259bo$259bo$261bo$260b2o2$219bo$219bo32bo3bo7bo$16bo32bo60bo14bo91b
o34bo4bo5bo$16bo33bo25b2o32bo14bo51b2o38b2o38b2o3b2o$18bo31b2o27b2o5b
2o24bo10bo42bo2bo5bo81bo5bo4bo$17b3o25bo4bo2bo24b3o5b2o23b2o10b2o34b2o
5b4o5b2o31b2o13b2o31bo7bo3bo$18bo26bo3bo3bo25b2o31bo10bo36bo5bo2bo46b
obo2bo$16bo6bo52b2o32bo14bo31b2o51b2o4bob2ob2o$16bo6bo86bo14bo85bo4bo
bo34bo3bo7bo$208b2o13b2o28bo4bo5bo$258b2o3b2o$214b2o42bo5bo4bo$215bo41b
o7bo3bo$213bo$213bo$260b2o$261bo$259bo$259bo2$14bo$14bo$11b2obob2o$14b
o3$13b3o$15bo$13bo$16b2o13$12b2o3$9b2o7b2o26b2o$9b2o7b2o29bo5b2o$12bo
3bo31b2o5bo$10bobo3bobo30bo7b2o$12bo3bo29b2o$9b2o7b2o$9b2o7b2o3$12b2o
14$19b2o$20bo$15bo2$16b3o2$8b2o$8bo7b3o5bo$12bo2bo3bo2bo$12bo2bo3bo2b
o$12bo2bo3bo2bo$10bo5b3o7bo$25b2o2$16b3o2$19bo$14bo$14b2o17$20b2o$20b
2o2$11bo$11bobo9bo$13b2o7b2o$13bo9bobo$25bo2$15b2o$15b2o11$131bo3bo$131b
o3bo3$77b2o53b3o$16b2o59b2o53b3o2bo$16b2o66bo52bo42bo$84bo95bo$9b2o21b
2o46b2o100bo4bo$12bo2bo11bo2bo40b2o7b2o99b2o4bo$11b6o9b6o42bo5b2o100b
o4bo9bo$12bo2bo11bo2bo42b2o9bo95bo16bo$9b2o21b2o50bo95bo9bo4bo$78bo111b
o4b2o$25b2o50b2o49bo61bo4bo$25b2o101bo2b3o63bo$131b3o63bo3$130bo3bo$130b
o3bo16$53b2o$53b2o2$16bo$16bo31bo$48bobo$50b2o11bo$50bo11b2o$63bobo$65b
o$12bo3bo$12b5o$14bo45b2o$60b2o19$54b2o3b2o$57bo$56b3o$57bo$97bo$14bo
82bobo$14bo33bo17bo32bo$12bobo33bo17bo32bo$12bo8b2o27bo13bo46bo$49b3o
11b3o45bo$50bo13bo46bobo$48bo17bo46bo$48bo17bo3$57bo$56b3o$57bo$54b2o
3b2o9$16bo3bo34bo$16bo3bo34bo3b2o47bo$53bo5b2o47bo$53b2o51bo$17b3o77b
2o7b2o$17b3o47b2o28b2o$53bobo9bo$53bob2o8b2o38bobo$53bobo41bo6b2obo$20b
2o26b2o55bobo$20b2o26b2o$59b2o48b2o$53b2o5bo39b2o7b2o$53b2o3bo42bo$58b
o40bo$99bo11$21b2o$21bo4$11bo7bo41b2o$11b2o6bo$19bo33bo$16b3ob3o30bob
o9bo$19bo35b2o7b2o$19bo6b2o27bo9bobo$19bo7bo39bo2$58b2o2$17bo$16b2o10$
20bo$20bo6$10bo3bo7bo$10bo4bo5bo$15b2o3b2o$15bo5bo4bo$14bo7bo3bo5$16b
2o15$15b2o3b2o$15b2o3b2o2$17b3o2$17b3o$18bo3$22bo$13bo8bo$13bo3$17bo$
16b3o2$16b3o2$14b2o3b2o$14b2o3b2o16$19b2o$19b2o$26bo$26bo$21bo2bo$21b
o2bo$21bo2bo$10bo15bo$10bo15bo$19b2o$19b2o14$22b2o3$131bo$22bo101b2o5b
o$20bo103b2o3bo$11bo8bo46bo11bo49b2o$11bo3bo4bo46bo3bo7bo37b2o$70bo46b
2o19b2o$16b3o3b3o44b2o53bo11bo$70bo53bo11b2o$20bo4bo3bo94bobo$20bo8bo
$20bo49b2o3b2o$18bo52bo3bo48b2o$69bo7bo47bo3b2o$69bo7bo45bo5b2o$123bo
$17b2o16$13bo$13bo$15bo$12b2obo4b2o$15bo$13bo$13bo19$12b2o6b2o$20b2o6$
11bo5b3o$11bo3bob3obo$15bob3obo$15bob3obo3bo$17b3o5bo5$23b2o$15b2o6b2o
$15b2o26$22b2o$22b2o2$27b2o$8b2o13b2o$12b2o9b2o$12b2o9b2o$12b2o13b2o$
8b2o2$13b2o$13b2o24$88b2o25b2o$21b2o65b2o25b2o63bo3bo59bo3bo$180bo3bo
59bo3bo$182bo63bo$181b3o61b3o$245b3o6b2o$111bo3bo74b2o62b2o$85b3o102b
2o$113bo$8bo10bo54b2o21b2o14bo67b3o53b2o$8bo10bo54b2o9b3o9b2o8bo5bo5b
o52b2o63b2o$19bo61bo2bo3bo2bo7bo72b2o$16b3ob3o58bo2bo3bo2bo6b3o8b3o3b
3o71bo63b2o$19bo61bo2bo3bo2bo7bo80b3o70b2o$19bo10bo54b3o13b2o4bo5bo5b
o4b2o64bo$19bo10bo70b2o10bo10b2o64bo$113bo58b2o62b2o$85b3o84b2o62b2o6b
3o$111bo3bo64b3o61b3o$181bo63bo$179bo3bo59bo3bo$179bo3bo59bo3bo2$16b2o
65b2o25b2o$83b2o25b2o27$12bo3bo$12bo3bo2$18bo$13b3o2b3o$13b3o4bo55b2o
$76b2o$80b2o$80b2o$6bo73b2o$6bo14bo54b2o15b2o$21bo54b2o15b2o$89b2o$89b
2o$89b2o$7bo4b3o78b2o$7b3o2b3o78b2o$9bo2$11bo3bo$11bo3bo24$27b2o$27b2o
$16b2o$16b2o7b3o$34b2o$8bo5b3o8b3o6b2o$8bo$6bo7b3o$6b2o$3b2o$3b2o2$37b
2o$37b2o$34b2o$25b3o7bo$33bo$6b2o6b3o8b3o5bo$6b2o$14b3o7b2o$24b2o$13b
2o$13b2o14$76b2o$79bo$78b2o10$7b2o11bo57bo$7b2o11bo56b3o$11bo$9bob2o50b
2o10bo2bo2bo58b2o22b2o$11bo52bo9b2obobob2o9b2o46b2o22b2o$7b2o52b2o12b
o2bo2bo10bo50bo18bo$7b2o85bo47b2o18b2o$77b3o14bo48bo18bo$78bo61b2o22b
2o$140b2o22b2o9$77b2o$78bo$76bo$76bo7$3b2o20b2o$3b2o20b2o$6bo16bo$6bo
16bo$6bo16bo$3b2o20b2o$3b2o20b2o23$17bo$17bo$19bo$18b2o2$9b2o$10bo$7b
2o3$15bo2bo4b2o$15bo2bo2bo$15bo2bo2b2o2$12b2o$12bo$14bo$14bo21$11b2o3b
2o$11b2o3b2o2$13b3o2$13b3o$14bo3$18bo$9bo8bo$9bo3$13bo$12b3o2$12b3o2$
10b2o3b2o$10b2o3b2o26$12bo7bo2bo$12bo7bo2bo$14bo3bo6bo$13b2o3b2o4b2o105b
o7bo2bo93bo34bo$109bo21bo7bo2bo6b2o85bo10b2o3b2o5b2o10bo$109bo10b2o11b
o3bo6bo4b2o87bo8b2o3b2o5b2o8bo$5b2o6bo97bo8b2o10b2o3b2o4b2o92b2o30b2o
$8bo4bo22b2o72b2o120b2o19bo$7b2o4bobo20b2o89bo10bo93b2o19bo23b2o$102b
2o23bo9bob2o8bo100bo4b2o18bo$105bo15bobo12b2ob2o8bo4b2o93b2obob3o18b2o
$104b2o15bo15bob2o6bobo4bo95bobo2b2o$18b2o20bobo4b2o72bo16bo4bo12b2o$
18b2o22bo4bo95bo111bo$42bo6b2o97b2o97b2o4b2o3b2o4b2o$115b2o4b2o3b2o10b
2o8bo88b2o8bo6bo3bo6bo4b2o$109b2o4bo6bo3bo11b2o10bo86b2o10bo2bo7bo2bo
6b2o$30b2o4b2o3b2o66b2o6bo2bo7bo21bo98bo2bo7bo2bo$30bo6bo3bo75bo2bo7b
o$32bo2bo7bo$32bo2bo7bo20$16b2o3b2o10$18b3o2$4bo29bo$4bo13b3o13bo$14b
o2bo3bo2bo$14bo2bo3bo2bo$14bo2bo3bo2bo$4bo13b3o13bo$4bo29bo2$18b3o10$
16b2o3b2o21$36b2o$36b2o$33b2o$33b3o$12b2o19b2o$12b2o22b2o$15b2o19b2o$
14b3o$15b2o$12b2o$12b2o25$6bobo$6bobo$3b2obobo12b2o$3b2o16b2o23$13bo3b
o$13bo3bo$15bo$14b3o5$14b3o$o$o30bo$31bo$13b3o5$13b3o$14bo$12bo3bo$12b
o3bo16$23b2o$23b2o$30bo$30bo$25bo2bo$25bo2bo$25bo2bo$30bo$10b2o18bo$10b
2o11b2o$4bo18b2o$4bo$6bo2bo$6bo2bo$6bo2bo$4bo$4bo$10b2o$10b2o15$62b2o
$125b2o$125b2o12b2o$7bo131b2o$7b2o43b2o18b2o60bo2bo$4b2obo13b2o29b2o18b
2o60bo2bo$4b2o15b2o32bo14bo44b2o17bo2bo$54b3o12b3o43b2o22b2o$55bo14bo
47bo2bo17b2o$52b2o18b2o44bo2bo$52b2o18b2o44bo2bo$115b2o$115b2o12b2o$129b
2o$62b2o10$9bo14bo$9bo14bo$11bo10bo$10b2o10b2o2$4b2o22b2o$7bo7b2o9bo$
6b2o5bob2o9b2o$15b2o$10b3o4$10b2o10b2o$10b2o10b2o22$19b2o$19b2o4b2o$23b
o$8b2o13b2o$20bo$10b2o7b2obo$11bo8bo$8b2o13b2o$23b2o$19b2o$19b2o16$17b
o6b2o$17bo6b2o$19bo$18b2o2$29b2o$29b2o$25b2o$25b2o$5b2o18b2o$5b2o22b2o
$9b2o18b2o$9b2o$9b2o$5b2o$5b2o2$16b2o$16bo$10b2o6bo$10b2o6bo19$29b2o$
29b2o4$37bo$8b2o27bo$8b2o$20bo4bo$19b2o4b2o$20bo4bo$36b2o$8bo27b2o$8b
o4$15b2o$15b2o16$21bo$20bo$19b2o$4b2o14bo4b2o$4b2o15bo3b2o19$8b2o16b2o
$11bo$10b2o3b3o6b2o$24bo$8b2o16b2o16$10b2o28b2o$10b2o28b2o3$b2o46b2o$
4bo19bo16bo5bo$3b2o9bo9bo13b2o7b2o$13bo7b2o15bo5b2o$12bobo5b3ob3o10b3o
4b3o$13bo7b2o15bo5b2o$3b2o9bo9bo13b2o7b2o$3b2o19bo16bo5b2o2$7b2o34b2o
$8bo4b2o22b2o4bo$6bo6b2o22b2o6bo$6bo38bo22$11b2o$11b2o2$23b2o$3b2o16b
o$3b2o16b2o$19bo$18b3o$19bo$3b2o16b2o$4bo16b2o$b2o2$13b2o$13b2o!

I also found this p17 partial:

Code: Select all

x = 21, y = 5, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2obo13bo$3bo13bo$3bo13bob2o$19b2o!

Ampere and bubblegum independently found completions.

Code: Select all

x = 74, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o$10b2o$64b2o$9bo54b2o$2o8bo$2obo13bo35b2o8bo$3bo3bob3obo3bo35b2ob
o13bo$3bo13bob2o35bo3bo5bo3bo$9bobo7b2o35bo13bob2o$9bobo50bobo7b2o$9b
3o50bobo$63b2o$60b2o$9b2o49b2o$9b2o!

Bubblegum also made a gun from it.

Code: Select all

x = 21, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o$11b2o2$9b3o3$4b2o9b2o$4b2o9b2o$6bo7bo$7bo5bo$2o4bobo3bobo$2obo3b
o5bo3bo$3bo6bo6bo$3bo13bob2o$19b2o!

Ampere also found a p25 oscillator.

Code: Select all

x = 21, y = 21, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o$11b2o2$9b3o3$8bo3bo2$2o4bo7bo$2obo13bo$3bo13bo$3bo13bob2o$6bo7bo
4b2o2$8bo3bo3$9b3o2$8b2o$8b2o!

Here are oscillators that iNoMed found:

Code: Select all

x = 70, y = 166, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo2b2o6b2o8b2o8bo8b2o8b2o2bo3b2o2bo$3o5bo2bo6b2o4bo6b5o6bo4b2o6bobo6b
3o$o7bo2b2o5bo2b2o2b2o4bo3bobo2b2o2b2o2bo5b2o10bo$8bo4bo3b3ob2o3bobo
11bobobo2b3o2bo3b3obo$2o4bo5bo3bo4bobo2b2o3bo12b2o5bob2o2bo5b2o$2o2b2o
2b2ob4o3bob3o3b3o4bobobo2bo2b3o4b2ob3o4bob4o3bo$2o4bo5bo3bo4bobo2b2o3b
o12b2o5bob2o2bo5b2o$8bo4bo3b3ob2o3bobo11bobobo2b3o2bo3b3obo$o7bo2b2o5b
o2b2o2b2o4bo3bobo2b2o2b2o2bo5b2o10bo$3o5bo2bo6b2o4bo6b5o6bo4b2o6bobo6b
3o$2bo2b2o6b2o8b2o8bo8b2o8b2o2bo3b2o2bo18$27bo2bo2bo$25b4o3b4o$25bobob
obobobo2$26b2o5b2o$27bob3obo$25bo2b5o2bo$25bo2bo3bo2bo$27bob3obo$26b2o
5b2o2$25b2o3bo3b2o$25b2o3bo3b2o$30bo$26b2ob3ob2o$26bo3bo3bo$25b2ob5ob
2o$30bo$28bo3bo2$28b5o$27bo2bo2bo$26b9o$27bo2bo2bo$29b3o$29b3o$25b2obo
3bob2o$26bo2b3o2bo$26b2o5b2o2$25bobo5bobo$25b3ob3ob3o$28bo3bo$27bob3ob
o$25b3o2bo2b3o$25bo3bobo3bo$30bo$26bo3bo3bo$26b2o2bo2b2o2$25b2o3bo3b2o
$25b2o3bo3b2o$30bo2$27bo2bo2bo$25b3ob3ob3o$25bo4bo4bo$28bo3bo$26b4ob4o
$26bobo3bobo$29bobo$27b2o3b2o$25bo2bo3bo2bo$25b2ob5ob2o$29bobo$26bo3bo
3bo$26bo3bo3bo2$30bo$25bo9bo$25b3o2bo2b3o$27bo5bo$29b3o$25bo3bobo3bo$
25bo3b3o3bo$27bo5bo$26b2o5b2o2$27bo5bo$25b3o5b3o$25bo2b5o2bo$27bo5bo$
26b2o5b2o$27bo2bo2bo$25bo3b3o3bo$25bo4bo4bo$27b2o3b2o21$30b2o2$31b3o2$
26bo8bo$26bobo2bo3bo$28bo3b2o$28bo3bo$34bo$30b2o2bo20$28bo3bo$28bo3bo$
30bo$29b3o2$30bo$28bo3bo$30bo$30bo$30bo$28bo3bo$28bo3bo!

Schiaparelliorbust found this p6 oscillator:

Code: Select all

x = 20, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
3$6b2o$6b3ob2o$3b2ob2o2b2o$3b2o!

It's similar to a p6 oscillator that I had found in the original version.

Code: Select all

x = 9, y = 7, rule = B2ci3ai4c8/S1e2aei3-cnry4eiz5air6i7e8
6b2o$6b2o2$3bob2o$3bobob2o$2obobob2o$2o!

Here are oscillators that Yto found:

Code: Select all

x = 14, y = 79, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
7b2o$7b2o2$2b2o5b2o$2b2o5b2o2$5b3o$6bo$3b2o3b2o$3b2o3b2o22$2o10b2o$6bo
$6bob2o$6bo$2o10b2o28$3b2o$3b2o11$6b3o$7bo$4b2o3b2o$4b2o3b2o!

[silversmith]

Here are some converters and conduits

Code: Select all

x = 92, y = 83, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
55b2o4$39b2o$39b2o$5b3o14b2o15b2o$5b3o14b2o$22b2o$bo31bo54b2o$b3o21b
2o6bob2o51b2o$3bo22bo8bo3bo12b3o33b2o$26b2o6b2ob3o12b3o15b3o$37bo32b3o
$85b2o$52bo32b2o$52b3o13b2o$14bo39bo$14bo7$12b3o$13bo20b2o$35bo6b2o$
35b2o5bo5b2o$41b2o3bo4bo$46b2o2b2o37bo$42bo17bo27bobo$43bo14b3o28bo$
43b2o13bo$43bo35bo$32b2o8bo36b3o$33bo47bo$12b3o16bo14b2o$11b2ob2o15bo
14bo10bo$11bobobo17bo6bo4b2o4bo3bob3o14bo14b2o$11b2ob2o5b2o9b2o6b3o9bob
o4bo14b3o13bo$12b3o7bo19bo10bo22bo13b2o$22b2o12bo10bo$2o8b2o3b2o13bo
4bobo9b3o6b2o$bo8b2o3b2o13b3obo3bo4b2o4bo6bo12bo14b2o$b2o29bo10bo14bo
10b3o13bo$42b2o14bo12bo13b2o$56bo$47bo8b2o$46bo17bo14b2o$31bo13bo18b3o
13bo$29b3o14bo19bo13b2o$29bo17bo$38b2o2b2o$38bo4bo3b2o19b3o3b2o$40b2o
5bo5b2o13b3o4bo$46b2o6bo20b2o$54b2o$66b2o3$62bobo$12bo49b3o$11bo$41b
2o15b2o$10bo34bo12bo8b2o$44bobo10b2o8b2o$43bo3bo4b2o16b2o$40b2o10bo17b
o5b2o$51b2o16b2o3bo4bo$74b2o2b2o$56bo13bo17bo$55bo15bo14b3o$2b2o11bo
24bo13bo7b3o7bo13bo$3bo11b2o21b3o14bo5b2ob2o5bo$3b2o10bo22bo17bo4bobob
o4bo$47b2o2b2o8b2ob2o$47bo4bo3b2o4b3o9b2o$13b2o34b2o5bo17bo10b2o$9bo
3b2o40b2o16b2o4bo3bo$9b3o68bobo$11bo48b2o3b2o14bo$60b2o3b2o17b2o!

As well as some partial results

Code: Select all

x = 54, y = 56, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
23b2o$23bo$22b2o3$8b2o$8bo$2bo5b2o$3o$o$6b2o14b2o5b2o$7bo15bo6bo20b3o
$7b2o14b2o5b2o4$52bo$52bo13$52b2o$52bo$51b2o13$10b2o$10bo$9b2o2$2o$9b
obo$b3o5bobo$b3o5bobo$2bo$9b2o$9b2o!

[bibunsekibun]

P27

Code: Select all

x = 5, y = 22, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o10$3bo$2b3o$2b3o7$b2o$b2o!

Edit:P82

Code: Select all

x = 4, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o13$b3o3$b3o4$2o$2o!

[MathAndCode]

Here are some converters and conduits

Thank you. Those ought to lead to a bunch of new periods. The first example that I noticed is 94.

Code: Select all

x = 25, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
20bo$18b3ob2o$18bo3bo$21b2obo$24bo3$16bo2bo$16bo2bo$16bo2bo2$o$ob2o$2b
o3bo$b2ob3o$4bo!

We might even be able to prove this rule omniperiodic.

As well as some partial results

The bottom-left partial can be completed by replacing the domino with a block (if I'm correct in assuming that its proximity to another conduit is merely a coincidence).

Code: Select all

x = 4, y = 6, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o2$b3o$b3o$2bo!

Edit: I found another conduit.

Code: Select all

x = 7, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
3o3bo$3ob3o$4bo3$b2o$b2o!

This allows a new p16 oscillator.

Code: Select all

x = 11, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o3$2bob3o$3o$o$4b3o2$10bo$8b3o$8bo3$5b2o$5b2o!

Another edit: Here is another conduit, which has a spark:

Code: Select all

x = 11, y = 3, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo!

Unfortunately, it can't be chained with itself. However, another way to restore the active region to the initial position would still result in a sparker.



Yet another edit: I got a period-eight sparker.

Code: Select all

x = 11, y = 5, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo2$6b2o!

Fourth edit: Here is a period-ten sparker:

Code: Select all

x = 11, y = 6, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo$4b3o2$6b2o!

It looks like only the frontend is important for the spark, which should open up more periods than otherwise.



Fifth edit: Here is a period-eleven sparker:

Code: Select all

x = 11, y = 8, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo$5bo4$7b2o!

Sixth edit: This delivers sparks separated by six, eight, and ten generations:

Code: Select all

x = 11, y = 6, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo3$2b2o3b2o!

Seventh edit: Here are more sparkers of that type:

Code: Select all

x = 13, y = 8, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o9b2o$3bo5bo$2b2o5b2o$5b3o$6bo$2b2o5b2o$3bo5bo$2o9b2o!

Code: Select all

x = 11, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo2bo2bo$3ob3ob3o$o3b3o3bo$5bo3$2b2o3b2o!

Code: Select all

x = 11, y = 10, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o2bo2b3o$o3b3o3bo5$o3b3o3bo$3o2bo2b3o$2bo5bo!

Here are some unrelated oscillators:

Code: Select all

x = 13, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o$2b2o2bo2bo$2bo3bo2b2o2$6bo$2b2obobob2o$6bo2$2b2o2bo3bo$3bo2bo2b
2o$2o!

Code: Select all

x = 16, y = 5, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o12b2o$6bo2bo$6b4o$6bo2bo$2o12b2o!

Here is a reduction to an already-known p15 oscillator:

Code: Select all

x = 14, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13bo$13bo$10bo$9b2obo$2b2o6bo$3bo9bo$2o11bo!

Eighth edit: Here are more oscillators, most of them with period over 100:

Code: Select all

x = 15, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o$11bo$11b2o$4bo4bo$4bo4b2o$4bo4bo$11b2o$11bo$13b2o2$2o!

Code: Select all

x = 17, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
b2o$b2o3$15b2o$13bo$13b2o$6bo4bo$6bo4b2o$6bo4bo$13b2o$13bo$15b2o2$2o4b2o$2o!

Code: Select all

x = 16, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2b2o$2b2o2$14b2o$12bo$12b2o$10bo$10bo$10bo$2o10b2o$12bo$14b2o2$5b2o$5b2o!

Code: Select all

x = 16, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
b2o2$14b2o$12bo$12b2o$10bo$10bo$10bo$2o10b2o$12bo$14b2o2$5b2o$5b2o!

Code: Select all

x = 16, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o2$14b2o$12bo$12b2o$3bo6bo$3bo6bo$3bo6bo$12b2o$3bo8bo$4bo9b2o$2bo$5b2o$5b2o!

Code: Select all

x = 17, y = 19, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
7bo$7bo$5bo$5b2o4$15b2o$13bo$13b2o$10bo$9b2obo$10bo$13b2o$13bo$15b2o2$2o4b2o$6b2o!

Code: Select all

x = 17, y = 17, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6b2o4$15b2o$13bo$13b2o$11bo$10b3o$11bo$13b2o$13bo$15b2o2$6b2o$2o4bo$8b2o!

Code: Select all

x = 12, y = 8, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
8b2o$o8bo$obobo$2bobo2bo$2bobo$8b2o$8bo$10b2o!

Code: Select all

x = 18, y = 22, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
7b2o$4bo5$2o7b2o$2o7b2o2$16b2o$14bo$14b2o$9bo2bo$9bo2bo$9bo2bo$14b2o$14bo$16b2o2$7b2o$b2o4bo$9b2o!

Code: Select all

x = 11, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo5bo$3o5b3o$o9bo$4bobo$b3o3b3o$4bobo$o9bo$3o5b3o$2bo5bo!

Code: Select all

x = 32, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
9bo4bo2bo$9bo4bo2bo6b2o$b2o4bo4bo6bo4b2o$bo5b2o3b2o4b2o$2o2$7bo12bo$6b
2o11b2o8b2o$7bo12b2o7bo$8bo9bo5bo6bo$2o16bo12bo$bo21b2o$b2o4b2o4b2o8bo
$7b2o4b2o10bo$25bo!

Code: Select all

x = 19, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
b2o$bo$2o$16b2o$4b2o2b2o7bo$2ob5o9b2o$4b2o2bo$10bo2b2o$2o9b5ob2o$bo7b2o2b2o$b2o$17b2o$17bo$16b2o!

Code: Select all

x = 11, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
b2o$bo$2o8bo$10bo$4b2o2bo$2ob5o$4b2o2b2o2$2o$bo$b2o!

Code: Select all

x = 15, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o3b2o3$2o11b2o$3bo7bo$2b2o7b2o$5bo3bo$4b2o3b2o$5bo3bo$2b2o7b2o$3bo
7bo$2o11b2o3$4b2o3b2o!

Code: Select all

x = 21, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6bo7bo$6bo7bo$8bo3bo$7b2o3b2o2$9b3o$17b2o$2b2o3bo5bo3bo$3bo15b2o$2o7b
3o2$7b2o3b2o$8bo3bo$6bo7bo$6bo7bo!

Code: Select all

x = 37, y = 37, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
14bo7bo$14bo7bo$10b2o4bo3bo4b2o$10b2o3b2o3b2o3b2o$12bo5bo5bo$11bo5b3o
5bo$11bo6bo6bo2$18bo$17b3o$2b2o14bo14b2o$2b2ob2o8b2o3b2o8b2ob2o$4bo11b
o3bo11bo$13b2o7b2o$2o11b2o7b2o11b2o$3bo7bo13bo7bo$2b2o7b2o11b2o7b2o$5b
o3bo17bo3bo$4b3ob3o15b3ob3o$5bo3bo17bo3bo$2b2o7b2o11b2o7b2o$3bo7bo13bo
7bo$2o11b2o7b2o11b2o$13b2o7b2o$4bo11bo3bo11bo$2b2ob2o8b2o3b2o8b2ob2o$
2b2o14bo14b2o$17b3o$18bo2$11bo6bo6bo$11bo5b3o5bo$12bo5bo5bo$10b2o3b2o
3b2o3b2o$10b2o4bo3bo4b2o$14bo7bo$14bo7bo!

Ninth edit: Here is a p18 oscillator:

Code: Select all

x = 19, y = 19, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
5bo7bo$5bo7bo$7bo3bo$6b2o3b2o2$8b3o2$17b2o$2o13bo$3bo11b2o$2b2o3$8b3o
2$6b2o3b2o$7bo3bo$5bo7bo$5bo7bo!

Tenth edit: Here is a p8 oscillator:

Code: Select all

x = 14, y = 19, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10bo$10bo2$9b3o3$9b3o2$2o6bobo$3bo3b2obob2o$2b2o4bobo2$9b3o3$9b3o2$10b
o$10bo!

Eleventh edit: Here is a p64 oscillator:

Code: Select all

x = 20, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
8bo7bo$8bo7bo$10bo3bo$9b2o3b2o$12bo$11b3o$12bo2$19bo$12bo6bo$2o9b3o$3b
o6b5o$2b2o7b3o$12bo3$12bo$11b3o$12bo$9b2o3b2o$10bo3bo$8bo7bo$8bo7bo!

Twelfth edit: Here is a p66 oscillator:

Code: Select all

x = 21, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6bo7bo$6bo7bo$8bo3bo$7b2o3b2o$10bo$9b3o$10bo$19b2o$2b2o13bo$2b2o13b2o
4$2b2o13b2o$3bo13b2o$2o$10bo$9b3o$10bo$7b2o3b2o$8bo3bo$6bo7bo$6bo7bo!

Thirteenth edit: Here is a p38 oscillator:

Code: Select all

x = 19, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
5bo7bo$5bo7bo$7bo3bo$6b2o3b2o$9bo$8b3o$9bo2$17b2o$17b2o2$7b5o2$2o$2o2$
9bo$8b3o$9bo$6b2o3b2o$7bo3bo$5bo7bo$5bo7bo!

Fourteenth edit: Here is a p128 oscillator:

Code: Select all

x = 29, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10bo7bo$10bo7bo$12bo3bo$11b2o3b2o$14bo$13b3o$14bo$2o25b2o$3bo21bo$2b2o
21b2o4$2b2o21b2o$3bo21bo$2o25b2o$14bo$13b3o$14bo$11b2o3b2o$12bo3bo$10b
o7bo$10bo7bo!

Fifteenth edit: Here is an impressively powerful (for its period) p3 dot sparker:

Code: Select all

x = 9, y = 5, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
3bobo$4bo$2o2bo2b2o$bo2bo2bo$b2o3b2o!

Sixteenth edit: Here is a p79 sparker:

Code: Select all

x = 21, y = 25, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6bo7bo$6bo7bo$8bo3bo$7b2o3b2o$10bo2$9b3o$b2o7bo7b2o$bo17bo$2o17b2o6$2o
17b2o$bo17bo$b2o7bo7b2o$9b3o2$10bo$7b2o3b2o$8bo3bo$6bo7bo$6bo7bo!

Seventeenth edit: Here are three more oscillators:

Code: Select all

x = 20, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
5b2o6b2o$o18bo$o18bo$2bo4bo4bo4bo$b3o2b3o2b3o2b3o$2bo4bo4bo4bo$o18bo$o
18bo$5b2o6b2o!

Code: Select all

x = 20, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
8bo$8b3o$4b2o4bo3b2o$4b2o8b2o$o18bo$o18bo$2bo14bo$b3o12b3o$2bo14bo$o
18bo$o18bo$4b2o8b2o$4b2o3bo4b2o$9b3o$11bo!

Code: Select all

x = 26, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o22b2o$3bo18bo$2b2o18b2o$11bo2bo$10b2o2b2o$11bo2bo$2b2o18b2o$3bo18bo$
2o22b2o!

Eighteenth edit: Here is a statorless p12 oscillator:

Code: Select all

x = 14, y = 3, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4bo4bo$2obob4obob2o$4bo4bo!

Nineteenth edit: Here is a p9 oscillator:

Code: Select all

x = 11, y = 10, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o4bo$o9bo$o7bo$2bo4b3o$b3o4bo$2bo7bo$o9bo$o4b2o$5b2o!

Twentieth edit: Here is a p10 sparker:

Code: Select all

x = 16, y = 6, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
14b2o$2o10bo$3bo8b2o$2b2o8bo$3bo10b2o$2o!

Twenty-first edit: Here is a p12 oscillator:

Code: Select all

x = 16, y = 8, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
15bo$o14bo$o6b2o4bo$2bo10b2o$b2o10bo$2bo4b2o6bo$o14bo$o!

[praosylen]

[21 edits worth of stuff]

I'm afraid I haven't been paying too much attention to this rule before now, but seeing everything here gathered in one place, there are a lot of really impressive oscillators here! I guess I don't have too much to say besides that — I mostly just always hate to see an unreplied post with that many edits because I know I'm probably one of the few people who's even seen half of it, and I want people to be able to see it and you not to have to worry about whether it's okay to double-post/bump or not to keep it from being relegated to that dust heap of old threads that died too soon, the second page...

[breaker's glider gun]

Wait, we have INFINITELY EXTENSIBLE DIAGONAL SLS?

Code: Select all

x = 19, y = 20, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
o$3o$2b3o$4b3o$6bo$6b3o$8bo$8b3o$10bo$10b3o$12bo$12b3o$14bo$14b2o$15b
o$15b2o$16bo$16b2o$17bo$17b2o!

[MathAndCode]

I'm afraid I haven't been paying too much attention to this rule before now, but seeing everything here gathered in one place, there are a lot of really impressive oscillators here! I guess I don't have too much to say besides that — I mostly just always hate to see an unreplied post with that many edits because I know I'm probably one of the few people who's even seen half of it, and I want people to be able to see it and you not to have to worry about whether it's okay to double-post/bump or not to keep it from being relegated to that dust heap of old threads that died too soon, the second page...

Thank you.

Wait, we have INFINITELY EXTENSIBLE DIAGONAL SLS?

Yes. I had seen the following still life, from which I could have deduced that.

Code: Select all

x = 4, y = 4, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
o$3o$2bo$2b2o!

However, the thought had not occurred to me.



Edit: Here is an oscillator with period 22, which was until now the smallest period without a known oscillator:

Code: Select all

x = 17, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
12bo$10b3o$10bo5bo$o15bo$o13bo$2bo10b3o$b3o10bo$2bo13bo$o15bo$o5bo$4b3o$4bo!

Another edit: Here is a p31 oscillator:

Code: Select all

x = 19, y = 18, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6b2o5b2o$6b2o4$18bo$o17bo$o10bo4bo$2bo4bo3bo4b2o$b2o4bo3bo4bo$2bo4bo10b
o$o17bo$o4$11b2o$4b2o5b2o!

Waiting longer to delete the extra regions produced results in a p48 oscillator.

Code: Select all

x = 25, y = 18, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
16b2o4$o$o20bo$3bo17bo$3bo10bo4bo$5bo4bo2b3o2b3o$4b3o2b3o2bo4bo$5bo4b
o10bo$3bo17bo$3bo20bo$24bo4$7b2o!

Yet another edit: Here is a p15 oscillator:

Code: Select all

x = 21, y = 8, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
20bo$o19bo$o14bo2bo$2bo2bo9bo2bo$2bo2bo9bo2bo$2bo2bo14bo$o19bo$o!

While I think that that particular oscillator is new, the basic mechanism is also present in at least two already-known p15 oscillators.



Fourth edit: Here is a p41 oscillator:

Code: Select all

x = 24, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o$13b2o2$22b2o$2o20b2o$2o17bo$4bo13b2obo$2bob2o13bo$4bo17b2o$2o20b
2o$2o2$9b2o$9b2o!

Fifth edit: Here is a p30 oscillator:

Code: Select all

x = 22, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
7b2o$7b2o7b2o$16b2o$21bo$o20bo$o13bo4bo$2bo4bo6bo4b2o$b2o4bo6bo4bo$2b
o4bo13bo$o20bo$o$4b2o$4b2o7b2o$13b2o!

Sixth edit: Here is a p37 oscillator that uses the same mechanism as at least two already-known p37 oscillators:

Code: Select all

x = 27, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
25b2o$23bo$2o21b2o$2o19bo$3bo16b3o$2b3o16bo$3bo19b2o$2o21bo$2o23b2o!

The two halves can be moved one cell farther apart, and the period would still be 37.



Seventh edit: Here is a variant of a p47 oscillator with the same minimal population:

Code: Select all

x = 27, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o2$25b2o$2o23b2o$2o21bo$3bo19b2o$2b2o19bo$3bo21b2o$2o23b2o$2o2$12b2o!

Eighth edit: Here is a p73 oscillator, which I think is the first known oscillator with that period in this rule:

Code: Select all

x = 29, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
9b2o2b2o$9b2o2b2o12b2o$25bo$2o23b2o$2o20bo$4bo16b2obo$2bob2o16bo$4bo20b
2o$2o23bo$2o25b2o$12b2o2b2o$12b2o2b2o!

Ninth edit: Here is an oscillator with period 62, which I also think is a new period:

Code: Select all

x = 29, y = 20, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
12b2o$13bo$10bo$10b2o2$27b2o$25bo$2o23b2o$2o20bo$4bo16b2obo$2bob2o16b
o$4bo20b2o$2o23bo$2o25b2o3$15b2o$16bo$13bo$13b2o!

Tenth edit: This oscillator has period 57, which I also think is new:

Code: Select all

x = 29, y = 20, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
17b2o$17b2o4$27b2o$25bo$2o23b2o$2o18bo2bo$3bo2bo13bo2bo$3bo2bo13bo2bo
$3bo2bo18b2o$2o23bo$2o25b2o5$8b2o$8b2o!

Eleventh edit: Here is another variant of the aforementioned p37 oscillator:

Code: Select all

x = 30, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
28b2o$26bo$2o24b2o$2o17bo4bo$3bo4bo10bo4b2o$2b2o4bo10bo4bo$3bo4bo17b2o
$2o24bo$2o26b2o!

There are at least four combined p37 variants and p47 variants that I have found recently but haven't bothered to post in here, but I'm posting this variant because it's especially sparky.



Twelfth edit: Here is a p34 oscillator, which I also think is the first known oscillator of this period (in this rule):

Code: Select all

x = 30, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
21b2o$9b2o10b2o$2o7b2o17b2o$3bo24b2o$2b2o22bo$5bo19b3o$4b3o19bo$5bo22b
2o$2b2o24b2o$3bo17b2o$2o7b2o10b2o$9b2o!

Thirteenth edit: Here is a p50 oscillator:

Code: Select all

x = 31, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
15b2o5b2o$15b2o5b2o$29b2o$29b2o$26bo$9b2o14b2obo$2o7b2o15bo$3bo25b2o$
2b2o25b2o$6bo15b2o$4bob2o14b2o$6bo$2b2o$3bo$2o7b2o5b2o$9b2o5b2o!

Fourteenth edit: Here is a p39 oscillator:

Code: Select all

x = 27, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o6b2o$19b2o$6b2o18bo$6b2o18bo$o18bo4bo$o18bo4b2o$2bo4bo11bo4bo$b2o
4bo18bo$2bo4bo18bo$o18b2o$o18b2o$6b2o$6b2o6b2o!

Fifteenth edit: Here is a p25 sparker:

Code: Select all

x = 32, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
23b2o$23b2o$30b2o$30b2o$19b2o5b2o$9b2o7b4o4b2o$2o7b2o8b2o5b2o$3bo26b2o
$2b2o26b2o$6b2o5b2o8b2o$6b2o4b4o7b2o$6b2o5b2o$2b2o$3bo$2o7b2o$9b2o!

If the two halves are staggered by one additional cell, the result would provide similar sparks at the same period.



Sixteenth edit: Here is an oscillator with period 75, which I think is new:

Code: Select all

x = 28, y = 17, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
15b2o3b2o$9b2o4b2o3b2o$9b2o16bo$27bo$23b2o$23b2o$6b2o15b2o$6b2o19bo$o
26bo$o19b2o$3b2o15b2o$3b2o$3b2o$o$o16b2o$6b2o3b2o4b2o$6b2o3b2o!

Seventeenth edit: Here is a p39 oscillator:

Code: Select all

x = 16, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6b2o$6b2o$o$o$3b2o$3b2o$3b2o9b2o$o13b2o$o$6b2o5b2o$6b2o!

Eighteenth edit: Here is a p40 oscillator:

Code: Select all

x = 29, y = 18, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
21b2o$21b2o$28bo$28bo$21bo4bo$21bo4b2o$21bo4bo$6b2o20bo$6b2o20bo$o20b
2o$o20b2o$2bo4bo$b2o4bo$2bo4bo$o$o$6b2o$6b2o!

Nineteenth edit: Here is an oscillator with period 65, which I think is new:

Code: Select all

x = 29, y = 19, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o$21b2o$21b2o$28bo$28bo$23bo2bo$23bo2bo$6b2o15bo2bo$6b2o20bo$o27b
o$o20b2o$2bo2bo15b2o$2bo2bo$2bo2bo$o$o$6b2o$6b2o$16b2o!

Twentieth edit: Here is an oscillator with period 55, which I think is new:

Code: Select all

x = 29, y = 21, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
16b2o$16b2o$21b2o$21b2o$28bo$28bo$21bo4bo$21bo4b2o$6b2o13bo4bo$6b2o20b
o$o27bo$o20b2o$2bo4bo13b2o$b2o4bo$2bo4bo$o$o$6b2o$6b2o$11b2o$11b2o!

Twenty-first edit: An interesting catalyst popped up:

Code: Select all

x = 17, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6b2o$6b2o7bo$o12b3o$o12bo$2bo2bo9b2o$2bo2bo9b2o$2bo2bo$o$o$6b2o$6b2o!

It's not necessary in that situation, but it might come in handy in other situations.



Twenty-second edit: Here is a p65 oscillator:

Code: Select all

x = 33, y = 18, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o$11b2o9b2o$7b2o14bo7b2o$7b2o20bo$29b2o$18b2o6bo$7b2o9b2o5b2obo$7b
o10b2o6bo$2o27b2o$2o27bo$4bo6b2o10bo7b2o$2bob2o5b2o9b2o$4bo6b2o$2o$2o
$7bo14b2o$7b2o9b2o2b2o$18b2o!

Twenty-third edit: Here is a p100 oscillator, which I think is the first of its period:

Code: Select all

x = 29, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
21b2o$12b2o7b2o$12b2o14bo$6b2o20bo$6b2o6bo10bo$o13bo9b2obo$o24bo$3bo24b
o$bob2o9bo13bo$3bo10bo6b2o$o20b2o$o14b2o$6b2o7b2o$6b2o!

Twenty-fourth edit: Here is a p85 oscillator, which I think yields another new period:

Code: Select all

x = 29, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
15bo$13b3o5b2o$13bo7b2o$28bo$6b2o20bo$6b2o15bo2bo$o22bo2bo$o22bo2bo$2b
o2bo22bo$2bo2bo22bo$2bo2bo15b2o$o20b2o$o$6b2o7bo$6b2o5b3o$13bo!

Twenty-fifth edit: Here is an oscillator with period 60, which I also think is new:

Code: Select all

x = 29, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
11b2o8b2o$11b2o8b2o$28bo$6b2o20bo$6b2o17bo$o23b2obo$o24bo$3bo24bo$bob
2o23bo$3bo17b2o$o20b2o$o$6b2o8b2o$6b2o8b2o!

Twenty-sixth edit: Here is a p75 oscillator:

Code: Select all

x = 33, y = 20, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
17bo$17bo$15bo$15b2o5b2o$10b2o11bo7b2o$10b2o17bo$7b2o20b2o$7b2o17bo$2o
7bo15b2obo$2o24bo$4bo24b2o$2bob2o15bo7bo$4bo17b2o7b2o$2o20b2o$2o17b2o
$7bo11b2o$7b2o5b2o$14bo$16bo$16bo!

Twenty-seventh edit: Here are p25 sparkers:

Code: Select all

x = 30, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
22b2o$22b2o$29bo$6b2o21bo$6b2o14bo4bo$o21bo4b2o$o21bo4bo$2bo4bo21bo$b
2o4bo21bo$2bo4bo14b2o$o21b2o$o$6b2o$6b2o!

Code: Select all

x = 30, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
22b2o$22b2o$29bo$29bo$25b2o$6b2o17b2o$6b2o17b2o$o28bo$o28bo$3b2o17b2o
$3b2o17b2o$3b2o$o$o$6b2o$6b2o!

Code: Select all

x = 30, y = 17, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
22b2o$22b2o$29bo$29bo$25b2o$25b2o$6b2o17b2o$6b2o21bo$o28bo$o21b2o$3b2o
17b2o$3b2o$3b2o$o$o$6b2o$6b2o!

Twenty-eighth edit: Here is an oscillator with period 125, which I think is a new period:

Code: Select all

x = 46, y = 31, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
16b2o3b2o2$18b3o3$18b3o$14b2o7b2o$14b2o7b2o5$44b2o$42bo$42b2o5$2b2o$3b
o$2o2$21b2o7b2o$21b2o7b2o$25b3o3$25b3o2$23b2o3b2o!

Twenty-ninth edit: Here is a p55 oscillator:

Code: Select all

x = 35, y = 29, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o6$24b2o$24b2o7b2o$31bo$31b2o$12b3o9bo4bo$12b3o9bo4b2o$13bo10bo4b
o$7b2o22b2o$7b2o22bo$2o22b2o7b2o$2o22b2o$3bo4bo10bo$2b2o4bo9b3o$3bo4b
o9b3o$2o$2o$7b2o$7b2o3$14b2o$15bo$15b2o!

Thirtieth edit: Here is a smaller p65 oscillator:

Code: Select all

x = 35, y = 17, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
24b2o$24b2o7b2o$31bo$31b2o$26bo2bo$26bo2bo$7b2o17bo2bo$7b2o22b2o$2o29b
o$2o22b2o7b2o$3bo2bo17b2o$3bo2bo$3bo2bo$2o$2o$7b2o$7b2o!

Thirty-first edit: Here is a p50 oscillator that I suspect can be made useful for something:

Code: Select all

x = 35, y = 26, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
19b2o$19b2o11$11b2o$11b2o2$7b2o15b2o$7b2o15b2o7b2o$2o13b3o13bo$2o29b2o
$4bo10bo12bo$2bob2o21b2obo$4bo23bo$2o29b2o$2o16bo12bo$7b2o3b2o4b3o3b2o
7b2o$7b2o3b2o6bo3b2o!

Thirty-second edit: Here is a p100 oscillator:

Code: Select all

x = 35, y = 28, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o$13b2o$19b2o$20bo$20b2o10$11bo$11b2o2$7b2o15b2o$7bo17bo7b2o$2o29b
o$2o29b2o$4bo6b2o7b2o6bo$2bob2o5b2o7b2o5b2obo$4bo6b2o7b2o6bo$2o29b2o$
2o16bo12bo$7bo4b2o4b3o4bo7b2o$7b2o3b2o6bo3b2o!

Thirty-third edit: Here is an example of a potentially useful catalyst:

Code: Select all

x = 7, y = 10, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6bo$4b3o$2o2bo$2o5$4b3o$5bo!

Thirty-fourth edit: Here is an oscillator with period 175, which I think is a new period:

Code: Select all

x = 35, y = 32, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o$13b2o2$16b2o2$9b2o$12bo$11b2o11$11b2o$11b2o2$7b2o15b2o$7bo17bo7b
2o$2o29bo$2o29b2o$4bo6b2o7b2o6bo$2bob2o5b2o7b2o5b2obo$4bo6b2o7b2o6bo$
2o29b2o$2o16bo12bo$7bo4b2o4b3o4bo7b2o$7b2o3b2o6bo3b2o!

Removing the domino at the top releases a spaceship, so it might be possible to turn the oscillator into a gun.



Thirty-fifth edit: I got a (p175) gun.

Code: Select all

x = 35, y = 34, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
17b2o$17b2o$13b2o$13b2o4$9b2o$12bo$11b2o11$11b2o$11b2o2$7b2o15b2o$7b2o
15b2o7b2o$2o13b3o13bo$2o29b2o$4bo10bo12bo$2bob2o21b2obo$4bo23bo$2o29b
2o$2o16bo12bo$7b2o3b2o4b3o3b2o7b2o$7b2o3b2o6bo3b2o!

Thirty-sixth edit: The fact that destroying the domino releases a spaceship allows shuttles at any period that is a multiple of 350. Here is an example with period 1,050:

Code: Select all

x = 277, y = 32, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
12b2o249b2o$12b2o249b2o$102b2o$15b2o85bo157b2o$102b2o$8b2o257b2o$11bo
253bo$10b2o253b2o4$14b3o243b3o$14b3o243b3o3$14b3o243b3o$14b3o243b3o2$
10b2o253b2o$10b2o3bo245bo3b2o$15bo245bo$6b2o15b2o227b2o15b2o$6b2o15b2o
227b2o15b2o$o29bo215bo29bo$o29bo215bo29bo$2b2o23b2o219b2o23b2o$b3o23b
3o217b3o23b3o$2b2o23b2o219b2o23b2o$o29bo215bo29bo$o16bo12bo215bo12bo16b
o$6b2o3b2o4b3o3b2o227b2o3b3o4b2o3b2o$6b2o3b2o6bo3b2o227b2o3bo6b2o3b2o!

Thirty-seventh edit: Domino deletion from another angle allows oscillators who periods are odd multiples of 175. Here's a p875 example:

Code: Select all

x = 467, y = 467, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
432b2o3bo6b2o3b2o$432bo4b3o4b2o4bo$426bo12bo16bo$426bo29bo$429bo6b2o7b
2o6bo$427bob2o5b2o7b2o5b2obo$429bo6b2o7b2o6bo$426bo29bo$426bo29bo$432b
o17bo$2b2o3b2o423b2o15b2o$5bo$445b2o$4b3o438b2o$5bo2$2o7b2o$o9bo$26bo
$26bo$4b3o5b2o10bo$2o2b3o5b2o10b2o$2o28b2o$30b2o$445b2o$28bo416bo$28b
o418b2o$b2o296b2o$bo297bo140b2o$2o2b3o292b2o$4b3o436b2o$443b2o2$o9bo$
2o7b2o2$5bo$4b3o2$5bo$2b2o3b2o126$27bobo$27b3o132$437b3o$437bobo126$458b
2o3b2o$461bo2$460b3o$461bo2$456b2o7b2o$456bo9bo2$22b2o$22b2o436b3o$166b
2o292b3o2b2o$25b2o140bo297bo$166b2o296b2o$18b2o418bo$21bo416bo$20b2o$
435b2o$435b2o28b2o$441b2o10b2o5b3o2b2o$442bo10b2o5b3o$440bo$440bo$456b
o9bo$456b2o7b2o2$461bo$20b2o438b3o$20b2o$461bo$16b2o15b2o423b2o3b2o$16b
o17bo$10bo29bo$10bo29bo$13bo6b2o7b2o6bo$11bob2o5b2o7b2o5b2obo$13bo6b2o
7b2o6bo$10bo29bo$10bo16bo12bo$16bo4b2o4b3o4bo$16b2o3b2o6bo3b2o!

There's probably a smaller way, though.



Thirty-eighth edit: Yes indeed.

Code: Select all

x = 237, y = 32, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
12b2o209b2o$12b2o209b2o$179b2o$15b2o161bob2o38b2o$179b2o$8b2o217b2o$11b
o213bo$10b2o3bo209b2o$13b5o$13b5o206b2o$12b2obob2o205b2o$15bo2$13bo3b
o$13b2ob2o$16bo202bo$15bo204b3o$17b2o202bo$10b2o2b2o209b2o$10b2obobo205b
o3b2o$14b3o204bo$6b2o15b2o187b2o15b2o$6bo7b3o7bo187b2o15b2o$o4bo19bo4b
o175bo29bo$o5b2o15b2o5bo175bo29bo$3bo5bo11bo5bo181bo23bo$2b4o3b2o9b2o
3b4o178bob2o21b2obo$3bo5bo11bo5bo181bo23bo$o5b2o15b2o5bo175bo29bo$o4b
o11bo7bo4bo175bo12bo16bo$6bo4b2o4b3o4bo187b2o3b3o4b2o3b2o$6b2o3b2o6bo
3b2o187b2o3bo6b2o3b2o!

Thirty-ninth edit: Here are p25 sparkers:

Code: Select all

x = 36, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
25b2o$25b2o7b2o$32bo$32b2o$25bo4bo$7b2o12bo3bo4b2o$7b2o16bo4bo$2o30b2o
$2o30bo$3bo4bo16b2o7b2o$2b2o4bo3bo12b2o$3bo4bo$2o$2o$7b2o$7b2o!

Code: Select all

x = 37, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
26b2o$27bo7b2o$33bo$33b2o$22b2o6bo$7b2o13b2o5b2obo$7bo14b2o6bo$2o31b2o
$2o31bo$4bo6b2o14bo7b2o$2bob2o5b2o13b2o$4bo6b2o$2o$2o$7bo$7b2o!

Code: Select all

x = 37, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
26b2o$26b2o7b2o$33bo$33b2o$7b2o19bo2bo$7b2o19bo2bo$2o26bo2bo$2o31b2o$
3bo2bo26bo$3bo2bo19b2o7b2o$3bo2bo19b2o$2o$2o$7b2o$7b2o!

Code: Select all

x = 38, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
27b2o$7b2o19bo7b2o$7bo26bo$2o32b2o$2o21b2o6bo$4bo6b2o10b2o5b2obo$2bob
2o5b2o10b2o6bo$4bo6b2o21b2o$2o32bo$2o26bo7b2o$7bo19b2o$7b2o!

Code: Select all

x = 38, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
27b2o$27b2o7b2o$34bo$7b2o25b2o$7b2o18bo4bo$2o24b3o2b3o$2o25bo4bo$3bo4b
o25b2o$2b3o2b3o24bo$3bo4bo18b2o7b2o$2o25b2o$2o$7b2o$7b2o!

Code: Select all

x = 38, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
27b2o$28bo7b2o$34bo$34b2o$7b2o14b2o6bo$7bo15b2o5b2obo$2o21b2o6bo$2o32b
2o$4bo6b2o21bo$2bob2o5b2o15bo7b2o$4bo6b2o14b2o$2o$2o$7bo$7b2o!

Fortieth edit: Here is an interesting p40 oscillator:

Code: Select all

x = 38, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
27b2o$16b2o9b2o7b2o$16b2o16bo$34b2o$27bo4bo$7b2o18bo4b2o$7b2o18bo4bo$
2o32b2o$2o32bo$3bo4bo18b2o7b2o$2b2o4bo18b2o$3bo4bo$2o$2o16b2o$7b2o9b2o
$7b2o!

Forty-first edit: Here is an interesting p50 oscillator:

Code: Select all

x = 39, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
28b2o$28b2o7b2o$7b2o26bo$7b2o26b2o$2o28bo2bo$2o28bo2bo$3bo2bo23bo2bo$
3bo2bo28b2o$3bo2bo28bo$2o26b2o7b2o$2o26b2o$7b2o$7b2o!

Forty-second edit: Here is a p25 sparker:

Code: Select all

x = 39, y = 12, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
28b2o$7b2o20bo7b2o$7bo27bo$2o33b2o$2o22b2o6bo$4bo6b2o11b2o5b2obo$2bob
2o5b2o11b2o6bo$4bo6b2o22b2o$2o33bo$2o27bo7b2o$7bo20b2o$7b2o!

Forty-third edit: Here is a p50 sparker:

Code: Select all

x = 40, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
14b2o13b2o$14b2o13b2o7b2o$7b2o27bo$7b2o27b2o$2o29bo2bo$2o29bo2bo$3bo2b
o24bo2bo$3bo2bo29b2o$3bo2bo29bo$2o27b2o7b2o$2o27b2o$7b2o13b2o$7b2o13b2o!

Forty-fourth edit: Here is a p25 sparker:

Code: Select all

x = 17, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
9b2o3bo$2o7b2o3b3o$3bo12bo$2b2o$6bo$4bob2o$6bo$2b2o$2b2o12bo$9b2o3b3o
$9b2o3bo!

[silversmith]

Here are three more conduits.

Code: Select all

x = 96, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$49b2o27b2o4bo$49bo28bo5bob2o$48b2o27b2o7bo3b2o$85b2o3b2o$bo
40b2o5b2o$2o39bob2o$bo40b2o50b2o$14b2o78b2o$14b2o78b2o$2b2o31b2o$2b2o
31b2o4b2o$41b2o47b2o$90b2o!

These are the patterns which I consider to be conduit endpoints.

Code: Select all

x = 44, y = 16, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
obo12b2o15bo9bo$3o12b2o15bo8b3o$15b2o15bo12$42bo$42bo!

[MathAndCode]

Here are three more conduits.

Keep up the good work. Also, here's a conduit that I found that has two outputs:

Code: Select all

x = 60, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
17bo$15b3o$15bo3$b2o$ob2o$b2o55b2o$58b2o2$18b2o11b2o20b2o$18b2o12bo20b
o$30bo5b2o17bo$30bo5b2o17bo!

Edit: Here is a p39 sparker;

Code: Select all

x = 32, y = 19, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o3b2o$13bo$2bo9b3o$3o10bo$o6$o$3o27b2o$2bo27b2o3$14bo$13b3o$14bo$
11b2o3b2o!

[silversmith]

Here is a failed snowflake to c/2 ship which becomes a gun

Code: Select all

x = 45, y = 22, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
30b2o$23b2o5bo$23b2o4b2o2$39bo$37b3o$37bo$21bo$2o19bo$2o$19b2o2b2o4b
2o13bo$19bo4bo4b2o11b3o$18b2o4b2o16bo2$33b2o$33bo5bo$32b2o5bo$39bo2$
38b2o$38bo$37b2o!

And here is a p20 shuttle and p50 shuttle

Code: Select all

x = 34, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2b2o7b2o19b2o$2b2o7b2o9b3o7b2o$22b3o2b2o$6bo20b2o$2o4bo6b2o$2o4bo6b2o
2$2b2o7b2o12b2o$2b2o7b2o12b2o!

The rule is apgsearchable with D8_4 symmetry
https://catagolue.hatsya.com/census/b2c ... r6ei8/D8_4

[bibunsekibun]

P23

Code: Select all

x = 12, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o7b2o$4bo5bo$4bo$4bobo$10b2o$10bo$9b2o!

[MathAndCode]

P23

Thank you. Now the lowest period without a known oscillator is 29 (if I recall correctly).

[bibunsekibun]

P26

Code: Select all

x = 17, y = 17, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o10b2o$2o10b2o$3bo$2b3o10b2o$3bo11b2o$2o$2o$6b2o$6bo$9bo$8b2o2$13bo$
12b3o$13bo$10b2o3b2o$10b2o3b2o!

[MathAndCode]

P26

Here are two monomers:

Code: Select all

x = 13, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o10bo$2o10bo$3bo$2b3o$3bo$2o10bo$2o10bo$6b2o$6b2o!

Code: Select all

x = 16, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o10bo$2o10bo$3bo10b2o$2b3o9bo$3bo9b2o$2o$2o$6b2o$6b2o!

Edit: Here is a p49 oscillator whose engine probably can yield more periods:

Code: Select all

x = 17, y = 20, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
7b2o$7b2o$2b2o$2b2o9b2o$5bo8bo$4b3o7b2o$5bo$2b2o$3bo$2o6$14b2o$11bo3b
o$11bo3b2o$5bo5bo$5b2o!

Another edit: I reduced it.

Code: Select all

x = 13, y = 22, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$o$o9b2o$2bo4bo3bo$b2o4bo3b2o$2bo4bo$o$o13$4b2o!

Yet another edit: Here is a p17 oscillator:

Code: Select all

x = 20, y = 5, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
16bo$2o14bo$2obo12bob2o$3bo14b2o$3bo!

Fourth edit: The p49 engine indeed can yield more periods. Here is an example with period 80:

Code: Select all

x = 21, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
9b2o$9b2o$4b2o$4b2o9b2o$8bo7bo$6bob2o6b2o$8bo$4b2o$5bo$2b2o$19b2o$17b
o$8bo8b2o$8bo$2o$2o5$8b2o$9bo$6b2o!

Fifth edit: Here is a p129 oscillator that uses the same engine:

Code: Select all

x = 18, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
5b2o$5b2o$bo$bo9b2o$4bo7bo$2bob2o6b2o$4bo$bo$bo2$15b2o$13bo$3b2o8b2o$
3b2o4$o$o$16b2o$4b2o10b2o$5bo$2b2o!

Sixth edit: Here is a p113 oscillator that uses that engine:

Code: Select all

x = 16, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$o$o9b2o$2bo4bo3bo$b3o2b3o2b2o$2bo4bo$o$o2$14b2o$12bo$12b2o3$
2b2o$2b2o3$10bo$3b2o5bo2b2o$4bo8b2o$b2o!

Seventh edit: Here are two versions of a p242 oscillator that uses that engine:

Code: Select all

x = 22, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o$10b2o$5b2o$5b2o9b2o$8bo2bo5bo$8bo2bo5b2o$8bo2bo$5b2o$6bo$3b2o$20b
2o$18bo$18b2o2$b2o$bo$2o2$bo$2b2o15b2o$3bo5b2o9bo$bo8bo9b2o$bo5b2o!

Code: Select all

x = 22, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o$10b2o$5b2o$5b2o9b2o$8bo2bo5bo$8bo2bo5b2o$8bo2bo$5b2o$6bo$3b2o$20b
2o$18bo$18b2o2$b2o$bo$2o2$b2o$19b2o$9b2o9bo$10bo9b2o$7b2o!

Eighth edit: Here is a p162 oscillator that uses that engine:

Code: Select all

x = 16, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$o$o9b2o$2bo2bo5bo$2bo2bo5b2o$2bo2bo$o$o2$14b2o$12bo$12b2o3$
2b2o$2b2o3$10b2o$3b2o5b2o$4bo8b2o$b2o10b2o!

Ninth edit: Here is a p17 oscillator that technically uses that engine:

Code: Select all

x = 13, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4bo$o$o9b2o$3bo7bo$bob2o6b2o$3bo3b2o$o$o2$6b2o$7bo$7b2o!

Tenth edit: Here is a p64 oscillator that uses that engine:

Code: Select all

x = 16, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4bo$o$o9b2o$3bo7bo$bob2o6b2o$3bo$o$o2$14b2o$12bo$12b2o3$2b2o$2b2o
4$3b2o$4bo6b2o$b2o8b2o!

Eleventh edit: Here is a p355 oscillator that uses the same engine:

Code: Select all

x = 27, y = 28, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o$10b2o$6bo$6bo9b2o$8bo2bo5bo$8bo2bo5b2o$8bo2bo$6bo$6bo2$20b2o$18b
o$18b2o2$b2o$bo$2o2$b2o21b2o$25bo$9b2o14b2o$10bo$7b2o$20b2o$15b2o3bo$
16bo5bo$14bo7bo$14bo!

Twelfth edit: Here is a p211 oscillator using that engine:

Code: Select all

x = 23, y = 28, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$o$o9b2o$2bo4bo3bo$b2o4bo3b2o$2bo4bo$o$o2$14b2o$12bo$12b2o$15b
o$15bo$2b2o$2b2o3$6bo$3b2obo14b2o$4bo16b2o$b2o2$12b2o$13bo$11bo$11bo!

Thirteenth edit: Here is a p226 oscillator using that engine:

Code: Select all

x = 17, y = 23, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o$4b2o$o$o9b2o$2bo2bo5bo$2bo2bo5b2o$2bo2bo$o$o2$14b2o$12bo$12b2o3$
2b2o$2b2o$15b2o$15b2o2$3b2o$4bo$b2o!

Fourteenth edit: Here is a p48 oscillator:

Code: Select all

x = 17, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
15b2o$13bo$13b2o$11bo$11b2o$2o9bo$2o11b2o$13bo$15b2o!

Fifteenth edit: Here are some high-period oscillators that I found while trying to monomerize xp120_c83jwgzc4gjw3zog44zo807w7zw33:

Code: Select all

x = 11, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
3b2o3b2o$4bo3bo$b2o7bo$b2o2b3o2bo3$5b3o3$5b3o2$o$o!

Code: Select all

x = 17, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o13b2o$15b2o3$3bo3b3o$b2o4b3o$b2o4b3o3$7b3o$3b2o2b3o2bo$3b2o3bo3b
o$6bo3bo$5b2o3b2o!

Code: Select all

x = 15, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
4b2o3b2o$5bo3bo$2b2o3bo3b2o$2bo3b3o3bo$6b3o4$13b2o$2o11b2o$2o2$5bo$5bo!

Code: Select all

x = 19, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2o$2o4$15b2o$2o13bo$2o15b2o3$7bo$2b2o2b3o2b2o$2b2o3bo3b2o$5bo3bo$4b2o3b2o!

Code: Select all

x = 20, y = 27, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13b2o$7b2o4b2o$7b2o$2b2o$2b2o$o$2o$3bo2bo2bo$3bo2bo2bo$3bo2bo2bo$2o$o
$2b2o$2b2o9$o18bo$o18bo2$7b2o3b2o$7b2o3b2o!

[silversmith]

I found a conduit which converts a bullet predecessor into a c/2 ship.

Code: Select all

x = 18, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
12b2o$b2o10bo$2bobo8b2o$2ob2o$obo$2b2o12bo$15bo$14b2o$15bo$16bo$11b2o
$12bo3b2o$12b2o2bo$15b2o!

This conduit can be combined with other conduits to make a splitter(repeat time 52) and 90 degree reflector (repeat time 66).

Code: Select all

x = 89, y = 68, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
62bobo$62b3o6$22bobo$22b3o25$22bobo37bobo$22b3o37b3o2$18b2o38b2o$18bo
8b2o29bo8b2o$12b2o3b2o8b2o28b2o8b2o$b2o10bo16b2o38b2o$2bobo8b2o15bo2b
2o35bo5b2o$2ob2o24b2o3bo34b2o3bo4bo$obo31b2o38b2o2b2o$2b2o12bo13bo39b
o17bo$15bo7bo7bo31bo7bo14b3o$14bo6b5o6bo28b5o6bo13bo$15bo5bobobo5bo
29bobobo5bo$16bo3b3ob3o3bo12b2o7b2o6b3ob3o3bo$11b2o8bobobo18bobo5b2o7bo
bobo$12bo3b2o3b5o16b2ob2o14b5o8b2o$12b2o2bo6bo8b2o8bobo18bo10bo10bo$
15b2o16bo10b2o27b2o4bo3bob3o$33b2o45bobo4bo$20b2o3b2o33b2o3b2o9bo4bo$
20b2o3b2o33b2o3b2o7b3o9bo$74bo9b3o$84bo7$76b2o$77bobo$75b2ob2o$75bobo$
77b2o!

The splitter can be used to make 0 degree and 180 degree reflectors, which can make ship loops with period 52 or greater.

Code: Select all

x = 53, y = 76, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
39b2o3b2o$39b2o3b2o$31b2o$20b2o10bo$21bobo8b2o7b3o$19b2ob2o17b3o$19bo
bo30bo$21b2o29bo2$40b5o3$30b2o$31bo3b2o4b3o$26bo4b2o2bo5b3o$25bobo6b
2o$21b2o2b3o9b2o8b2o$21bo4bo3b2o5b2o8bo$15b2o3b2o8b2o14b2o$4b2o10bo$5b
obo8b2o$3b2ob2o$3bobo$5b2o6b2o2b2o$13b2o3bo7bo$13b2o3bo5b5o$17bo6bobo
bo$23b3ob3o6bo$14b2o8bobobo7bo$15bo3b2o3b5o$15b2o2bo6bo14b3o$18b2o21b
obo2$23b2o3b2o$23b2o3b2o7$23b2o3b2o$23b2o3b2o2$9bobo21b2o$9b3o14bo6bo
2b2o$24b5o3b2o3bo$24bobobo8b2o$23b3ob3o$24bobobo6bo$24b5o5bo3b2o$26bo
7bo3b2o$16bo17b2o2b2o6b2o$16bo30bobo$45b2ob2o$35b2o8bobo$36bo10b2o$5b
2o14b2o8b2o3b2o$5bo8b2o5b2o3bo4bo$4b2o8b2o9b3o2b2o$17b2o6bobo$9b3o5bo
2b2o4bo$9b3o4b2o3bo$21b2o3$8b5o2$o29b2o$o30bobo$9b3o17b2ob2o$9b3o7b2o
8bobo$20bo10b2o$20b2o$7b2o3b2o$7b2o3b2o!

[MathAndCode]

I found a conduit which converts a bullet predecessor into a c/2 ship.

I reduced the population of one of the catalysts.

Code: Select all

x = 18, y = 14, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo9b2o$2bo10bo$o3bo8b2o$2ob2o$2bo$2b2o12bo$15bo$14b2o$15bo$16bo$11b2o
$12bo3b2o$12b2o2bo$15b2o!

The splitter can be used to make 0 degree and 180 degree reflectors, which can make ship loops with period 52 or greater.

That means that the only period left is 43. Here's the closest that I've gotten so far:

Code: Select all

x = 29, y = 27, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
13bo$13bo$15bo$14b2ob2o3b2o$17b2o3b2o$3b2o$3b2o14b3o$6bo$6bo$6bo$3b2o
$3b2o2$2b2o23b2o$3bo21bo$2o23b2o2$24b2o$24b2o$22bo$22bo$22bo$7b3o14b2o
$13b2o9b2o$5b2o3b2obo$5b2o3b2o3bo$15bo!

[silversmith]

That means that the only period left is 43. Here's the closest that I've gotten so far:

Code: Select all

snip

Here is a p43 based on your partial result.

Code: Select all

x = 15, y = 13, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
b2o3b2o$4bob2o$3b2o$bo11b2o$bo11b2o$9b2o$8b4o$9b2o$2o11b2o$13b2o$b2o$
2bo$2b2o!

[MathAndCode]

Here is a p43 based on your partial result.

That proves blizzard to be omniperiodic. What shall we do next? (I'm favoring proving the rule to be Turing complete building a Rule 110 unit cell.)

[silversmith]

A rule with splitters, reflectors, crossovers, and ANDNOT gates is essentially Turing complete, so making a Rule 110 emulator isn't very productive. I may continue finding conduits which can lead to a better toolkit and more interesting constructions.

[MathAndCode]

A rule with splitters, reflectors, crossovers, and ANDNOT gates is essentially Turing complete, so making a Rule 110 emulator isn't very productive. I may continue finding conduits which can lead to a better toolkit and more interesting constructions.

Okay. How is this?

Code: Select all

x = 31, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
10b2o6b2o$13bo4b2o$12b2o15b2o$29b2o3$8bo$8b2o19b2o$8bo20b2o3$7b2o$2o5b
o$2o7bo$9bo!

[silversmith]

The output of the conduit produces a good pre-beehive predecessor and a T-tetromino output, both with good clearance.
One problem is that the input pattern produces a fairly large mess in both directions, so it would be difficult to place it after another conduit.
I would recommend starting with the output of an existing conduit, or a common predecessor such as this:

Code: Select all

x = 12, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo2bo$2bobob2o$3bo3bo$5o2b2ob2o$3bo3bo$2bobob2o$2bo2bo!

Then make sure the reaction doesn't move too far backwards into its own input area.

[MathAndCode]

The output of the conduit produces a good pre-beehive predecessor and a T-tetromino output, both with good clearance.
One problem is that the input pattern produces a fairly large mess in both directions, so it would be difficult to place it after another conduit.
I would recommend starting with the output of an existing conduit, or a common predecessor such as this:

Code: Select all

x = 12, y = 7, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
2bo2bo$2bobob2o$3bo3bo$5o2b2ob2o$3bo3bo$2bobob2o$2bo2bo!

Then make sure the reaction doesn't move too far backwards into its own input area.

It's possible to clean up the mess in the back (although this does make the input clearance suboptimal).

Code: Select all

x = 42, y = 15, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
21b2o6b2o$24bo4b2o$23b2o15b2o$40b2o3$19bo$19b2o19b2o$19bo20b2o3$2bo2b
o12b2o$3o2b3o10bo$o6bo12bo$20bo!

[LaundryPizza03]

T flip-flop. The toggle input (T) has repeat time 66.

Code: Select all

x = 518, y = 237, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8Super
380.J$379.IJI2.10J$379.3I2.10J$379.3J6.2J$379.3J6.2J$379.3J6.2J$379.
3J6.2J$379.3J6.2J$379.3J6.2J$379.3J6.2J$379.3J6.2J$379.3J6.2J$379.3J
6.2J$379.3J6.2J$379.3J6.2J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$
379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J
$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.
3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J$379.3J11.
2I3.2I$379.3J11.2I.J.2I$379.3J13.3J8.2I9.I$379.3J13.3J8.I10.I$379.3J
12.2JI2J6.2I8.I3.I$379.3J11.J5IJ4.J2.J.2J.2J.2I.2I$379.3J11.JIJIJIJ4.
11J2.I$379.3J6.3J.J3IJ3IJ.13J.2I$379.3J5.7JIJIJI17J$379.3J5.7J5I17J$
379.3J6.8JI12J.5J$379.3J4.I2.2J.9J.2J.2J2.J.3J$379.3J4.I7.5J2.J2.J2.
2I2.3J$379.3J12.5J3.2I3.I3.3J$378.4J13.3J5.I2.2I3.3J$377.5J13.3J.J3.
2I6.3J$375.2I.JIJI2J6.2I2.5J.2I9.3J$375.I2.J3IJ.2I5.I2.5J.2I9.3J$359.
I9.2I3.2I2.5J.2I5.2I.6J11.3J$359.I10.I8.3J.J3.2I4.5J13.3J$357.I3.I8.
2I7.3J5.I2.2I2.4J13.3J$357.2I.2I.2J.2J.J2.J5.5J3.2I3.I3.3J13.3J$359.I
2.11J5.5J2.J2.J2.2I2.3J13.3J$359.2I.13J.9J.2J.2J2.J.3J13.3J$361.19JI
12J.5J12.3J$361.17J5I17J11.3J$362.5J.10JIJIJI17J11.3J$363.3J.J2.2J.2J
.J3IJ3IJ.13J.2I9.3J$363.3J2.2I2.J2.J.JIJIJIJ4.11J2.I9.3J$363.3J3.I3.
2I2.J5IJ4.J2.J.2J.2J.2I.2I7.3J$363.3J3.2I2.I4.2JI2J6.2I8.I3.I7.3J$
363.3J6.2I5.3J8.I10.I9.3J$363.3J13.3J8.2I9.I9.3J$363.3J11.2I.J.2I27.
3J$363.3J11.2I3.2I27.3J$363.3J45.4J$363.3J45.5J$363.3J43.6J.2I$363.3J
41.2I.5J2.I$363.3J41.2I.5J2.2I3.2I9.I$363.3J43.J.3J8.I10.I$363.3J45.
3J7.2I8.I3.I$363.3J44.5J5.J2.J.2J.2J.2I.2I$363.3J36.I7.5J5.11J2.I$
363.3J36.I2.2J.9J.13J.2I$363.3J38.8JI19J$363.3J37.7J5I17J$363.3J37.7J
IJIJI10J.5J$363.3J38.3J.J3IJ3IJ.2J.2J2.J.3J$363.3J43.JIJIJIJ.J2.J2.2I
2.3J$363.3J43.J5IJ2.2I3.I3.3J$363.3J44.2JI2J4.I2.2I3.4J$363.3J45.3J5.
2I6.5J$363.3J45.3J11.6J.2I$363.3J43.2I.J.2I7.2I.5J2.I$363.3J43.2I3.2I
7.2I.5J2.2I3.2I9.I$363.3J59.J.3J8.I10.I$363.3J61.3J7.2I8.I3.I$363.3J
60.5J5.J2.J.2J.2J.2I.2I$363.3J52.I7.5J5.11J2.I$363.3J52.I2.2J.9J.13J.
2I$363.3J54.8JI19J$363.3J53.7J5I17J$363.3J53.7JIJIJI10J.5J$363.3J54.
3J.J3IJ3IJ.2J.2J2.J.3J$363.3J59.JIJIJIJ.J2.J2.2I2.3J$363.3J59.J5IJ2.
2I3.I3.3J$363.3J60.2JI2J4.I2.2I3.3J$363.3J61.3J5.2I5.4J$363.3J61.3J
11.5J$363.3J59.2I.J.2I7.2I.6J$363.3J59.2I3.2I7.I2.5J.2I$363.3J57.I9.
2I3.2I2.5J.2I$363.3J57.I10.I8.3J.J$363.3J55.I3.I8.2I7.3J$363.3J55.2I.
2I.2J.2J.J2.J5.5J$363.3J57.I2.11J5.5J7.I$363.3J57.2I.13J.9J.2J2.I$
363.3J59.19JI8J$363.3J59.17J5I7J$363.3J60.5J.10JIJIJI7J$363.3J61.3J.J
2.2J.2J.J3IJ3IJ.3J$363.3J61.3J2.2I2.J2.J.JIJIJIJ$363.3J61.3J3.I3.2I2.
J5IJ$363.3J61.3J3.2I2.I4.2JI2J$363.3J61.4J5.2I5.3J$363.3J61.5J11.3J$
363.3J59.6J.2I7.2I.J.2I$363.3J57.2I.5J2.I7.2I3.2I$363.3J57.2I.5J2.2I
3.2I9.I$363.3J59.J.3J8.I10.I$363.3J61.3J7.2I8.I3.I$363.3J60.5J5.J2.J.
2J.2J.2I.2I$363.3J52.I7.5J5.11J2.I$363.3J52.I2.2J.9J.13J.2I$363.3J54.
8JI19J$363.3J53.7J5I17J$363.3J53.7JIJIJI10J.5J$363.3J54.3J.J3IJ3IJ.2J
.2J2.J.3J$363.3J59.JIJIJIJ.J2.J2.2I2.3J$363.3J59.J5IJ2.2I3.I3.3J$363.
3J60.2JI2J4.I2.2I3.3J$363.3J61.3J5.2I5.4J$363.3J61.3J11.5J$363.3J59.
2I.J.2I7.2I.6J$363.3J59.2I3.2I7.I2.5J.2I$363.3J57.I9.2I3.2I2.5J.2I$
363.3J57.I10.I8.3J.J$363.3J55.I3.I8.2I7.3J$363.3J55.2I.2I.2J.2J.J2.J
5.5J$363.3J57.I2.11J5.5J7.I$363.3J57.2I.13J.9J.2J2.I$363.3J59.19JI8J$
363.3J59.17J5I7J$363.3J60.5J.10JIJIJI7J$363.3J61.3J.J2.2J.2J.J3IJ3IJ.
3J$363.3J61.3J2.2I2.J2.J.JIJIJIJ$363.3J61.3J3.I3.2I2.J5IJ$363.3J61.3J
3.2I2.I4.2JI2J$363.3J61.3J6.2I5.3J$363.3J61.3J13.3J$363.3J61.3J11.2I.
J.2I$363.3J61.3J11.2I3.2I$3.6D354.3J61.3J77.6B$3.6D354.3J61.3J77.6B$.
2D6.2D352.3J61.3J75.2B6.2B$.2D6.2D352.3J61.3J75.2B6.2B$.2D360.3J61.3J
75.2B6.2B$.2D360.3J61.3J75.2B6.2B$.2D360.3J61.3J75.2B6.2B$.2D360.3J
61.3J75.2B6.2B$.2D360.3J61.3J75.2B2.2B2.2B$.2D360.3J61.3J75.2B2.2B2.
2B$.2D6.2D352.3J61.3J75.2B4.2B$.2D6.2D352.3J61.3J75.2B4.2B$3.6D354.3J
61.3J77.4B2.2B$3.6D354.3J61.3J77.4B2.2B$363.3J61.3J$363.3J61.3J$.2C
62D2C296D153B$2DC63DC296D154B$.2C62D2C296D153B$363.3J58.2D.J2DJ85.2A$
363.3J57.J2DJ.2D86.2A$363.3J57.4J$363.3J58.4J$363.3J58.4J$363.3J58.3J
$363.3J58.3J$363.3J58.3J$362.4J58.3J$361.5J42.2I14.3J$359.2I.6J41.I6.
2I6.3J$359.I2.5J.2I39.2I5.I2.2I3.3J$358.2I2.5J.2I38.J2.2J2.2I3.I3.3J$
363.3J.J3.2I36.6J2.J2.2I2.3J$363.3J5.I5.2I30.5J.2J.2J2.J.3J$362.5J3.
2I3.I4.I27.14J.5J$362.5J2.J2.J2.2I2.2I27.21J$356.3J.9J.2J.2J2.J4.2J2.
J2.I19.20J$355.9JI21J.3I16.2I.5J.13J.2I$355.7J5I19J.I19.I.5J3.11J2.I$
356.6JIJIJI20J18.I3.5J3.J2.J.2J.2J.2I.2I$353.2I2.2J.J3IJ3IJ.17J18.I2.
6J4.2I8.I3.I$353.2I6.JIJIJIJ4.J.J2.9J21.I.4J.I4.I10.I$361.J5IJ7.2I4.
3J.J20.2I.4J.3I2.2I9.I$362.2JI2J8.I4.5J.I21.6J2.I$363.3J8.2I4.5J.3I
19.5J$363.3J12.6J.J2.I15.I2.J.5J$361.2I.J.2I9.I.6J19.3I.5J$361.2I3.2I
7.3I.6J2.I18.I.5J$375.I2.6J.3I14.2I3.J.3J$379.5J.I16.2I4.5J$378.5J.J
16.J2.J3.4JI2J3.2I$378.6J17.3J2.4J5IJ2.2I$379.31JIJIJI3J$378.31J3IJ3I
3J$378.32JIJIJI3J$379.5J15.5J2.4J5IJ2.2I$377.2I2.2J17.J7.4JI2J3.2I$
378.I.I20.I6.5J$375.2I2.2I20.3I5.3J$378.I24.I4.5J$377.2I29.5J$408.4J$
409.2J$412.2I$412.2I!

[LaundryPizza03]

I did an analysis of the reflector, splitter, and lane-changer conduits. I found that when the 180 reflector is connected to the backward input of the splitter, packed as closely as possible, this output will be precisely 111 generations behind the forward output.

Code: Select all

x = 63, y = 35, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
36b2o3b2o$36b2o3b2o$49b2o9bo$49bo10bo$39bo8b2o8bo3bo$37b5o16b2ob2o$37b
obobo18bo$36b3ob3o16b2o$37bobobo$37b5o$39bo$29bo$29bo20b2o$45b2o3bo$
46bo2b2o$46b2o$18b2o2bobo8b2o8b2o$18bo3b3o2b2o5bo8b2o$2bo9b2o3b2o8b2o
5b2o$2bo10bo16b2o$o3bo8b2o15bo2b2o$2ob2o24b2o3bo$2bo31b2o$2b2o$23bo$
21b5o$21bobobo$20b3ob3o16b2o$11b2o8bobobo18bo$12bo3b2o3b5o16b2ob2o$12b
2o2bo6bo8b2o8bo3bo$15b2o16bo10bo$33b2o9bo$20b2o3b2o$20b2o3b2o!

One lane-changer pushes the spaceship behind by 47 generations, while the combination of two 90 reflectors pushes it back 188 + 2n generations for n ≥ 0; here, I chose n = 5 for a delay of 198 generations.

Code: Select all

x = 122, y = 55, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
obo24bobo29bobo$3o24b3o29b3o2$23b2o$23bo8b2o$7bo9b2o3b2o8b2o21b2o$7bo
10bo36bo8b2o$5bo3bo8b2o34b2o8b2o$5b2ob2o57b2o$7bo30bo28bo5b2o$7b2o29bo
27b2o3bo4bo$28bo42b2o2b2o$26b5o54bo$26bobobo29bo22b3o$25b3ob3o26b5o20b
o$16b2o8bobobo27bobobo$17bo3b2o3b5o18b2o6b3ob3o$17b2o2bo6bo20b2o7bobob
o$20b2o36b5o8b2o28b2o$60bo10bo10bo18b2o$25b2o3b2o38b2o10b3o$25b2o3b2o
52bo$57b2o3b2o9bo$57b2o3b2o7b3o9bo8bo$71bo9b3o6b3o$81bo8bo$101bo5b2o$
99b5o3b2o$99bobobo$98b3ob3o$99bobobo$99b5o3b2o$73b2o26bo5b2o$74bobo14b
2o$71b2o2b2o14b2o$74bo20bo$73b2o18b3o$93bo2$105bo$95b2o6b3o2b2o9bo$96b
o6bo4bo10bo$94bo12b2o8bo3bo$94bo22b2ob2o$96bo22bo$95b2o21b2o5$109b2o$
104b2o3bo$98b2o5bo2b2o$98bo6b2o$97b2o!

We find that 15 copies of the former on the forward output, plus 3 copies of the latter with n = 5 on the delayed output, gives two streams 118 cells apart that are exactly in sync.

Code: Select all

x = 140, y = 289, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
55b2o3b2o$55b2o3b2o$68b2o9bo$68bo10bo$58bo8b2o8bo3bo$56b5o16b2ob2o$56b
obobo18bo$55b3ob3o16b2o$56bobobo$56b5o$58bo$48bo$48bo20b2o$64b2o3bo$
65bo2b2o$65b2o$37b2o2bobo8b2o8b2o$37bo3b3o2b2o5bo8b2o$21bo9b2o3b2o8b2o
5b2o$21bo10bo16b2o$19bo3bo8b2o15bo2b2o$19b2ob2o24b2o3bo$21bo31b2o$21b
2o$42bo$40b5o24b2o$40bobobo24bo8b2o$39b3ob3o16b2o4b2o8b2o$30b2o8bobobo
18bo17b2o$31bo3b2o3b5o16b2ob2o15bo5b2o$31b2o2bo6bo8b2o8bo3bo14b2o3bo4b
o$34b2o16bo10bo21b2o2b2o$21b2o29b2o9bo35bo$21bo8b2o7b2o3b2o28bo22b3o$
5bo9b2o3b2o8b2o7b2o3b2o26b5o20bo$5bo10bo55bobobo$3bo3bo8b2o45b2o6b3ob
3o$3b2ob2o55b2o7bobobo$5bo30bo35b5o8b2o28b2o$5b2o29bo37bo10bo10bo18b2o
$26bo57b2o10b3o$24b5o69bo$24bobobo42b2o3b2o9bo$23b3ob3o41b2o3b2o7b3o9b
o8bo$14b2o8bobobo56bo9b3o6b3o$15bo3b2o3b5o66bo8bo$15b2o2bo6bo88bo5b2o$
18b2o93b5o3b2o$113bobobo$14b2o7b2o3b2o82b3ob3o$5b2o8bo7b2o3b2o83bobobo
$5b2o8b2o3b2o9bo81b5o3b2o$20bo10bo55b2o26bo5b2o$19b2o8bo3bo54bobo14b2o
$29b2ob2o51b2o2b2o14b2o$o30bo56bo20bo$o29b2o55b2o18b3o$10bo96bo$8b5o$
8bobobo106bo$7b3ob3o95b2o6b3o2b2o9bo$8bobobo8b2o87bo6bo4bo10bo$8b5o3b
2o3bo86bo12b2o8bo3bo$10bo6bo2b2o86bo22b2ob2o$17b2o91bo22bo$109b2o21b2o
$7b2o3b2o7b2o$7b2o3b2o7bo8b2o$5bo9b2o3b2o8b2o$5bo10bo$3bo3bo8b2o105b2o
$3b2ob2o110b2o3bo$5bo30bo75b2o5bo2b2o$5b2o29bo75bo6b2o$26bo84b2o19b2o$
24b5o94b2o8bo$24bobobo94b2o8b2o$23b3ob3o90b2o$14b2o8bobobo85b2o5bo$15b
o3b2o3b5o83bo4bo3b2o$15b2o2bo6bo85b2o2b2o$18b2o83bo$103b3o22bo$14b2o7b
2o3b2o75bo20b5o$5b2o8bo7b2o3b2o96bobobo$5b2o8b2o3b2o9bo93b3ob3o6b2o$
20bo10bo94bobobo7b2o$19b2o8bo3bo52b2o28b2o8b5o$29b2ob2o52b2o18bo10bo
10bo$o30bo72b3o10b2o$o29b2o72bo$10bo104bo9b2o3b2o$8b5o83bo8bo9b3o7b2o
3b2o$8bobobo83b3o6b3o9bo$7b3ob3o84bo8bo$8bobobo8b2o57b2o5bo$8b5o3b2o3b
o58b2o3b5o$10bo6bo2b2o63bobobo$17b2o65b3ob3o$85bobobo$7b2o3b2o7b2o57b
2o3b5o$7b2o3b2o7bo8b2o48b2o5bo26b2o$5bo9b2o3b2o8b2o64b2o14bobo$5bo10bo
79b2o14b2o2b2o$3bo3bo8b2o75bo20bo$3b2ob2o85b3o18b2o$5bo30bo58bo$5b2o
29bo$26bo56bo$24b5o40bo9b2o2b3o6b2o$24bobobo40bo10bo4bo6bo$23b3ob3o37b
o3bo8b2o12bo$14b2o8bobobo38b2ob2o22bo$15bo3b2o3b5o40bo22bo$15b2o2bo6bo
42b2o21b2o$18b2o2$14b2o7b2o3b2o$5b2o8bo7b2o3b2o$5b2o8b2o3b2o9bo46b2o$
20bo10bo47bo3b2o$19b2o8bo3bo45b2o2bo5b2o$29b2ob2o48b2o6bo$o30bo37b2o
19b2o$o29b2o37bo8b2o$10bo57b2o8b2o$8b5o68b2o$8bobobo68bo5b2o$7b3ob3o
66b2o3bo4bo$8bobobo8b2o62b2o2b2o$8b5o3b2o3bo77bo$10bo6bo2b2o52bo22b3o$
17b2o53b5o20bo$72bobobo$7b2o3b2o7b2o40b2o6b3ob3o$7b2o3b2o7bo8b2o31b2o
7bobobo$5bo9b2o3b2o8b2o40b5o8b2o28b2o$5bo10bo57bo10bo10bo18b2o$3bo3bo
8b2o66b2o10b3o$3b2ob2o90bo$5bo30bo34b2o3b2o9bo$5b2o29bo34b2o3b2o7b3o9b
o8bo$26bo58bo9b3o6b3o$24b5o66bo8bo$24bobobo86bo5b2o$23b3ob3o83b5o3b2o$
14b2o8bobobo84bobobo$15bo3b2o3b5o83b3ob3o$15b2o2bo6bo86bobobo$18b2o93b
5o3b2o$87b2o26bo5b2o$14b2o7b2o3b2o58bobo14b2o$5b2o8bo7b2o3b2o55b2o2b2o
14b2o$5b2o8b2o3b2o9bo56bo20bo$20bo10bo55b2o18b3o$19b2o8bo3bo73bo$29b2o
b2o$o30bo87bo$o29b2o77b2o6b3o2b2o9bo$10bo99bo6bo4bo10bo$8b5o95bo12b2o
8bo3bo$8bobobo95bo22b2ob2o$7b3ob3o96bo22bo$8bobobo8b2o86b2o21b2o$8b5o
3b2o3bo$10bo6bo2b2o$17b2o2$7b2o3b2o7b2o100b2o$7b2o3b2o7bo8b2o86b2o3bo$
5bo9b2o3b2o8b2o80b2o5bo2b2o$5bo10bo95bo6b2o$3bo3bo8b2o93b2o$3b2ob2o$5b
o30bo$5b2o29bo$26bo$24b5o$24bobobo$23b3ob3o$14b2o8bobobo$15bo3b2o3b5o$
15b2o2bo6bo$18b2o2$14b2o7b2o3b2o$5b2o8bo7b2o3b2o$5b2o8b2o3b2o9bo$20bo
10bo$19b2o8bo3bo$29b2ob2o$o30bo$o29b2o$10bo$8b5o$8bobobo$7b3ob3o$8bobo
bo8b2o$8b5o3b2o3bo$10bo6bo2b2o$17b2o2$7b2o3b2o7b2o$7b2o3b2o7bo8b2o$5bo
9b2o3b2o8b2o$5bo10bo$3bo3bo8b2o$3b2ob2o$5bo30bo$5b2o29bo$26bo$24b5o$
24bobobo$23b3ob3o$14b2o8bobobo$15bo3b2o3b5o$15b2o2bo6bo$18b2o2$14b2o7b
2o3b2o$5b2o8bo7b2o3b2o$5b2o8b2o3b2o9bo$20bo10bo$19b2o8bo3bo$29b2ob2o$o
30bo$o29b2o$10bo$8b5o$8bobobo$7b3ob3o$8bobobo8b2o$8b5o3b2o3bo$10bo6bo
2b2o$17b2o2$7b2o3b2o7b2o$7b2o3b2o7bo8b2o$5bo9b2o3b2o8b2o$5bo10bo$3bo3b
o8b2o$3b2ob2o$5bo30bo$5b2o29bo$26bo$24b5o$24bobobo$23b3ob3o$14b2o8bobo
bo$15bo3b2o3b5o$15b2o2bo6bo$18b2o2$14b2o7b2o3b2o$5b2o8bo7b2o3b2o$5b2o
8b2o3b2o9bo$20bo10bo$19b2o8bo3bo$29b2ob2o$o30bo$o29b2o$10bo$8b5o$8bobo
bo$7b3ob3o$8bobobo8b2o$8b5o3b2o3bo$10bo6bo2b2o$17b2o2$7b2o3b2o7b2o$7b
2o3b2o7bo8b2o$5bo9b2o3b2o8b2o$5bo10bo$3bo3bo8b2o$3b2ob2o$5bo30bo$5b2o
29bo$26bo$24b5o$24bobobo$23b3ob3o$14b2o8bobobo$15bo3b2o3b5o$15b2o2bo6b
o$18b2o2$23b2o3b2o$23b2o3b2o!

[silversmith]

Here is a period tripling pre-bullet to pre-hive converter, attached to a c/2 ship converter for demonstration purposes.

Code: Select all

x = 72, y = 36, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
62b2o$62b2o4$53bo$51b3o$51bo2bo$62bo5b2o$60b5o3b2o$2o24b2o24b2o6bobob
o$bo25bo25bo5b3ob3o$2o24b2o24b2o6bobobo$60b5o3b2o$62bo5b2o$52b2o$52b
2o$56bo$54b3o$54bo12b2o$65bo$65b2o$57bo10b2o$55b3o8bo$55bo10b2o2$57bo$
55b3o$55bo3$61b2o$61bo7b2o$60b2o7bo$71bo$71bo!

A snowflake to pre-bullet

Code: Select all

x = 20, y = 9, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
6bo$5bobo8bo$2bobo11b3o$3o15bo$o$13b3ob3o2$18bo$18bo!

Another snowflake to snowflake conduit

Code: Select all

x = 16, y = 11, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
5bo$4bobo$5bo$12bo$12b3o$14bo2$9b3ob3o2$2o12bo$14bo!

That conduit allows for the creation of snowflake conduit loops, with repeat time 58, but it can be overclocked to several shorter periods.

Code: Select all

x = 47, y = 47, rule = B2ci3aik4c5ry6a7e/S1e2aei3-cnry4eiyz5aeir6ei8
21bo$18b2obob2o$18bo2bo$17b2o12bo$29b3o$13b2o14bo$14bo$14b2o$36bo$34b
3o$8b2o24bo$9bo$9b2o$26b2o13bo$23bo2bo12b3o$3b2o13bo4bob2o8b3obo$4bo
13b3o$4b2o14bo3b2o17bo$30b2o11b3o$13bo16bo4bo4bo4bo$13b3o13b2o5bo$15bo
bo26b3o$bo15bo17bo$bo12b2o15b2o3bo8bo$29bo15bo$3o26bobo$16b2o13b3ob3o
$bo14bo16bo$b3o11b2o$3bo17b2o3bo14b2o$26b3o13bo$7bo12b2obo4bo6bobo4b
2o$5b3o12bo2bo13bo$5bo13b2o$36b2o$12bo24bo$10b3o24b2o$10bo2$31b2o$32bo
$17bo14b2o$15b3o$15bo12b2o$25bo2bo$22b2obob2o$25bo!