The Omnifrequency Project

[WhiteHawk]

This thread is for the investigation into a conjecture (and related question) I posed a while ago that I believe should get it's own thread to avoid cluttering up the Unproven Conjectures

The conjecture can be stated as follows

"In B3/S23, there exists a nontrivial oscillator (without a non-interacting weld) for every period n where every possible instance of cells oscillating at any given frequency value between n and 1 inclusive can be found in said oscillator"

(EDIT: see trivial page for examples of oscillators which may be considered "trival" without modification to make them nontrivial, as well as Honey thieves with test tube baby for an example of what is considered trivial in terms of weld)

The question that thus follows is:

"If there is known to be a period n where it is proven that an oscillator exists which expresses cells oscillating at all frequencies, what is the smallest such oscillator of period n which has this property?"

This thread is aimed at proving the conjecture (proof for 61+ coming in the next post, which could likely be extended to several high periods with multi-barreled guns, though that is an unsatisfying solution to the conjecture), and also answering the question posed above.

Note that neither the conjecture nor the question prohibit solutions which are not volmatchstrict, a problem which can be addressed later, likely once the conjecture is proven.

To check the frequency tabultation in LifeViewer, click Settings (gear icon in lower right) > Pattern > Identify > "Frq" in column of controls on right.

Below is a collection of the current smallest oscillators between period-2 and period-20, minus period 19 which currently has no non-weld example.

Code: Select all

x = 320, y = 116, rule = B3/S23
181bo$175b2o4bobo$174bo5bobo86b2o$177bo4bo3b2o78b2o2bo$133b2o20bo19b2o
9b2o6b2o51b2o15b3ob2o$18bo97b2o16bo2b2o16b3o36bo19bo23bo9bo5b2o7bo54b
2o$b2o15bo93b2o3bo16bobobo19bo22bo10bobo17b3o23bo8bo5bobo8b3ob2o27b2o
17bob2o$b2o15bo10bobo5b2o13bo2b2o4bo9b2ob2o34bo4bobob2o12b2obo20b2o19b
2obo10b2o9b2o6bo35b2o5bo11bob2o28bo16bo$9bo8b2o12bo4bo14b2o2bob2obo10b
obo13b2o25bobo2bo10bo2bo2bo29bo10b2o23bobo5b2o85bobo17bo$9bo11bo6bo2b
o6bo2bo14bobo12bo4bobo9b2o2b2o15bo3bobob2o12b2o3bo28b3o10bo5b3ob2o14b
o3bo38b2o3b5o13b3o26b2o7bo5b2obo$bo7bo7bo4bo4bobobo8b2o15b2o13b4o2bo14b
2o14b2o4bo24b2o18b2o2bo23b2o19bo5b2o5b2o11b2ob3o5bobo2bo4bo12bo3bo6b2o
25bo6b2o$obo19bo4bo2bo9bo3bob2o11bo17b2o13bo2bo17bob4o20bobo2bo15bo4b
o26b3o7b8o4bobo6bo17bo4b2o3bobo14bo5bo4bobo20bo4bo2bo$bo16b3o7b2o9bo4b
2obo11bo3bo10bo20bo2b2o12bo6bo17bobobobobo14bob4o27b3o6bo7b2o3bo7bobo
15b2o9b2o15bo3bo5bo21bobo4b2o$39b2o20bobo9bobo4b2o11bobo2b2o12bobobob
o17bo4bo2bo12bo2bo15b2o27bob2obo13b2o7b2o35b3o5b2obo22bo$62bo10b2o5bo
29b3obob2o18b4obo14bobo3b2o14bob2o4b2o17b2obo2b7o10b2o4bo43bo2bo2bo16b
obo$81b3o25bo3bobo24bo16bo5bo10bo2bo2b2o4b2o20bo8bo9bobo5b3ob2o10b2o25b
obob2obo16bo$83bo25b2o2bobo22bo24bobo8bobo31b2o3b2o12b2o22b2o18bo6bo2b
o2b2o$114bo23b2o24b2o9bo37b2o52bo2bobobo9bo$267b4ob2obo3bobo3b3o9b3o$
175b2o60bo33bo3bo4bo6bo8b3o$175b2o60bo31bobo3b2o$269b2o31bo$302b2o12$
62b2o22b2o$63bo22bo$63bob2o16b2obo$64bo20bo65bo7bo$68bo12bo69b3o4b2o$
66bo16bo70bo3b2o53bo5bo$60b2o5bo14bo5b2o63b2o3bo55bo3bo$61bo26bo59b2o
13b2o50bobo$61bobo4bo12bo4bobo60bo13bo52bo43bo$62b2o3b3o10b3o3b2o61bo
bo4bo4bobo51bobo41bobo$66b2ob2o8b2ob2o66b2o4bo4b2o51bo3bo40bobo$65b3o
b3o6b3ob3o71bo56bo5bo38b2ob2o$56b2o8b2ob2o8b2ob2o8b2o150b2o6bo9bo$56b
o10b3o10b3o10bo62b2o5b2o4b2o72bo6b3o5b2obo$53b2obo11bo12bo11bob2o60bo
3bo2bo3bobo75bo2bo8b2obobo$52bobob2o5b2o20b2o5b2obobo70bo75b2o3b2o11b
2o$51bo11b2o20b2o11bo52bob2o5bo5b3o87bo$50bo4b3o10b2o10b2o10b3o4bo49b
3ob2o5bo2bobo3b2o84b2o$36bobo10bo4bo2bo10b2o10b2o10bo2bo4bo47bo18b2o2b
o83bo$36b2obo8bo4bobo8bo20bo8bobo4bo47b3ob2o6b5o3b2o75b3o6b4o$34b2o3b
o8b2o2bobo8b3o18b3o8bobo2b2o49bobo5bo5bob2o76bo2bo10bo$33bo3b2ob2o9bo
bo8b2ob2o16b2ob2o8bobo52bobo5b5obo2bo76b3o7b2ob2o$34b3obobobo3b4obo9b
3ob3o14b3ob3o9bob4o48bo10bobobo88bobo$36bo6bo2bo2bob2o9b2ob2o16b2ob2o
9b2obo2bo57bo4bo89bobo$31b2o4b6o20b3o3b2o8b2o3b3o74b2o88b2o4bo$24b2o5b
o32bo4bobo6bobo4bo161b2obobo$25bo11b2obo30bo6bo30bo138bobobob2o$25bob
2o8b2ob3o13bo14b2o4b2o14bo13b3o143bobo$26bo16bo11b3o34b3o11bo8bo131bo
bobobo$14b2o14bo3bobo5b2o5b2o3b5o32b5o3b2o5b2o5b3o129b3obo3bo$15bo15b
obo2bo12b2o2b2o3b2o30b2o3b2o2b2o11bo131bo5b3o$15bobo4b2ob2obobo3bobo8b
o8b5o32b5o8bo8bo131b4obo$16b2o6b3o11b2o4b3o8b3o34b3o8b3o4bo2bo133bobo
$22bo4bo10bobo2b5o8bo36bo8b5o2bo$21b2ob3o11bo3b2o3b2o2b2o44b2o2b2o3b2o
3bo$25b2o6bo9b5o3b2o5b2o30b2o5b2o3b5o$16b2o3b3o8b2o10b3o11bo32bo11b3o
$15bobo3bo23bo13b3o26b3o13bo$15bo45bo26bo$14b2o4$61bo26bo$45bo13b3o26b
3o13bo$44b3o11bo32bo11b3o$43b5o3b2o5b2o30b2o5b2o3b5o$38bo3b2o3b2o2b2o
44b2o2b2o3b2o3bo$40bo2b5o8bo36bo8b5o2bo$36bo2bo4b3o8b3o34b3o8b3o4bo2b
o$36bo8bo8b5o32b5o8bo8bo$37bo11b2o2b2o3b2o30b2o3b2o2b2o11bo$34b3o5b2o
5b2o3b5o32b5o3b2o5b2o5b3o$34bo8bo11b3o34b3o11bo8bo$40b3o13bo14b2o4b2o
14bo13b3o$40bo30bo6bo30bo$64bo4bobo6bobo4bo$63b3o3b2o8b2o3b3o$46bo2bo
b2o9b2ob2o16b2ob2o9b2obo2bo$46b4obo9b3ob3o14b3ob3o9bob4o$51bobo8b2ob2o
16b2ob2o8bobo$48b2o2bobo8b3o18b3o8bobo2b2o$48bo4bobo8bo20bo8bobo4bo$49b
o4bo2bo10b2o10b2o10bo2bo4bo$50bo4b3o10b2o10b2o10b3o4bo$51bo11b2o20b2o
11bo$52bobob2o5b2o20b2o5b2obobo$53b2obo11bo12bo11bob2o$56bo10b3o10b3o
10bo$56b2o8b2ob2o8b2ob2o8b2o$65b3ob3o6b3ob3o$66b2ob2o8b2ob2o$62b2o3b3o
10b3o3b2o$61bobo4bo12bo4bobo$61bo26bo$60b2o5bo14bo5b2o$66bo16bo$68bo12b
o$64bo20bo$63bob2o16b2obo$63bo22bo$62b2o22b2o!

Above p20, only two periods had been proven at the time of this post (see below for more) - p30 (originally 604 cells) and p37 (294 cells)

Code: Select all

x = 169, y = 95, rule = B3/S23
12b2o$12b2o4$27b2o$27b2o4$27bo14b2o$26b3o13b2o$9b2o3b2o9bo3bo$11b3o10b
ob3obo$10bo3bo10b5o$11bobo43b2o$12bo44b2o2$57bo$56bobo$26bo2b2o11bo13b
obo13b2o$13b3o10bobo12b3o13bo14b2o$b2o4bobo15b2o13b5o$bobo3b2o4bobo8b
2o13b2o3b2o$3bo4bo3b5o7b2obo12b5o9b2obob2o$o2b3o5b2o3b2o7b3o12bo3bo9b
o5bo26b2o$3o3bo4b2o3b2o23bobo11bo3bo27b2o$3b3obo34bo13b3o12b3o$2bo4bo
18b2o3b2o$bob2obo7bo14bo41bobo$bo2bobobo4bobo10bo5bo11bo25b5o27b2o$2b
o3b2obo3bobo2bobo6b2ob2o10b2ob2o22b2o3b2o26b2o$3b3o3bo4bo3b2o8bobo6bo
31b2o3b2o$5bo3b2o8bo9bo6bo4bo5bo$29bo6b3o16bo45b3o$41b2obob2o6bo17b2o
27b3o13b2o$54b3o13b2ob2o42b2o$70bo2bo10b2o3b2o$73bo12b3o$44b2o24bo14b
o3bo9b2o3b2o$43bo3bo23b2o13bobo11b5o27b2o$43bo3bo9b5o25bo13b3o13bo14b
2o$44b2o10bob3obo39bo14bo$47b3o7bo3bo9b2o3b2o38bobo$47b2o9b3o5bo5b5o38b
2ob2o$59bo4b2o7b3o38bo5bo26b2o$65b2o7bo13b3o26bo29b2o$82bobo29b2o3b2o
$82b2o4bobo$83bo3b5o9bo43bo$74bo11b2o3b2o6b2o15b4o12bo13bo$86b2o3b2o7b
2o13b2o2bo11b3o12bo$76bo38b2obo11b5o$76bo52b2o3b2o$89bo26b2o12b5o9b2o
3b2o$88bob2o24bo13bo3bo12bo$88bob3o8b2o3b2o23bobo10bo5bo$89b2o3bo8b3o
26bo12b2ob2o$92b2o8bo3bo9b2obob2o23bobo$93bo9bobo4bo5bo5bo24bo12b2o$104b
o4bo7bo3bo12bo12bo12bo$109b3o6b3o11b2ob2o24bo5b2o$127bo30b3obo3bobo$126b
o4bo5bo19bo4bo3bo$126b3o29b3ob2ob2o$131b2obob2o22bobo$143bobo14bobob3o
$143b2o16b2obo2bo$144bo3b3o6b3o6b2o$147bo3bo7bo$133bo12bo5bo5bo$133bo
b2o9b2obob2o$134bo2bo2$136b2o14bo$151b2o2$150bob2o$149bo2b2o$149b4o3$
148b2o3b2o$151bo$148bo5bo$136bobo10b2ob2o$135bo3bo10bobo$136bo3bo10bo
$138b2o11bo$141bo2bo$139bo2bo2bo$140bobo2bo$139b2ob5ob2o$139bo2bo3b2o
bo$140b2o6bo!

Code: Select all

x = 69, y = 62, rule = B3/S23
50bo$50b3o14b2o$53bo13bo$52b2o11bobo$65b2o$55b2o$54b2o$55b2o$56b3o$42b
2o14bo$43bo14bo$43bobo19b2o$44b2o19bobo$52bo14bo$52bo14b2o$52b3o$37bo
8b2o6b2o$24bo12b3o6b2o7b2o$23bobo14bo13b2o$23bobo13b2o$22b2ob3o29b2o$
17b2o9bo15bobo4bo5bo$17b2o3b2ob3o15bo2bo3b2o6b3o$22b2obo17bo2bo3b2o8b
o$8b2o34b2o$8bo9b2o9b2o$9b3o5bo2bo9bo$11bo5bobo10bobo19b2o$18bo12b2o19b
obo$54bo$54b2o$15b2o22b2o$3b2o8b2o2bo2b2o11b2o3bo2bo$3bo9bo2bo3b2o12b
o3bo2bo$2obo9b3o15b2o5bobo$o2b3o24bobo$b2o3bo23bo13b2o$3b4o22b2o13bo$
3bo25b2obo2bo9b3o$bobob2o23bobobobo10bo$b2o2bo25b2o$5bobo25b3o$6b2o17b
2o$22bo3bobo$15b3o4bo4b2o9b2o$9b2o3bo2bo4bo15bobo$9b2o2bo2b2o22bo$14b
2o24b2o$24b2o$24bobo$12bo13bo9b2o$11bobo5bo6b2o8bobo$10bo2bo5b3o16bo$
11b2o9bo15b2o$21b2o$5bob2o$3b3ob2o3b2o$2bo9b2o$3b3ob2o$5bobo$5bobo$6b
o!

The complete list (to be updated upon discovery up to 61) is as follows:

1 - 4 cells (PROVEN SMALLEST)
2 - 3 cells (PROVEN SMALLEST)
3 - 12 cells (PROVEN SMALLEST)
4 - 12 cells (PROVEN SMALLEST)
5 - 17 cells
6 - 20 cells
7 - 28 cells (SKOP*)
8 - 17 cells
9 - 42 cells
10 - 39 cells
11 - 33 cells (SKOP*)
12 - 63 cells
13 - 52 cells
14 - 67 cells
15 - 76 cells (reducible?)
16 - 41 cells
17 - 653 cells (reducible eventually?)
18 - 97 cells
19 - N/A
20 - 91 cells (reducible?)
21 - 139 cells (reducible?)
22 - 195 cells (reducible?)
23 - 170 cells
24 - 184 cells (reducible?)
25 - 86 cells
26 - 260 cells
27 - 330 cells (reducible?)
28 - 151 cells
29 - 319 cells (maybe reducible)
30 - 134 cells (reducible?)
31 - N/A
32 - 410 cells (likely reducible)
33 - 433 cells (likely reducible)
34 - 643 cells (likely reducible)
35 - 807 cells (likely reducible)
36 - 234 cells (reducible?)
37 - 294 cells (reducible?)
38 - 457 cells (reducible?)
39 - 1467 cells (likely reducible)
40 - 440 cells (likely reducible)
41 to 42 - Undefined (double-barreled guns, Still-life construction/deconstruction method)
43 - 595 cells (reducible)
44 - 1327 cells (reducible)
45 - Undefined (four-barreled gun, Still-life construction/deconstruction method)
46 - 561 cells
47 to 49 - Undefined (double-barreled guns, Still-life construction/deconstruction method)
50 - 604 cells (reducible?)
51 to 60 - Undefined (double-barreled guns, Still-life construction/deconstruction method)
61+ - Undefined (Infinite herschel conduits with infinite barrels of different colors possible for SL construction/deconstruction)



EDIT: Ah, yes - the goal. The objective of this thread is to simply provide a thread to answer the conjecture and from there answer the follow-up question. If anyone finds an oscillator below p61 which satisfies the conjecture or better answers the question, they can post it here.

[LuveelVoom]

Caterer is the smallest P3 oscillator, so that's also proven
Mold is tied with mazing as the smallest P4 oscillator, so that's also proven

[WhiteHawk]

Incomplete proof for periods 61+ which relies on the assumption that colour-preserving and colour-changing herschel conduits/glider splitters exist which can produce gliders which can then be configured into the right places at the right times by snarks/snark64/other stable colour-preserving reflectors.

Below shows a way to use 2g-block synthesis + 1g deletion to get cells oscillating at every period between 1 and n-7 in this way. This shows that, assuming eaters that can provide cells with frequency n-6 to n-2 exist, it is almost certain that omnifrequent oscillators exist for all periods that have oscillators which can produce an infinite amount of gliders and can be configured in various ways to have gliders synthesize & destroy blocks or other SL - all Herschel Conduit supported periods (61+). The only step now for those periods is to actually build such a POC oscillator, which would probably be enormous.

Code: Select all

x = 204, y = 126, rule = B3/S23
124bob2o$124b2obo$16bob2o$16b2obo102b5o$121bo4bo12b2o$14b5o101bo2bo14b
o2bo$13bo4bo12b2o87bob2o$12bo2bo15b2o84b2obo5bo$12bob2o102bobo4bobo11b
o2bo3b2o$9b2obo5bo98bo2b2o2bo2bo10b2o2bo2bo2bo$10bobo4bobo11b2o5b2o77b
2o6b2o13bo4b2obo$9bo2b2o2bo2bo10bobo4bo2bo89b3o15b2o$9b2o6b2o13bo4b2o
bo88bo3bo11b2o3bo$31bo8b2o86bo4bo10bo2b3o$24bo4b2o6b2o3bo77bo6bo3bobo
9bob2o$22b2obo5bo4bo2b3o78b3o4bo4bo11bo2bo$12bo9b2obo3b2o4bob2o84bo5b
obobo12b2o$12b3o6bo2bo11bo2bo82bobo5b3o4bo$15bo6b2o14b2o82b2o12bo$14b
obo5b2o5bo106b2obo$14b2o13b2o91b2o12bobo2bo9bo$27b5o90bo12b2obo2bo7b3o
$14b2o14b2o11bo80bo23bo$14bo15bobo8b3o79b2o3b2o18b2o3b2o$16bo15bo7bo88b
o23bo$15b2o3b2o8b2o8b2o3b2o79b3o7bo2bob2o12bo$21bo7bo15bo80bo9bo2bobo
12b2o$18b3o8bobo15bo90bob2o$18bo11b2o14b2o93bo12b2o$30b5o105bo4b3o5bo
bo$31b2o13b2o82b2o12bobobo5bo$32bo5b2o5bobo82bo2bo11bo4bo4b3o$22b2o14b
2o6bo84b2obo9bobo3bo6bo$22bo2bo11bo2bo6b3o78b3o2bo10bo4bo$23b2obo4b2o
3bob2o9bo77bo3b2o11bo3bo$20b3o2bo4bo5bob2o88b2o15b3o$19bo3b2o6b2o4bo91b
ob2o4bo13b2o$20b2o8bo98bo2bo5b2o10bo2bo2b2o$21bob2o4bo13b2o85b2o5b2o11b
obo4bo$21bo2bo4bobo10bo2bo2b2o101bo5bob2o$22b2o5b2o11bobo4bo84b2o18b2o
bobo$43bo5bob2o82bo18bo2bo2bo$26b2o18b2obobo80b3o16bo4bo2b2o$27bo18bo
2bo2bo79bo18b5o$24b3o16bo4bo2b2o$24bo18b5o105b2obo$153bob2o$45b2obo$45b
ob2o3$153bo$43bo110bo$44b2o106b3o$43b2o3$156b2o$156b2o2$50b2o$50bobo$
50bo110b2o$44b2o114b2o$43bobo116bo$45bo103b2o$150b2o$149bo8$66bo97b2o
bo$56b2obo5b2o97bob2o$56bob2o5bobo108b2o$29bo114bob2o17b5o6bobo9bo$29b
2o5bob2o17b5o18bo63b2obo12b2o2bo4bo6bo9b3o$28bobo5b2obo12b2o2bo4bo16b
3o53b2o24bo2bo2bo18bo$52bo2bo2bo18bo45bo9bobo6b5o14bobob2o18b2o$15bo18b
5o14bobob2o18b2o44b3o9bo6bo4bo2b2o8b2obo5bo$15b3o16bo4bo2b2o8b2obo5bo
64bo18bo2bo2bo11bo4bobo18b2o$18bo18bo2bo2bo11bo4bobo18b2o42b2o18b2obo
bo12b2o2bo2bo17bo2bo$17b2o18b2obobo12b2o2bo2bo17bo2bo58bo5bob2o16b2o18b
2obo$34bo5bob2o16b2o18b2obo37b2o18bobo4bo30bo11b2o$13b2o18bobo4bo42b2o
35bo2bo17bo2bo2b2o28b3o8b2o3bo$12bo2bo17bo2bo2b2o39b2o3bo34bob2o18b2o
34bo8bo2b3o$12bob2o18b2o43bo2b3o34b2o11bo30bo22bob2o$11b2o42bo17bo4bo
b2o36bo3b2o8b3o28b3o9bobo9bo2bo$10bo3b2o39b3o14bobo4bo2bo36b3o2bo8bo32b
o14bo7b2o$11b3o2bo41bo12b2ob2o5b2o39b2obo22bo16bobo12bobo$14b2obo4bo17b
o16bobo11bo2bo46bo2bo9bobo9b3o16b2o7bo3bo2bo$13bo2bo4bobo14b3o16b2o13b
2o47b2o7bo14bo32bo$13b2o5b2ob2o12bo91bobo12bobo18b2o8bo2bo15bo$21bo2b
o11bobo18b2o27bo43bo2bo3bo7b2o18bo10bo15b3o$22b2o13b2o18bo26b3o46bo33b
o23bo$59bo23bo33bo15bo2bo8b2o19b2o3b2o18b2o3b2o$9bo27b2o19b2o3b2o18b2o
3b2o27b3o15bo10bo25bo23bo$9b3o26bo25bo23bo31bo23bo24b3o15bo10bo$12bo23b
o24b3o26bo23b2o3b2o18b2o3b2o23bo15bo2bo8b2o$6b2o3b2o18b2o3b2o23bo27b2o
24bo23bo45bo$7bo23bo81bo10bo15b3o39bo2bo3bo7b2o$5bo26b3o39b2o13b2o22b
2o8bo2bo15bo38bobo12bobo$5b2o27bo38bo2bo11bobo35bo46b2o7bo14bo$65b2o5b
2ob2o12bo23b2o7bo3bo2bo43bo2bo9bobo9b3o$5b2o13b2o43bo2bo4bobo14b3o20b
obo12bobo43b2obo22bo$5bobo11bo2bo43b2obo4bo17bo21bo14bo7b2o32b3o2bo8b
o$6bo12b2ob2o5b2o32b3o2bo42b3o9bobo9bo2bo31bo3b2o8b3o$3b3o14bobo4bo2b
o31bo3b2o43bo22bob2o33b2o11bo$3bo17bo4bob2o33b2o61bo8bo2b3o31bob2o18b
2o6b2o$27bo2b3o31bob2o18b2o6b2o29b3o8b2o3bo30bo2bo17bo2bo2b2o2bo$28b2o
3bo30bo2bo17bo2bo2b2o2bo31bo11b2o32b2o18bobo4bobo$31b2o32b2o18bobo4bo
bo13b2o6b2o18b2obo54bo5bob2o$2o6b2o18b2obo54bo5bob2o12bo2b2o2bo2bo17b
o2bo57b2obo$o2b2o2bo2bo17bo2bo57b2obo16bobo4bobo18b2o41b2o15bo2bo$bob
o4bobo18b2o41b2o15bo2bo15b2obo5bo62b2o12bo4bo$2obo5bo62b2o12bo4bo19bo
b2o79b5o$3bob2o79b5o20bo2bo15b2o$3bo2bo15b2o88bo4bo12b2o61bob2o$4bo4b
o12b2o61bob2o24b5o75b2obo$5b5o75b2obo$115b2obo$7b2obo104bob2o$7bob2o!

[WhiteHawk]

Some near-misses

Almost p21, missing F13 (though F15 is in the p7 pipsquirter). The p21 glider gun has F13, but I haven't been able to find any good sparks to delete gliders with

Code: Select all

x = 37, y = 23, rule = B3/S23
7b2o$8bo2bo$5b3o3b3o$4bo3b3o3bo$4b2obo3b3o$8b2obo7b2o$3bob2obobo8bo3b
2o$3b2ob2o13bo2bo$20b2obo$20bo2b4o8bo$10bobo7b3o3bo6b3o$9bobob2o5bo2b
4o5bo$9bobo8b2obo2bo4bobo$4b2o4bo5bo4bob2o2bo2b4o$3bobo10bo4bobobo2bo
5b2o$3bo18b2ob4obob2o2bo$2b2o20bo4b2obo2bo$o2bobob2o15bob2o5b2o$2o2b2o
bo15b2obo$7bobo16bo$7b2obo15b2o$10bo$10b2o!

P23, missing F18 and F19

Code: Select all

x = 43, y = 49, rule = B3/S23
28b2o$28bo$29bo$26b4o$17b2o7bo$17bo11b3o$14b2obo11bo2bob2o$12bo2bob2o
2b2o8b2obo2bo$12b2obo4bo5b2o6bob2o$15bo4bo2bobobo6bo$15b2o3b3ob3o6b2o
$25b2o3$21bobo$21b2o4bo$16b2o8bobo$16bo9bobo3b2o$17bo9bo4b2o$14b4o$5b
2o7bo12bo$5bo11b3o6bobo$2b2obo10b2o2bo4bo3bo8b2o$o2bob2o9b2ob2o4bo3bo
2bo6bo$2obo6bo2b2ob2o7b2ob2o2bo6bob2o$3bo6bo2bo3bo4b2ob2o9b2obo2bo$3b
2o8bo3bo4bo2b2o10bob2o$14bobo6b3o11bo$15bo12bo7b2o$25b4o$9b2o4bo9bo$9b
2o3bobo9bo$14bobo8b2o$9b2o4bo$9bobo3$7b3o$3b2o7b3o6b2o$3bo5bo5bo6bo$2o
bo5b2o2bobo6bob2o$o2bob2o3bo3bo4b2obo2bo$2b2obo11bo2bob2o$5bo11b3o$5b
2o7bo$14b4o$17bo$16bo$16b2o!

[LuveelVoom]

Some near-misses

Almost p21, missing F13 (though F15 is in the p7 pipsquirter). The p21 glider gun has F13, but I haven't been able to find any good sparks to delete gliders with

Code: Select all

x = 37, y = 23, rule = B3/S23
7b2o$8bo2bo$5b3o3b3o$4bo3b3o3bo$4b2obo3b3o$8b2obo7b2o$3bob2obobo8bo3b
2o$3b2ob2o13bo2bo$20b2obo$20bo2b4o8bo$10bobo7b3o3bo6b3o$9bobob2o5bo2b
4o5bo$9bobo8b2obo2bo4bobo$4b2o4bo5bo4bob2o2bo2b4o$3bobo10bo4bobobo2bo
5b2o$3bo18b2ob4obob2o2bo$2b2o20bo4b2obo2bo$o2bobob2o15bob2o5b2o$2o2b2o
bo15b2obo$7bobo16bo$7b2obo15b2o$10bo$10b2o!

P23, missing F18 and F19

Code: Select all

x = 43, y = 49, rule = B3/S23
28b2o$28bo$29bo$26b4o$17b2o7bo$17bo11b3o$14b2obo11bo2bob2o$12bo2bob2o
2b2o8b2obo2bo$12b2obo4bo5b2o6bob2o$15bo4bo2bobobo6bo$15b2o3b3ob3o6b2o
$25b2o3$21bobo$21b2o4bo$16b2o8bobo$16bo9bobo3b2o$17bo9bo4b2o$14b4o$5b
2o7bo12bo$5bo11b3o6bobo$2b2obo10b2o2bo4bo3bo8b2o$o2bob2o9b2ob2o4bo3bo
2bo6bo$2obo6bo2b2ob2o7b2ob2o2bo6bob2o$3bo6bo2bo3bo4b2ob2o9b2obo2bo$3b
2o8bo3bo4bo2b2o10bob2o$14bobo6b3o11bo$15bo12bo7b2o$25b4o$9b2o4bo9bo$9b
2o3bobo9bo$14bobo8b2o$9b2o4bo$9bobo3$7b3o$3b2o7b3o6b2o$3bo5bo5bo6bo$2o
bo5b2o2bobo6bob2o$o2bob2o3bo3bo4b2obo2bo$2b2obo11bo2bob2o$5bo11b3o$5b
2o7bo$14b4o$17bo$16bo$16b2o!

Implies omnifrequent p21:

Code: Select all

x = 37, y = 30, rule = B3/S23
7b2o$8bo2bo$5b3o3b3o$4bo3b3o3bo$4b2obo3b3o$8b2obo7b2o$3bob2obobo8bo3b
2o$3b2ob2o13bo2bo$20b2obo$20bo2b4o8bo$10bobo7b3o3bo6b3o$9bobob2o5bo2b
4o5bo$9bobo8b2obo2bo4bobo$4b2o4bo5bo4bob2o2bo2b4o$3bobo10bo4bobobo2bo
5b2o$3bo18b2ob4obob2o2bo$2b2o20bo4b2obo2bo$o2bobob2o15bob2o5b2o$2o2b2o
bo15b2obo$7bobo16bo$7b2obo15b2o$10bo$10b2o5$25b3o$25bo$26bo!

[WhiteHawk]

Some near-misses

Almost p21, missing F13 (though F15 is in the p7 pipsquirter). The p21 glider gun has F13, but I haven't been able to find any good sparks to delete gliders with

Code: Select all

Implies omnifrequent p21:

Code: Select all

Explicit Omnifrequent p21 - 287 cells

Code: Select all

x = 45, y = 48, rule = B3/S23
21b2o$2b2o5b2o9bobo$2b2o5b2o10bo2$3bo5bo$3b2o3b2o8bo$3bobobobo9b2o13b
2o$5bobo8b2o10b2o4b2o$5bobo10bo5b2ob2obo$2obobobobob2o4bo5b4obob3o$bo
3bobo3bo4b4o$3b2o3b2o6b4o7b3obob4o$18bo10bob2ob2o$17bo6b2o4b2o$18b2o4b
2o$7b2o6b2o$8bo8bo$8bobo$9b2o$14bo3bo$13bo5b2o$12b2o4b2o$13b2o$10bo2b
o2bo$6b2obobobob2o7bo$6bob2obobo11bo7b2o$12b2o9b3o8bo$17b2o15bob2o$18b
o16bobo$18bob2o15bob2o2b2o$10b2o5b2obo15b2obobo2bo$9bo2bob2o4bo8bo11b
2o$8bo2b2obob4ob2o18bo$9b2o3bobo4bobo15bobo$11b2obob2o2b2obo8b3o4b2o$
11bo2bob2obobob2o7b2obo$12bo2b3o2b2o4bo4bo3bo$9b3o5bo4b3obo4bob2o$9bo
8b4o4bo5b3o$21bob2o$20bo2bo13b2ob2o$20b2o3bo8bobob2obo$24b2o7bob2o$31b
3o3bob2o$30bo3b3o3bo$31b3o3b3o$33bo2bo$36b2o!

EDIT - Omnifrequent p25 - 86 cells

Code: Select all

x = 31, y = 26, rule = B3/S23
9b2o$6b2o2bo$4b3ob2o$3bo$4b3ob2o$6bobo8b2o$17b2o4$11b2o10b2o$bo4bo3b2o
bo5b4obo$obo3bob3obo6b3obo$bo3bob4o10b2o4b2o$5b4o18b2o$4bo$4b2o13b2o$
20bo$11bo5b3o$11bo5bo8b2o$11bo12bo4bo$24bo4bo$24bo4bo$25bo2bo$23bobo2b
obo$23b2o4b2o!

Periods are now 1-18, 20-21, 25, 30, 37, & theoretical 61+

[KtT]

173-cell omnifrequent p23:

Code: Select all

x = 42, y = 26, rule = B3/S23
17b2o14b2o$12bo4bobob2o10bo$4b2o6b3o4bobo2bo10bo$3bobo2b2o5bo3b2o2b2o
6b5o$2bo2bobobo4b2o15bo$2b2obobo26b2o$5bob2o25bobo$2b2obo26bo3bo$o2bo
bo10bo2bo11b2o3bob2obo$2o2bo4b2o5b2o7b2o3b2o4bobob2o$8bo2bo12bo2bob2o
2bo4bo$2o2bo4b2o6b2o6b2o3b2obo3b2o$o2bobo9bo2bo12b3o$2b2obo26bo$5bob2o
$2b2obobo18b2o$2bo2bobobo9b2o5b2o$3bobo2b2o4b2o3bo$4b2o4b2obobo4b3o$10b
ob2obobo4bo11bo2bo$16b2o16b4o$31bo$31b5o$35bo$33bo$33b2o!

[WhiteHawk]

How many p41 frequencies could a beehive vex provide (capped with 204p41s)? That could be a way to omnifrequent p41

EDIT: Omnifrequent p22, likely not minimal at 276 cells. (also not super-satisfying but self-supporting)

Code: Select all

x = 81, y = 48, rule = B3/S23
54b2o$55bo7bo$55bobo14b2o$56b2o12b2o2bo$60b3o7b2ob2o$60b2ob2o7b3o$29b
2o29bo2b2o12b2o$25b2o2bo2b2o27b2o14bobo$24bo2bobo3bo37bo7bo$23bo2bobo
b3o46b2o$23bob2obobo$22b2o4bobo5b2o23bo$24b3o2bo7bo21bobo$24bo2b2o2b3o
3bobo13b3o4b2o$25bo5bo6b2o3bo8bo3bo$22b3o7bo9bob2o6bo4bo$22bo18bo4bo6b
2obo$42bo3bo8bo3b2o12b2o$37b2o4b3o13bobo8b2o2bo$37bobo21bo6bo2b3o$37b
o23b2o4bobo$65b3ob2ob2o$18b2o44bo4bo3bo$19bo7bo37b3obo3bobo$19bobo14b
2o30bo5b2o$20b2o12b2o2bo28bo$24b3o7b2ob2o28b2o$24b2ob2o7b3o$24bo2b2o12b
2o$25b2o14bobo$35bo7bo$43b2o2$2o23bo$bo21bobo$bobo13b3o4b2o9b2o$2b2o3b
o8bo3bo14bobo$6bob2o6bo4bo15bo$5bo4bo6b2obo9bo5b2ob2o$6bo3bo8bo3b2o6b
o5bo2bo$7b3o13bobo3b3o2b3o2bo$25bo7bo3b2o$25b2o6b4o$36bo$33b2obobo$34b
o2b2o$32bobo$32b2o!

EDIT 2: Reduced to exactly 195 cells!

Code: Select all

x = 63, y = 32, rule = B3/S23
36b2o$37bo$37bobo13b3o$38b2o3bo8bo3bo$42bob2o6bo4bo$41bo4bo6b2obo$11b
2o29bo3bo8bo3b2o$7b2o2bo2b2o27b3o13bobo$6bo2bobo3bo45bo$5bo2bobob3o46b
2o$5bob2obobo$4b2o4bobo5b2o22bo$6b3o2b4o4bo16bo6b2o$6bo2b2ob3o4bobo13b
3o4b2o$7bo5bobo4b2o3b2o7bob3o$4b3o17b4o6bo2b3o$4bo18b3o2bo6b4o$24b3ob
o7b2o3b2o12b2o$19b2o4b3o13bobo8b2o2bo$18b2o6bo16bo6b2ob3o$20bo22b2o4b
obo$47b3ob5o$2o44bo3bo4bo$bo44b2o2bobo$bobo13b3o31b2o$2b2o3bo8bo3bo$6b
ob2o6bo4bo$5bo4bo6b2obo$6bo3bo8bo3b2o$7b3o13bobo$25bo$25b2o!

EDIT 4: Omnifrequent P24 achieved, but probably could be smaller (184 cells)

Code: Select all

x = 38, y = 43, rule = B3/S23
8b2o$8b2obo$12bo17b2o$9bo12bo2bo4bo2b2o$10bob2o12bo4bobobo$12b2o16b2o
3bo$27bo2bo2bobobo$26bo4b2obob2o$17bobo2bo9bobo$9bo7bo6b2o5bo2bo$8bob
o10bo4b2o4b2ob2o$8bobo5bo10bo5bobo$7b2ob2o4b2o4bo10bobo$9bo2bo5b2o6bo
7bo$9bobo9bo2bobo$6b2obob2o4bo$6bobobo2bo2bo$8bo3b2o16b2o$8bobobo4bo12b
2obo$9b2o2bo4bo2bo12bo$12b2o17bo$22b2o8bob2o$23b2o9b2o$9b3o10bo$7bob3o
$6bobobo$6bo2bo$7b2o7b2o$17b2o$16b2o$15b3o$14b2o$2bo2bobo7bo$2obob3o10b
2o$bo6bo8bo2bo$2o5bo9bo$17bo$bo5b2o8bob2o$o6bo11b2o$b3obob2o$bobo2bo$
18b2o$18b2o!

EDIT 5: Omnifrequent p27 (330 cells)

Code: Select all

x = 44, y = 54, rule = B3/S23
18bo3b3o3bo10bo$17bobo7bobo8bobo$18bo3bobo3bobo6bo2bo$29bo$9b2o11b4o12b
obo$10bo6bobobo4bo13b2o$2b2o5bo7bo3bob2obobobo9b2o$2bobo3bob3o4bobobo
b2obo3bo5b2ob2o$4bo3bo4bo7bo4bobobo5bo$4b2ob2ob3o9b4o8bobobo$8bobo7bo
15b2ob2o$4b3obobo6bobo3bobo3bo7bo2bo$3bo2bob2o8bobo7bobo6b2ob3o$3b2o14b
o3b3o3bo5bobo$32bo2bo$31bob2obo4bo$5b2o24b2o6b3o$6bo24b2o2bo2bo$6bobo
11bo11bo2bo2b4o$7b2o3b2o7bo10bo2bo2bo2bo$11bo2bo5bo4b3o9bob2o$12bobo10b
obo8b2o$12b3o4bo5bo2bo6bo$18bo7b2o3b2o3b4obo$19bo11bobo6b2o$33bo2b3o$
8b2o23bobobo$7bobo24bo4bo$7bo30b2o$6b2o6bo$13bob2o$13bob2o26bo$10bo3b
2o25b3o$9bobo7b2o19bo$9bobo6bo2bo15b2o2bo$10bo8b2o15bo2b3o$35bobo4b2o
$2o4b2o14b2o11bobob2obo$2o4b3o12bo2bo8b3obobo2bo$5bo2bo12b3o4b2o2bo3b
obo2bo$6b2o14b2o4b2o2b2o2bo2b2o$35b2o$9b2o8bo$8bo2bo6bobo$9b2o7bobo$14b
2o3bo$13b2obo$13b2obo$15bo4$13b2o$13b2o!

EDIT 6: Omnifrequent p30 reduced, though now with a Pentadecathlon (203 cells)

Code: Select all

x = 53, y = 47, rule = B3/S23
3b2o$3b2o7$42b2o$37b2o2bobo$37bo3bo4bo$2o3b2o31b3ob5o$40bobo$bo3bo34b
obob3o$2b3o11bo24b2obo2bo$2b3o10bobo28b2o$15b2obo7b2o9b2o$15b2ob2o6bo
bo7bobo$15b2obob3o6bo8bo5bo$15bobo2bo2bo2bo2bo13bobo$16bo4b2o6bo13b2o
bo$26bobo14b2ob2o3b2o$26b2o15b2obo4b2o$43bobo$13bobo28bo$13b2o11b2o$14b
o8b2o2bo2b2o$23bo3bobo2bo$20bo3b3obobo2bo$18b3o5bobob2obo$17bo8bobo4b
2o$2bo14b2o8bo2b3o$b3o6bo17b2o2bo$obobo4b2o2bo8bo8bo$obobo5b2o10b2o8b
3o$b3o3b5obo7bobo10bo$2bo4bo2b2o2bo$8b7o$8b2o5bo$2bo5b2o2b3o$b3o8b4o$
obobo9b2o$obobo10bo$b3o$2bo$14b2o$14b2o!

[Anivec]

How many p41 frequencies could a beehive vex provide (capped with 204p41s)? That could be a way to omnifrequent p41

EDIT: Omnifrequent p22, likely not minimal at 276 cells. (also not super-satisfying but self-supporting)

Code: Select all

x = 81, y = 48, rule = B3/S23
54b2o$55bo7bo$55bobo14b2o$56b2o12b2o2bo$60b3o7b2ob2o$60b2ob2o7b3o$29b
2o29bo2b2o12b2o$25b2o2bo2b2o27b2o14bobo$24bo2bobo3bo37bo7bo$23bo2bobo
b3o46b2o$23bob2obobo$22b2o4bobo5b2o23bo$24b3o2bo7bo21bobo$24bo2b2o2b3o
3bobo13b3o4b2o$25bo5bo6b2o3bo8bo3bo$22b3o7bo9bob2o6bo4bo$22bo18bo4bo6b
2obo$42bo3bo8bo3b2o12b2o$37b2o4b3o13bobo8b2o2bo$37bobo21bo6bo2b3o$37b
o23b2o4bobo$65b3ob2ob2o$18b2o44bo4bo3bo$19bo7bo37b3obo3bobo$19bobo14b
2o30bo5b2o$20b2o12b2o2bo28bo$24b3o7b2ob2o28b2o$24b2ob2o7b3o$24bo2b2o12b
2o$25b2o14bobo$35bo7bo$43b2o2$2o23bo$bo21bobo$bobo13b3o4b2o9b2o$2b2o3b
o8bo3bo14bobo$6bob2o6bo4bo15bo$5bo4bo6b2obo9bo5b2ob2o$6bo3bo8bo3b2o6b
o5bo2bo$7b3o13bobo3b3o2b3o2bo$25bo7bo3b2o$25b2o6b4o$36bo$33b2obobo$34b
o2b2o$32bobo$32b2o!

EDIT 2: Reduced to exactly 200 cells!

Code: Select all

x = 63, y = 32, rule = B3/S23
36b2o$37bo$37bobo13b3o$38b2o3bo8bo3bo$42bob2o6bo4bo$41bo4bo6b2obo$11b
2o29bo3bo8bo3b2o$7b2o2bo2b2o27b3o13bobo$6bo2bobo3bo45bo$5bo2bobob3o46b
2o$5bob2obobo$4b2o4bobo5b2o22bo$6b3o2b4o4bo16bo6b2o$6bo2b2ob3o4bobo13b
3o4b2o$7bo5bobo4b2o3b2o7bob3o$4b3o17b4o6bo2b3o$4bo18b3o2bo6b4o$24b3ob
o7b2o3b2o12b2o$19b2o4b3o13bobo8b2o2bo$18b2o6bo16bo6b2ob3o$20bo22b2o4b
obo$47b3ob2ob2o$2o44bo4bo3bo$bo45b3obo3bobo$bobo13b3o30bo5b2o$2b2o3bo
8bo3bo28bo$6bob2o6bo4bo27b2o$5bo4bo6b2obo$6bo3bo8bo3b2o$7b3o13bobo$25b
o$25b2o!

EDIT 3: Almost p24, missing F14

Code: Select all

x = 33, y = 32, rule = B3/S23
7b2o$8bo$2o5bo$obo3bob3o$2bo3bo4bo$2b2ob2ob3o$6bobo$2b3obobo8bo2b2o$b
o2bob2o8bo3b2o2b2o$b2o13bo7b2o$17b4o2$12b2o$12bo2bo$4b2o7b3o$3bo2bo7b
o9b3o$3bobobo16b3obo$4bob3o16bobobo$6b3o9bo7bo2bo$17b3o7b2o$17bo2bo$19b
2o11bo$30b3o$12b4o13bo$7b2o7bo9b2o2bo$7b2o2b2o3bo8bo2b3o$11b2o2bo8bob
o4b2o$24bobob2obo$22b3obobo2bo$21bo3bobo2bo$21b2o2bo2b2o$24b2o!

EDIT 4: Omnifrequent P24 achieved, but probably could be smaller (184 cells)

Code: Select all

x = 38, y = 43, rule = B3/S23
8b2o$8b2obo$12bo17b2o$9bo12bo2bo4bo2b2o$10bob2o12bo4bobobo$12b2o16b2o
3bo$27bo2bo2bobobo$26bo4b2obob2o$17bobo2bo9bobo$9bo7bo6b2o5bo2bo$8bob
o10bo4b2o4b2ob2o$8bobo5bo10bo5bobo$7b2ob2o4b2o4bo10bobo$9bo2bo5b2o6bo
7bo$9bobo9bo2bobo$6b2obob2o4bo$6bobobo2bo2bo$8bo3b2o16b2o$8bobobo4bo12b
2obo$9b2o2bo4bo2bo12bo$12b2o17bo$22b2o8bob2o$23b2o9b2o$9b3o10bo$7bob3o
$6bobobo$6bo2bo$7b2o7b2o$17b2o$16b2o$15b3o$14b2o$2bo2bobo7bo$2obob3o10b
2o$bo6bo8bo2bo$2o5bo9bo$17bo$bo5b2o8bob2o$o6bo11b2o$b3obob2o$bobo2bo$
18b2o$18b2o!

EDIT 5: Omnifrequent p27 (330 cells)

Code: Select all

x = 44, y = 54, rule = B3/S23
18bo3b3o3bo10bo$17bobo7bobo8bobo$18bo3bobo3bobo6bo2bo$29bo$9b2o11b4o12b
obo$10bo6bobobo4bo13b2o$2b2o5bo7bo3bob2obobobo9b2o$2bobo3bob3o4bobobo
b2obo3bo5b2ob2o$4bo3bo4bo7bo4bobobo5bo$4b2ob2ob3o9b4o8bobobo$8bobo7bo
15b2ob2o$4b3obobo6bobo3bobo3bo7bo2bo$3bo2bob2o8bobo7bobo6b2ob3o$3b2o14b
o3b3o3bo5bobo$32bo2bo$31bob2obo4bo$5b2o24b2o6b3o$6bo24b2o2bo2bo$6bobo
11bo11bo2bo2b4o$7b2o3b2o7bo10bo2bo2bo2bo$11bo2bo5bo4b3o9bob2o$12bobo10b
obo8b2o$12b3o4bo5bo2bo6bo$18bo7b2o3b2o3b4obo$19bo11bobo6b2o$33bo2b3o$
8b2o23bobobo$7bobo24bo4bo$7bo30b2o$6b2o6bo$13bob2o$13bob2o26bo$10bo3b
2o25b3o$9bobo7b2o19bo$9bobo6bo2bo15b2o2bo$10bo8b2o15bo2b3o$35bobo4b2o
$2o4b2o14b2o11bobob2obo$2o4b3o12bo2bo8b3obobo2bo$5bo2bo12b3o4b2o2bo3b
obo2bo$6b2o14b2o4b2o2b2o2bo2b2o$35b2o$9b2o8bo$8bo2bo6bobo$9b2o7bobo$14b
2o3bo$13b2obo$13b2obo$15bo4$13b2o$13b2o!

EDIT 6: Omnifrequent p30 reduced, though now with a Pentadecathlon (208 cells)

Code: Select all

x = 53, y = 47, rule = B3/S23
3b2o$3b2o5$40b2o$40bo$41bo5b2o$38b3obo3bobo$37bo4bo3bo$2o3b2o31b3ob2o
b2o$40bobo$bo3bo34bobob3o$2b3o11bo24b2obo2bo$2b3o10bobo28b2o$15b2obo7b
2o9b2o$15b2ob2o6bobo7bobo$15b2obob3o6bo8bo5bo$15bobo2bo2bo2bo2bo13bob
o$16bo4b2o6bo13b2obo$26bobo14b2ob2o3b2o$26b2o15b2obo4b2o$43bobo$13bob
o28bo$13b2o11b2o$14bo8b2o2bo2b2o$23bo3bobo2bo$20bo3b3obobo2bo$18b3o5b
obob2obo$17bo8bobo4b2o$2bo14b2o8bo2b3o$b3o6bo17b2o2bo$obobo4b2o2bo8bo
8bo$obobo5b2o10b2o8b3o$b3o3b5obo7bobo10bo$2bo4bo2b2o2bo$8b7o$8b2o5bo$
2bo5b2o2b3o$b3o8b4o$obobo9b2o$obobo10bo$b3o$2bo$14b2o$14b2o!

Replacing the catalyst on the left with the one on the right yields a reduction of five less cells to five out of the six oscillators:

Code: Select all

x = 34, y = 10, rule = B3/S23
7b2o$8bo$2o5bo19b2o$obo3bob3o16bobo2b2o$2bo3bo4bo12bo4bo3bo$2b2ob2ob3o
13b5ob3o$6bobo19bobo$2b3obobo15b3obobo$bo2bob2o15bo2bob2o$b2o20b2o!

[WhiteHawk]

A much smaller p18 (97 cells) and a smaller p9 (42 cells)

Code: Select all

x = 24, y = 22, rule = B3/S23
3bo7bo$3b3o4b2o$6bo3b2o$5b2o3bo$2o13b2o$bo13bo$bobo4bo4bobo$2b2o4bo4b
2o$8bo2$8b2o5b2o4b2o$9bo3bo2bo3bobo$20bo$3bob2o5bo5b3o$b3ob2o5bo2bobo
3b2o$o18b2o2bo$b3ob2o6b5o3b2o$3bobo5bo5bob2o$3bobo5b5obo2bo$4bo10bobo
bo$13bo4bo$13b2o!

Code: Select all

x = 13, y = 12, rule = B3/S23
4b2o4b2o$2bo2bo3bobo$9bo$bo5b3o$bo2bobo3b2o$8b2o2bo$2b5o3b2o$o5bob2o$
5obo2bo$4bobobo$2bo4bo$2b2o!

EDIT: Almost p28 solution, missing F18

Code: Select all

x = 46, y = 58, rule = B3/S23
37b2o$34b2o2bo2b2o$34bo3bobo2bo$35b3obobo2bo$37bobob2obo$37bobo4b2o$38b
o2b3o$39b2o2bo$42bo$22bo9bo10b3o$22b3o7b2o6bo4bo$15b2o8bo5bobo4b3o$14b
obo7b2o11bo$14bob3o18b2o$13b2obo2b2o$15bobob2o13b2o$15bobobo7b3o5bobo
$16b2o2bo5bo3bo4bo2bo$18bo6bo9bo2bo$14b4o2bo3bo3bo3bo2bo$14bo2b5o5bob
o5b5o2bo$21bo2bo3bo3bo3bo2b4o$18bo2bo9bo6bo$18bo2bo4bo3bo5bo2b2o$19bo
bo5b3o7bobobo$21b2o13b2obobo$36b2o2bob2o$18b2o18b3obo$19bo11b2o7bobo$
16b3o4bobo5bo8b2o$16bo6b2o7b3o$24bo9bo$12bo$12b3o$15bo$2b2o5b2o3b2o10b
2o$2b2o5b2o15bo$24bobo$24b2o2$3bo5bo8bo10b2o5b2o$2b2o5b2o6b3o9b2o5b2o
$b2obo3bob2o5bo11b2o5b2o$2o2bo3bo2b2o16bo7bo$2ob2o3b2ob2o14b2ob2o3b2o
b2o$2ob2o3b2ob2o14b2ob2o3b2ob2o$2bo7bo16b2o2bo3bo2b2o$2b2o5b2o11bo5b2o
bo3bob2o$2b2o5b2o9b3o6b2o5b2o$2b2o5b2o10bo8bo5bo2$14b2o$13bobo$13bo15b
2o5b2o$12b2o10b2o3b2o5b2o$24bo$25b3o$27bo!

[KtT]

EDIT: Almost p28 solution, missing F18

Code: Select all

x = 46, y = 58, rule = B3/S23
37b2o$34b2o2bo2b2o$34bo3bobo2bo$35b3obobo2bo$37bobob2obo$37bobo4b2o$38b
o2b3o$39b2o2bo$42bo$22bo9bo10b3o$22b3o7b2o6bo4bo$15b2o8bo5bobo4b3o$14b
obo7b2o11bo$14bob3o18b2o$13b2obo2b2o$15bobob2o13b2o$15bobobo7b3o5bobo
$16b2o2bo5bo3bo4bo2bo$18bo6bo9bo2bo$14b4o2bo3bo3bo3bo2bo$14bo2b5o5bob
o5b5o2bo$21bo2bo3bo3bo3bo2b4o$18bo2bo9bo6bo$18bo2bo4bo3bo5bo2b2o$19bo
bo5b3o7bobobo$21b2o13b2obobo$36b2o2bob2o$18b2o18b3obo$19bo11b2o7bobo$
16b3o4bobo5bo8b2o$16bo6b2o7b3o$24bo9bo$12bo$12b3o$15bo$2b2o5b2o3b2o10b
2o$2b2o5b2o15bo$24bobo$24b2o2$3bo5bo8bo10b2o5b2o$2b2o5b2o6b3o9b2o5b2o
$b2obo3bob2o5bo11b2o5b2o$2o2bo3bo2b2o16bo7bo$2ob2o3b2ob2o14b2ob2o3b2o
b2o$2ob2o3b2ob2o14b2ob2o3b2ob2o$2bo7bo16b2o2bo3bo2b2o$2b2o5b2o11bo5b2o
bo3bob2o$2b2o5b2o9b3o6b2o5b2o$2b2o5b2o10bo8bo5bo2$14b2o$13bobo$13bo15b
2o5b2o$12b2o10b2o3b2o5b2o$24bo$25b3o$27bo!

287-cell omnifrequent p28:

Code: Select all

x = 57, y = 69, rule = B3/S23
48b2o$45b2o2bo2b2o$45bo3bobo2bo$46b3obobo2bo$48bobob2obo$48b3obo2b2o$
49b2o2b2o$54bo$53bo$33bo20b3o$33b3o15bo4bo$26b2o8bo12b3o$25bobo7b2o3b
3o5bo$25bo4bo11bo6bo$24b2ob2obo10bo3bo3bo$26bo3bo14bo$26bobobo15bobo$
27b2ob2o15b2o$29b2o16b2o$25b3o3bo5b2o8bo2bo$25bo2bob2o6bobo6b2obo2bo$
28bo2bo8b2o5bo3b3o$30b2o16b2o$30b2o15b2ob2o$30bobo15bobobo$33bo14bo3b
o$29bo3bo3bo10bob2ob2o$29bo6bo11bo4bo$30bo5b3o3b2o7bobo$27b3o12bo8b2o
$27bo15b3o$45bo2$30bo$29bo$11bo17b3o$11b3o$14bo20bo$b2o5b2o3b2o18b3o$
obo5bobo21bo$32b2o2$3b2ob2o21b2o$4bobo22bobo$3b2ob2o13bo8b2o$2b2o3b2o
8b3obo$2obo3bob2o6bo2bo$b2o5b2o$31b2o$17bo2bo10b2o$16bob3o9bo$b2o5b2o
6bo12b3o$b2o5b2o2$13b2o19b3o$12bobo20bo$12bo20b2o$11b2o10b2o8b2o$23bo
$24b3o$26bo$34b2o$34bobo$35b2o2$32b2o$33bo$30b3o$30bo!

[WhiteHawk]

An analysis of eater-supplied frequencies and usefulness for omnifrequency (judged using GGG). "n" stands for the max frequency (equivalent to any undying cell/the stator), and "f=" stands for any specific frequency which will always be provided no matter the period/value of n

Less useful eaters

Eater 1 - for standard single-glider eating purposes, eater 1 provides n-1 (and f=1) frequencies. This limits it's usefulness for providing new frequencies in instances of simple interactions. However, it does provide an n-2 frequency cell in the presence of a domino spark (helpful tip - if an eater doesn't recover in the standard way, it can't be replaced with an eater 2) - both types of interactions are shown in the below omnifrequent p9 (Eater on Snacker).

Code: Select all

x = 20, y = 15, rule = B3/S23
13bo$11b3o$10bo$10b2o$2o16b2o$bo16bo$bobo12bobo$2b2o12b2o$7bo4bo$5b2o
b4ob2o$7bo4bo$2b2o12b2o$bobo12bobo$bo16bo$2o16b2o!

Eater 2 - Symmetric Eater 2 (& Bounding Box variations) is a little more useful, providing n-1 and n-2 frequencies along all four eating lanes. However, gliders eaten along the middle two lanes provide n-3 frequencies, and it can also be used for extra periods in most instances where an eater 1 works. Still, compared to other eaters, it's frequency-providing capabilities are limited.

Code: Select all

x = 84, y = 44, rule = LifeHistory
54.D.2D10.D$54.2D2.D8.2D$54.D3.D2.3D4.D$54.D3.D9.D$54.D3.D9.D$54.D3.D
8.3D3$11.D.2D10.D28.D.2D9.2D$11.2D2.D8.2D28.2D2.D7.D2.D$11.D3.D2.3D4.
D28.D3.D2.3D5.D$11.D3.D9.D28.D3.D9.D$11.D3.D9.D28.D3.D8.D$11.D3.D8.3D
27.D3.D7.4D3$11.D.2D9.2D41.2D$11.2D2.D7.D2.D27.D.2D8.D2.D$11.D3.D2.3D
5.D27.2D2.D10.D$11.D3.D9.D28.D3.D2.3D3.2D$11.D3.D8.D29.D3.D10.D$11.D3.
D7.4D27.D3.D7.D2.D$54.D3.D8.2D3$24.A47.A$22.A.A45.A.A$12.2A6.2A12.2A24.
2A6.2A12.2A$11.A3.A4.2A12.2A23.A3.A4.2A12.2A$2A8.A5.A3.2A26.2A8.A5.A3.
2A$2A8.A3.A.2A4.A.A23.2A8.A3.A.2A4.A.A$10.A5.A7.A33.A5.A7.A$11.A3.A43.
A3.A$12.2A46.2A4$27.2A.A43.2A.A$27.2A.3A41.2A.3A$33.A46.A$27.2A.3A41.
2A.3A$28.A.A44.A.A$28.A.A44.A.A$29.A46.A!

Code: Select all

x = 23, y = 14, rule = B3/S23
18bo$17bobo$17bobo$2o14b2ob3o$bo20bo$bobo12b2ob3o$2b2o12b2obo$7bo4bo$
5b2ob4ob2o$7bo4bo$2b2o12b2o$bobo12bobo$bo16bo$2o16b2o!

Eater 3 - like the most optimal eater 2, it provides n-1, n-2, and n-3 (plus f=2 and f=1) frequencies, but also provides f=3 through f=5, and n-6. Still, there exist much better eaters, including it's drifty variant below.

Code: Select all

x = 38, y = 24, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o4$27b2o$26bo2bo2b2o$26bobo4bo2bo$27bo5bob
obo$30b2obo2bo$30bo2bo$27bo4bo$27b5o2$29bo$28bobo$29bo!

More useful eaters

Drifty eater 3 (15 tick recovery time) - Frequencies provided by this eater are (skip), n-2, n-3, (skip), n-5, n-6, n-7, and n-8 (plus f=5 and below)

Code: Select all

x = 36, y = 19, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o3$31b2o$26b2obo2bo$25bobob3o$25bobo$23b3o
b5o$22bo3bo4bo$22b2o2bobo$27b2o!

Unnamed 13-tick eater (Apgcode xs38_0o4iq4o7p8a6zhhma24521z1) - this eater (which can also sub for eater 3) has the unusual property of providing all frequencies between f=1 and f=7. At the other end of the frequency list, it provides n-1, (skip), n-3, n-4, n-5, n-6, and n-9 (combined with drifty eater 3, all frequencies from f=n to f=n-9 are covered, as well as f=1 to f=7).

Code: Select all

x = 36, y = 19, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o20bo$32b3o$31bo$28b2o2bo$27bo2b3o$26bobo4b
2o$26bobob2obo$24b3obobo2bo$23bo3bobo2bo$23b2o2bo2b2o$26b2o!

Unnamed 14-tick eater (Apgcode xs34_39e0o4cz0355lq2kozx643) - this eater is not as good as the other two, but could have use if more frequencies are covered. It only provides n-1, n-2, (skip), n-4, n-5, n-6, f=7, and f=5 and lower, but has lower population than the 13-tick eater if such thing matters.

Code: Select all

x = 36, y = 20, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o3$29b2o$24b2obo2bo$23bobob3o$18b2o3bobo$18b
o2bobob3o$19b4obo3bo$24bo2b2o$21bobo$21b2o!

(EDIT 4:) Sparky drifty eater 3 (xs37_0g89fgkczg5d1fg4cz19l91) - this variant of the drifty eater 3 provides a duoplet spark and an unusual frequency cell distribution of (skip), n-2, n-3, (skip), n-5, n-6, n-12, and n-14, plus f=7, and f=5 and lower.

Code: Select all

x = 40, y = 22, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o$24bo$25bo$23b3o3$34b2o$29b2obo2bo2bo$28b
obob2obobobo$25bo2bobo4bo2bo$25b4ob4obo$29bo4bo$27bobo2bo$27b2o3b2o!

Loaf Catalyst Eater (constellation) - a very interesting eater, provides n-1, n-3, n-7, n-13, n-15, n-17, f=15, f=14, f=9, and f=7 and lower

Code: Select all

x = 36, y = 23, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o6$25bo$24bobo$23bo2bo3b2o$24b2o4b2o$20bo$
19bobo$19b2o$25b2o$25b2o!

EDIT 2:
Two Pond & Two Block (2p2b)

2p2b provides a fairly unique n-1, n-4, n-5, n-6, n-8, n-9, n-11, n-12, n-15 and n-17, plus n=7 and lower. Potentially useful if there are sparks

Code: Select all

x = 25, y = 42, rule = B3/S23
20b2o$20b2o6$20b3o2$20bobo$19b5o$18b2o3b2o$18b2o3b2o2$8b2o$8b2o11bo$19b
2o2$8b2o4b2o2bo$7bo2bo2bo2bo$2b2o3bo2bo2bo2bo2bo2bo$2bo2bo2b2o4b2o5b2o
2$6bo$14b2o$4b2o8b2o$3bo3$2o3b2o$2o3b2o$b5o$2bobo2$2b3o6$3b2o$3b2o!

EDIT 3:
Overkill eaters

50-cell 20-tick eater possesses frequencies n-1, n-2, (skip), n-4, n-5, n-6, and n-11, along with n=6, and n=4 to n=1. Since it is fairly large, it is not of much use (2p2b is more effective)

Code: Select all

x = 37, y = 23, rule = B3/S23
24bo$22bobo$12b2o6b2o12b2o$11bo3bo4b2o12b2o$2o8bo5bo3b2o$2o8bo3bob2o4b
obo$10bo5bo7bo$11bo3bo$12b2o$23bo8b2o$24b2o5bobo$23b2o6bo$29b3o$28bo3b
2o$28b4o2bo$32b3o$28b4o$23b2o3bo3b5o$23bo2bobob2o4bo$24b3obobo2bo$29b
o2b2o$26b3o$26bo!

[WhiteHawk]

Change of topic: This p29 oscillator is missing only f=14, f=15, and f=20

Code: Select all

x = 52, y = 41, rule = B3/S23
10b2o$9bobo$9bo$7b2ob4o$6bo3bo2bo$6bob2o15b2o$4b2o2b2o15b2o$3bo12b2o11b
o$3bob2o8bo2bo4b7o$b2o2b2o16bo2bo$o2b2o16bobo5b3o$2obo17b2o6bo2bobo$3b
o26b2ob2o$3b2o5bobo18bo$11bo19bo$11bo4bobo11b2ob2obo$17bo15bob2o$17bo
8bo6bo$25b3o4b2o$10bo13bobobo$9bobo$10bo5b2o16bo8b2o$16b2o14b3o5bo2bo
bob2o$31bo6b3o4bobo$31b2o4bo6b2obo$37b2o5bo2b2o$23b2o4bo15b2o2bo$23b2o
5bo15bobo$28bobo4bo10bob2o$27bobo4b3o8b2obo2bo$27b2o12bo6bob2o$40b3o5b
o$32bo14b2o$32bo4$34bo$33bobo$34bo5b2o$40b2o!

Related attempt at p26, missing f=21, f=19, f=18, f=17, f=12, and f=11

Code: Select all

x = 39, y = 39, rule = B3/S23
25b2o$17bo3bo3b2o$11b2o4bo3bo$11bo5bo3bo$8b2obo15bo$7bobob2o13bobo$7b
obo5b3o3b3o3bo$5b2o2bo5bobo3bobo$4bo4b2o4b3o3b3o$4b5o$8bo24bo$2b4o26b
obo$2bo2bo27bo3b2o$37b2o$16b2o3b2o$bo4b3o8bo3bo8b3o$obo3bobo5bo9bo5bo
bo$obo3b3o5b2o7b2o5b3o2b3o$bo2$bo$obo3b3o5b2o7b2o5b3o2b3o$obo3bobo5bo
9bo5bobo$bo4b3o8bo3bo8b3o$16b2o3b2o$37b2o$2bo2bo27bo3b2o$2b4o26bobo$8b
o24bo$4b5o$4bo4b2o4b3o3b3o$5b2o2bo5bobo3bobo$7bobo5b3o3b3o3bo$7bobob2o
13bobo$8b2obo15bo$11bo5bo3bo$11b2o4bo3bo$17bo3bo3b2o$25b2o!

EDIT: One frequency off p34 (missing F21)

Code: Select all

x = 85, y = 142, rule = B3/S23
34b2o$29b2o2bobo$29bo3bo4bo$30b3ob5o$26bo5bo$24b3o5bob5o$23bo9bo2bo2b
o$24bo13b2o$21bob2o32b2o$20b2o31b2o2bo$35b2o12bo3bobobo$35bo11b3o6bo$
33bobo10bo$20bobo4b3o3b2o11b2o11b2o$20b2o4bo3bo20b2o5bo2bo$11b3o7bo3b
o5bo20b2o4b2obo$10bo3bo11bo3bo5bo15bo8b2o$3b2o4bo5bo3bo7b3o5b4o12bobo
4b2o3bo$3bo2bo3bo3bo4b2o13bo2b2o6b2o4b2o4bo2b3o$4b2obo3b3o4bobo14bo3b
o4bobo4bo4bob2o$b3o2bo29b3o4b2o7bo4bo2bo$o3b2o30b3o5b2o13b2o$b2o$2bob
2o13b2o20b2o5b3o$2bo2bo10b2obo22b2o4b3o$3b2o11bo12b2o9bobo4bo3bo$17bo
10bobo9b2o6b2o2bo$7bo6b3o11bo19b4o$6bobobo3bo12b2o6bo14bo$6bo2b2o7b2o
13b2o$5b2o12bo14b2o19b2o$19bobo17b2o14bo$20b2o18bo11b2obo$37b3o7b2o2b
obobob2o$25bo11bo9bo3bobobo2bo$25b2o21b3obobobo$17bo6b2ob2o21bobobob2o
$15b3o8b3o23bobo3bo$5b2o7bo9b2ob2o23bob4obo$6bo7b2o9b2o26bo5bo$6bobo16b
2o23bo5b2ob2o$7b2o12bo28bo6bo$20b2o3b2o28bobo$2b2o20bobo9bo18b2o$3bo16b
6o8bobo$3bobo13bob4o10b2o$4b2o49bo$12bo14b2o24b3o$10b2ob2o12bo13b2o9b
o$10b2ob2o10bobo14b2o8b2o$25b2o14b2o15b2o$38b2ob2o15bobob2o$4b2o34bo10b
o8bob2o$3bobo10b2ob2o29bobo6b2o$3bo12b2ob2o28b3o5bo2bob2o$2b2o14bo30b
obo3bo2bobobo$25b2o9b2o6b2o8bo2b4obo$25bobo3b2o4bo5bobo15bob2o$27bo3b
o2b3o6bo10bob4obo2bo$27b2o3bobo7b2o14bobob2o$31b2o22b2o3bo$22b2o8bo23b
obobo$22bobo7bobo18b3o2b2o$15b2o7bo8b2o18bo2b2o$16bo7b2o29bo2b2o$13b3o
20bo14bo4b2o2bo$13bo15b2o26bob2o$30bo26bo$30bobo3b3o10b3o3bobo$31b2o2b
o3bo8bo3bo2b2o$34bo5bo6bo5bo$34bo5bo6bo5bo$25b2o7bo5bo6bo5bo7b2o$25bo
9bo3bo8bo3bo9bo$22b2obo10b3o10b3o10bob2o$21bobob2o5b2o20b2o5b2obobo$20b
o11b2o20b2o11bo$19bo4b3o10b2o10b2o10b3o4bo$18bo4bo2bo10b2o10b2o10bo2b
o4bo$17bo4bobo7b3o18b3o7bobo4bo$17b2o2bobo7bo3bo16bo3bo7bobo2b2o$20bo
bo7bo5bo14bo5bo7bobo$15b4obo9bo5bo14bo5bo9bob4o$15bo2bob2o8bo5bo14bo5b
o8b2obo2bo$31bo3bo2b2o8b2o2bo3bo$32b3o3bobo6bobo3b3o$9bo30bo6bo30bo$9b
3o12b3o13b2o4b2o13b3o12b3o$3bo8bo10bo3bo32bo3bo10bo8bo$3b3o5b2o5b2o2b
o5bo30bo5bo2b2o5b2o5b3o$6bo11b2o2bo5bo30bo5bo2b2o11bo$5b2o6b3o6bo5bo30b
o5bo6b3o6b2o$12bo3bo6bo3bo32bo3bo6bo3bo$8bo2bo5bo6b3o34b3o6bo5bo2bo$11b
o5bo2b2o44b2o2bo5bo$11bo5bo2b2o5b2o30b2o5b2o2bo5bo$12bo3bo10bo32bo10b
o3bo$13b3o12b3o26b3o12b3o$30bo26bo5$30bo26bo$13b3o12b3o26b3o12b3o$12b
o3bo10bo32bo10bo3bo$11bo5bo2b2o5b2o30b2o5b2o2bo5bo$11bo5bo2b2o44b2o2b
o5bo$8bo2bo5bo6b3o34b3o6bo5bo2bo$12bo3bo6bo3bo32bo3bo6bo3bo$5b2o6b3o6b
o5bo30bo5bo6b3o6b2o$6bo11b2o2bo5bo30bo5bo2b2o11bo$3b3o5b2o5b2o2bo5bo30b
o5bo2b2o5b2o5b3o$3bo8bo10bo3bo32bo3bo10bo8bo$9b3o12b3o13b2o4b2o13b3o12b
3o$9bo30bo6bo30bo$32b3o3bobo6bobo3b3o$31bo3bo2b2o8b2o2bo3bo$15bo2bob2o
8bo5bo14bo5bo8b2obo2bo$15b4obo9bo5bo14bo5bo9bob4o$20bobo7bo5bo14bo5bo
7bobo$17b2o2bobo7bo3bo16bo3bo7bobo2b2o$17bo4bobo7b3o18b3o7bobo4bo$18b
o4bo2bo10b2o10b2o10bo2bo4bo$19bo4b3o10b2o10b2o10b3o4bo$20bo11b2o20b2o
11bo$21bobob2o5b2o20b2o5b2obobo$22b2obo10b3o10b3o10bob2o$25bo9bo3bo8b
o3bo9bo$25b2o7bo5bo6bo5bo7b2o$34bo5bo6bo5bo$34bo5bo6bo5bo$31b2o2bo3bo
8bo3bo2b2o$30bobo3b3o10b3o3bobo$30bo26bo$29b2o26b2o$36bo14bo2$33b2o18b
2o$32bobo18bobo$32bo22bo$31b2o22b2o!

EDIT 2 (8/26): New smallest p16, at 41 cells

Code: Select all

x = 24, y = 18, rule = B3/S23
22b2o$b2o17bob2o$2bo16bo$2bobo17bo$3b2o7bo5b2obo$11bo6b2o$6bo4bo2bo$5b
obo4b2o$8bo$5bobo$6bo3$b3o$3o2$6bo$6b2o!

[WhiteHawk]

Omnifrequent p34 achieved - at 1556 cell definitely reducible

Code: Select all

x = 97, y = 202, rule = B3/S23
17bo$16bobo$14b3obo$13bo4bob2o$13bobobobobo$8bo5b2obobo$8b3o7bobo61bo
$11bo7bo61bobo$10bo70bob3o$9bo11bo56b2obo4bo$9b2o9bobo55bobobobobo$19b
o3bo56bobob2o5bo$19bo3bo55bobo7b3o$19bo3bo56bo7bo$10b2o8bobo66bo$11bo
9bo62b3o3bo$11bob2o67b3obo2b2o$12bobo66bo4bo$19bo56b2o5bo$14b2o4b2o50b
2obo2bo$15bo3b2o3b2o3bo41bo3bo2bo9b2o$23b2o4b2o47bo9bo$25bo46b2o3bo8b
obo$30bobo47b2o4b2o$6b2o22b2obo44b3obo$2b2obobo15bo9bo40bo3b2ob2o$3bo
bo16bobo8b2o38b2o5b2o$3bob2o3bo10bo3bo46b2ob2o3bo$2obo6b3o8bo3bo46bob
3o$o2b4o6bo7bo3bo41b2o4b2o$b2o3bo5b2o8bobo41bobo8bo3b2o$3b3o17bo42bo9b
o$3bo30bo30b2o9bo2bo3bo$bobo5bo15b2o5bobo41bo2bob2o6bo$b2o5b2o10bo4bo
7b2o42b2o8b3o$8bobo8bobo4b3o39bo17bo8b2o$17b2o2b2o5bo39bobo15b2o7bo$4b
2o11b2ob2o46b2o13bo9bobo$5bo11b2ob2o60bo10b2o$5bobo11bo53b2o6bo$6b2o4b
2o28bo31bo5b2o2bo2b2o$12bo2bo27bo27b3o5b3obobob3o$13b3o25b3o27bo8b2o2b
o2b2o$14bo3bo41bo20bo5bo6b2o$17b3o39bo22b5o7bo$17bo2bo38b3o21b3o6bobo
$19b2o4b2o57bo7b2o$13bo11bobo$11b2ob2o11bo$11b2ob2o11b2o22bo$10b2o2b2o
33bo$11bobo5b3o2bo25bo2b2o$12bo5bobob3o29bo18b2o7bo$21bobo4b2o24bo17b
obo6b3o$29bo42bo7b5o$28bo42b2o6bo5bo$19bo7bo50b2o2bo2b2o$18bobo7b3o46b
3obobob3o$19bobob2o5bo47b2o2bo2b2o$17bobobobobo44b2o13bo$17b2obo4bo18b
3o23bo13bo$20bob3o21bo24bo9bobo$20bobo22bo26bo6b2obo$21bo47b3o7bobo$34b
o34bo5b2obobo$32b3o39bobobobobo$31bo42bo4bob2o$31b2o42b3obo$36b2o27b2o
10bobo$35bobo23b2o2bo12bo$37bo5b2o12bo3bobobo$20b3o20bo11b3o6bo$19bo2b
2o6b2o9bobo10bo$20bo3bo4bo2bo8b2o11b2o11b2o$21b3o5bo22b3o11bo2bo$22bo
6b2o21bo13b2obo$52bo16b2o$11b2o13b2o6bo31b2o3bo$11bo2bo3b2o7bo5b3o16b
o12bo2b3o$12b2obo4bo3bo2bo4bo3bo14bo6b2o4bob2o$9b3o2bo3b2o5b2o6b2o2bo
13b3o3bo2b2o3bo2bo$8bo3b2o6bo13b3o6bo13b2ob2o5b2o$9b2o8bo21b2ob2o11b2o
b2o$10bob2o5bobo19b2ob2o13bo$10bo2bo5b2o20b2o2bo3b3o$11b2o11b2o11b2o4b
2o6bo$25bo10bobo11bo$15bo6b3o11bo$14bobobo3bo12b2o13bo$14bo2b2o7b2o22b
o$13b2o12bo20b3o12b2o$27bob2o2bo13b2o14bo$28bo5bo4bo8bo11b2obo$37b2o6b
3o7b2o2bobobob2o$35bo2b2o5bo9bo3bo3bo2bo$30b2o24b3obobobo$25bo32bobob
ob2o$23b3o6b3o23bobobo3bo$13b2o7bo16bo19b2ob4obo$14bo7b2o16bo26bo$14b
obo21b3o23b2ob2o$15b2o11b2o35bo$19b3o5bo2bo2b2o28bobo$10b2o16b2o3b2o28b
2o$11bo7bobo31b2o$11bobo6bo3b3o27b2o$12b2o39bo9bo$23bo11b2o11bo12b3o$
19b2o2bo11bo10bobo11bo$15b2obobo2bo8b2obo11b2o11b2o$14bo3b2o4b2o4bo3b
o31b2o$49b2o15bobob2o$12bo3bo4b2o4b2o3bo15bo2bo7bo8bob2o$11bob2o8bo2b
obob2o16bobo7bobo7bo$11bo11bo2b2o21bo7bobo5bo2bob2o$10b2o11bo32bo7bob
obobo$33b2o9b2o6b2o4b2o3b3ob2obo$20b3o3bo6bobo3b2o4bo5bobo8b2o5bob2o$
25bobo7bo3bo2b3o6bo10b6obo2bo$35b2o3bobo7b2o14bobob2o$25b3o11b2o21b3o
3bo$30b2o8bo23bobobo$30bobo7bob2o16b4o2b2o$23b2o7bo8bo22b2o$24bo7b2o11b
o12bo4bo2b2o$21b3o19bo16bo3b2o2bo$21bo15b2o5bo14bo5bob2o$38bo26bo$38b
obo4bo12bo4bobo$39b2o3b3o10b3o3b2o$43b2ob2o8b2ob2o$42b3ob3o6b3ob3o$33b
2o8b2ob2o8b2ob2o8b2o$33bo10b3o10b3o10bo$30b2obo11bo12bo11bob2o$29bobo
b2o5b2o20b2o5b2obobo$28bo11b2o20b2o11bo$27bo4b3o10b2o10b2o10b3o4bo$26b
o4bo2bo10b2o10b2o10bo2bo4bo$25bo4bobo8bo20bo8bobo4bo$25b2o2bobo8b3o18b
3o8bobo2b2o$28bobo8b2ob2o16b2ob2o8bobo$23b4obo9b3ob3o14b3ob3o9bob4o$23b
o2bob2o9b2ob2o16b2ob2o9b2obo2bo$40b3o3b2o8b2o3b3o$41bo4bobo6bobo4bo$17b
o30bo6bo30bo$17b3o13bo14b2o4b2o14bo13b3o$11bo8bo11b3o34b3o11bo8bo$11b
3o5b2o5b2o3b5o32b5o3b2o5b2o5b3o$14bo11b2o2b2o3b2o30b2o3b2o2b2o11bo$13b
o8bo8b5o32b5o8bo8bo$13bo2bo4b3o8b3o34b3o8b3o4bo2bo$17bo2b5o8bo36bo8b5o
2bo$15bo3b2o3b2o2b2o44b2o2b2o3b2o3bo$20b5o3b2o5b2o30b2o5b2o3b5o$21b3o
11bo32bo11b3o$22bo13b3o26b3o13bo$38bo26bo5$38bo26bo$22bo13b3o26b3o13b
o$21b3o11bo32bo11b3o$20b5o3b2o5b2o30b2o5b2o3b5o$15bo3b2o3b2o2b2o44b2o
2b2o3b2o3bo$17bo2b5o8bo36bo8b5o2bo$13bo2bo4b3o8b3o34b3o8b3o4bo2bo$13b
o8bo8b5o32b5o8bo8bo$14bo11b2o2b2o3b2o30b2o3b2o2b2o11bo$11b3o5b2o5b2o3b
5o32b5o3b2o5b2o5b3o$11bo8bo11b3o34b3o11bo8bo$17b3o13bo14b2o4b2o14bo13b
3o$17bo30bo6bo30bo$41bo4bobo6bobo4bo$40b3o3b2o8b2o3b3o$23bo2bob2o9b2o
b2o16b2ob2o9b2obo2bo$23b4obo9b3ob3o14b3ob3o9bob4o$28bobo8b2ob2o16b2ob
2o8bobo$25b2o2bobo8b3o18b3o8bobo2b2o$25bo4bobo8bo20bo8bobo4bo$26bo4bo
2bo10b2o10b2o10bo2bo4bo$27bo4b3o10b2o10b2o10b3o4bo$28bo11b2o20b2o11bo
$29bobob2o5b2o20b2o5b2obobo$30b2obo11bo12bo11bob2o$33bo10b3o10b3o10bo
$33b2o8b2ob2o8b2ob2o8b2o$42b3ob3o6b3ob3o$43b2ob2o8b2ob2o$39b2o3b3o10b
3o3b2o$38bobo4bo12bo4bobo$38bo26bo$37b2o5bo14bo5b2o$43bo16bo$45bo12bo
$41bo20bo$40bob2o16b2obo$40bo22bo$39b2o22b2o!

The p34 oscillator above suggests the method of proof for omnifrequent oscillators 61+ can likely be extended to periods of oscillators which support double-barreled guns (p57 comes to mind, though there are others)

EDIT: After a re-evaluation of guns which could be made into double-barreled forms (or period-doubled versions of double-barreled guns at 1/2 period), there are now only six periods which don't have an obvious nontrivial double-barreled gun (or have a gun outright) to prove omnifrequency.

While some of the guns technically would be "trivial" (e.g. a p41 gun with mutiple barrels would only involve adding another 204p41 to the side of guntrue_41 (see below), they would still count towards nontrivial omnifrequent oscillators.

Code: Select all

x = 150, y = 106, rule = B3/S23
69b3o39bo$69bo39b3o$70bo37bo$93b2o13b2o$94bo$94bobo$95b2o2$101bo$100b
3o9bo$80b2o18bo2bo6bobo$79b2o20b3o7b2o$81bo20bo3$102bo5b2o$71bo28b2ob
2o3bo$71b3o35b3o$74bo14b2o7b2obob2o6bo$73b2o13b2o8bo22bo$87bob2o3bo3b
3o21b2o$81bo4bo7bo8b2o16b2o$80bobo3b2o6b2o6bo$79b2ob2o10bo8b3o$80bobo
9b3o$77b2obo3b2o6b2o$77bo2b2obo17bo$68bobo7b3o19bobo$55bo12b2o30b2o$55b
3o11bo23b3o36bo$58bo34bo39bo$41bo15b2o14b2o19bo36b3o10bo$41b3o30bo50b
2o15b3o$44bo26b3o6bo10b2o31bobo14bo$43b2o26bo8bo3bo6bo33bo15b2o5bo$83b
obo3bobo41b2o11b3o$60b2o21b2o4b2o41b3o10bo$59b2obo6b2o50b3o8bo13bo$58b
o3bo6b2o53bo6b2o6b2o4b2o$59b3o23b2o17b2o16b2o8bo7bo3bo2b2o$60bo14b2o8b
obo15b2o21b3o3bo3b2obo4b3o2bo$74bobo8bo19bo22bo8b2o9bo$47bo26bo40bo6b
2obob2o7b2o6b4o$46bob2o23b2o40b3o27bo$47b2o13b2o54bo3b2ob2o16bo$34bo27b
o54b2o5bo18b2o$32b3o5b2o11b2o8b3o$31bo7bobo11bobo9bo16b2o$16b2o13b2o6b
o15bo26b2o40bo$17bo20b2o15b2o39bo17b2o7b3o$17bobo75b2o17bobo6bo2bo$18b
2o75bobo16bo9b3o$125bo$24bo$23b3o9bo16bobo75b2o$23bo2bo6bobo17b2o75bo
bo$24b3o7b2o17bo39b2o15b2o20bo$25bo40b2o26bo15bo6b2o13b2o$66b2o16bo9b
obo11bobo7bo$84b3o8b2o11b2o5b3o$5b2o18bo5b2o54bo27bo$6bo16b2ob2o3bo54b
2o13b2o$4bo27b3o40b2o23b2obo$2b4o6b2o7b2obob2o6bo40bo26bo$bo9b2o8bo22b
o19bo8bobo$o2b3o4bob2o3bo3b3o21b2o15bobo8b2o14bo$b2o2bo3bo7bo8b2o16b2o
17b2o23b3o$3b2o4b2o6b2o6bo53b2o6bo3bo$3bo13bo8b3o50b2o6bob2o$4bo10b3o
41b2o4b2o21b2o$b3o11b2o41bobo3bobo$bo5b2o15bo33bo6bo3bo8bo26b2o$8bo14b
obo31b2o10bo6b3o26bo$5b3o15b2o50bo30b3o$5bo10b3o36bo19b2o14b2o15bo$16b
o39bo34bo$17bo36b3o23bo11b3o$48b2o30b2o12bo$47bobo19b3o7bobo$48bo17bo
b2o2bo$56b2o6b2o3bob2o$55b3o9bobo$44b3o8bo10b2ob2o$47bo6b2o6b2o3bobo$
27b2o16b2o8bo7bo4bo$26b2o21b3o3bo3b2obo$28bo22bo8b2o13b2o$38bo6b2obob
2o7b2o14bo$38b3o35b3o$41bo3b2ob2o28bo$40b2o5bo3$47bo20bo$37b2o7b3o20b
2o$37bobo6bo2bo18b2o$37bo9b3o$48bo2$53b2o$53bobo$55bo$40b2o13b2o$41bo
37bo$38b3o39bo$38bo39b3o!

[dvgrn]

I've been terribly puzzled by what "frequency" means in this context, since this thread started. I figured I must be missing something obvious.

Here's the clue that I was missing: in LifeViewer, click Settings (gear icon in lower right) > Pattern > Identify > "Frq" (i.e., Frequency) in the column of controls on right. Maybe this could be added to the first post?

To verify these examples, go to settings, select pattern, then select identify, and check frequency.

[WhiteHawk]

I've been terribly puzzled by what "frequency" means in this context, since this thread started. I figured I must be missing something obvious.

Here's the clue that I was missing: in LifeViewer, click Settings (gear icon in lower right) > Pattern > Identify > "Frq" in column of controls on right. Maybe this could be added to the first post?

To verify these examples, go to settings, select pattern, then select identify, and check frequency.

"Frq" would stand for "Frequency", correct?

[dvgrn]

"Frq" would stand for "Frequency", correct?

I assume so. Other parts of LifeViewer's "Identify" labeling definitely say "frequency".

Oscillator cells have a "frequency" in the sense of

"How frequently is such-and-such cell in this oscillator ON?"

In other words, the "frequency" of a cell is the count of how many times the cell is ON during each oscillator cycle.

When I first read the definition in the first post, I was thinking in terms of "high-frequency" and "low-frequency", as if the period could somehow change. We've got old uses of "frequency" on the LifeWiki, but they're mostly a completely different concept, along the lines of "Relative frequency".

I didn't find the intended LifeViewer meaning of the term in the LifeViewer article on my first couple of tries. Now I've gone back and discovered the "Frequency map" part of the "Map" article -- which is linked to from the "Pattern identification" section, just not the way that I was looking for it.

[WhiteHawk]

P30 now at 133 cells and 5 QBs

Code: Select all

x = 62, y = 31, rule = B3/S23
57b2o$57b2o3$58bo$57b3o$56bo3bo$58bo$26b2o27bo5bo$26b2o27bo5bo$16bo39b
o3bo$15bobo4b2o33b3o$15b2obo3b2o7bo$15b2ob2o10bobo$15b2obo10bob2o15b2o
$3bo11bobo10b2ob2o14bobo8bo$b2ob2o10bo7b2o3bob2o13bo6b2o2bobo$24b2o4b
obo13bo2bo2bo2bobobo$o5bo24bo5bo8bo6b2o3bo$20b2o15bobo7bobo$2obob2o13b
2o15b2o9b2o$28b2o$28bo2bob2o$29b3obobo$33bobo$29b5ob3o$29bo4bo3bo$32b
obo2b2o$32b2o$3b2o$3b2o!

Oops! Missed f16, so now 136 cells

EDIT: Smaller p34 with no p17 parts (606 cells)

Code: Select all

x = 86, y = 115, rule = B3/S23
48bo6b2o$46b3o6bo$45bo7bobo$45b2o6b2o$79b2o$49b3o23b2o2bo$51bo5b2o12b
o3bobobo$34b2o14bo6bo11b3o6bo$33bo2bo18bobo10bo$34bob2o6b3o8b2o12bo11b
2o$35b2o7bo21bo2bo10bo2bo$44bobo19bo5bobo5b2obo$39bo5bo20bo6bo9b2o$25b
2o11bobo39b2o3bo$25bo2bo3b2o6bo7b2o16bo12bo2b3o$26b2obo2b2o4b3o6b2obo
15bobo3b2o4bob2o$23b3o2bo19bo2bo14b2o3bo2bo4bo2bo$22bo3b2o6bo14b2o21b
obo6b2o$23b2o8bo22b3o13b3o$24bob2o5b3o20bobo$24bo2bo28bo2bo3b2o$25b2o
11b2o11b2o4b2o3bobo$39bo10bobo11bo$29bo6b3o11bo$28bobobo3bo12b2o13bo$
28bo2b2o31bo$27b2o32bo2bo$61bo$36b2o6b2o6bobo7bo$36bo7bo7b2o5b3o$37b3o
b2obo8bo5bo$32b2o5bobobo5b2o$33bo8bo5bo2bo$33bobo13bobo$34b2o14bo$43b
2o$42b2o$43b2o4$34bobo$35bo20bo$55bobo4$28b2o6b2o9b2o$28bo7bo11b2o$29b
3ob2obo10b2o$24b2o5bobobo5bo14b2o$25bo8bo5bobo13bobo$25bobo12bo2bo5bo
8bo$26b2o13b2o5bobobo5b2o$47bob2ob3o$47bo7bo$46b2o6b2o$32b2ob2o$32b2o
b2o$34bo3$21b2o4b2o$20bobo4bo13bo$20bo18b2ob2o$19b2o18b2ob2o4$33b2o13b
2o$32bo2bo12bobo$26bo6bobo5bo8bo$24b3o7bo5bobobo5b2o$23bo15bob2ob3o$23b
2o14bo7bo$38b2o6b2o9b2o$20b3o30b2o2bo$35b2o12bo3bobobo$35bo11b3o6bo$22b
o10bobo10bo$20b2o5b2o4b2o11b2o11b2o$21b2o3bo2bo21bo6bo2bo$12bo13b2ob2o
20b2o5b2obo$11bobo13bobo20bobo8b2o$3b2o5b2ob2o13bo6b2o21b2o3bo$3bo2bo
4bo2bo3b2o14bo2b2o7bo5bo4bo2b3o$4b2obo4b2o5b2o14bo2bo6b2o5b2o2bob2o$b
3o2bo11bo17b3o5b2obo4b2o3bo2bo$o3b2o39bo13b2o$b2o9bo27bo5bo$2bob2o6bo
5b3o20bo$2bo2bo33bob2o5b3o$3b2o11b2o11b2o9b2o6bo2bo$17bo10bobo9bo7b2o
2bo$7bo6b3o6b2o3bo21b2o$6bobobo3bo5b2o2bo2b2o5bobo$6bo2b2o7b3ob2o10b2o
$5b2o10bo17bo$18b3ob2o15b2o$20bob2o16bo$37b3o$37bo3$19bo6b2o$18bobo4b
o2bo$17bo3bo2b2ob2o$18bobo$19bo2$31b2o$21b2o8bo$21bo10b3o$22b3o9bo$24b
o!

[WhiteHawk]

A very close attempt at a period not covered by glider guns - p39 missing F=35

Code: Select all

x = 201, y = 201, rule = B3/S23
91b2o$86b2o2bobo$86bo3bo4bo$87b3ob5o$80bo8bo$80b3o7b2ob3o$83bo6b2obo2b
o$82b2o8bo2b2o3$56b2o29bo$52b2obobo8bo19b2o$53bobo8b3o20bo$53bob2o6bo
28b2o$50b2obo3bo5b2o3bo23bobo$50bo2bob2o10bobo3b2o19bo$51b2o2b2o11bo4b
2o19b2o$53b2o36bo$53bo36bobo$51bobo6b3o28bo$51b2o8bo11bo$73bo6bo$72b2o
6b3obo$56b2o22b3ob3o3b2o$55bobo14b2o16b2o$55bo16b2o64b2o$54b2o15b3o59b
2o2bobo$133bo3bo4bo$134b3ob5o$127bo8bobo$83b3o15b2o24b3o6bobob3o$83b2o
16bo28bo6b2obo2bo$65b2o16b2o14bobo27b2o11b2o$65b2o3b3ob3o22b2o32b3o$72b
ob3o6b2o$76bo6bo47bo$83bo11bo17bo17bo$65bo28b3o14b3o17bo$64bobo43bo28b
2o$65bo36bo7b2o3bo17b3o3bobo$61b2o19b2o4bo12bobo10bobo3b2o11bo7bo$62b
o19b2o3bobo10bo2bo11bo4b2o9b2o8b2o$62bobo23bo3b2o7b2o28bo2bo3bo$63b2o
28bo11bo5bo4bo7bo5bo3bo2bobo$69bo20b3o12bo5bo2b3o7b3o4bo2b2o2bo$69b2o
19bo14bo5b2o4bo5bo3bo5bo$69bo43bo4bo3bo4bo3b2o$107b3o3b2obobo3bobob2o
$103b2o10bo9bo11b2o$73b2o27bobo32b2o$65bo7bo28bo28b2o52b2o$55bo8bobo7b
3o24b2o14b3o13bo46b2o2bobo$55b3o6bo2bo8bo39bo2bo11bo2b2o44bo3bo4bo$58b
o6b2o49bo3bo9bo3bo46b3ob5o$57b2o3bo52b2o2bo11bo2bo39bo8bo$62bo54bo13b
3o14b2o24b3o6bob5o$62bo55b2o28bo28bo6b2obo2bo$31b2o79b2o32bobo27b2o11b
2o$27b2obobo8bo16b3o51b2o11bo9bo10b2o$28bobo8b3o81b2obobo3bobob2o3b3o
37bo$28bob2o6bo23bo4b2o49b2o3bo4bo3bo4bo42b3o$25b2obo9b2o3bo17b2o4bob
o47bo5bo3bo5bo4b2o5bo14bo18b2ob2o$25bo2b4o10bobo3b2o11bo7bo42bo2b2o2b
o4b3o7b3o2bo5bo12b3o19b3o$26b2o3bo11bo4b2o9b3o7b2o40bobo2bo3bo5bo7bo4b
o5bo11bo23bo4b2o$28b3o27b4o4bo45bo3bo2bo28b2o7b2o3bo23bobo$28bo15bo7b
o5b2ob2o2bobo40b2o8b2o9b2o4bo11bo2bo10bobo3b2o19bo$26bobo3b3o3b2o3b3o
5b4o6b3o2bo42bo7bo11b2o3bobo10bobo12bo4b2o19b2o$26b2o11b7o5b3obo3bob2o
46bobo3b3o17bo3b2o7bo6bo29bo$36bo4b2o3bo3bo4b2o3bo49b2o28bo13b3o27bob
o$36bo4b3obo5bob3o63bo17b3o13b2ob2o27bo$31b2o3bo5b2o9b2o10b2o52bo17bo
16b3o9b3o$30bobo32b2o52bo35bo9bo3bo8b2o$30bo15bo13bo104b2ob2o3b2o3bob
o$29b2o14b3o11bob2o52b3o32b2o28bo3b2o$44bo2b2o12b3o56b2o27bobo26bobo3b
2o$44b2ob2o9b2ob2o49b2o6bo28bo28b2o$43b3o12b2o2bo39bo8bo2bo6b3o24b2o16b
o$44b2obo11b3o14b2o24b3o7bobo8bo42bo$46bo13bo15bo28bo7bo$40b2o32bobo27b
2o72bo$40b2o10b2o9b2o5bo3b2o102bo16b2o$51b3obo5bob3o4bo94b2o28bo$46bo
3b2o4bo3bo3b2o4bo37b3o48b2o3bobo26bobo$44b2obo3bob3o5b7o20bo19bobo48b
2o3bo28b2o$40bo2b3o6b4o5b3o3b2o3b3o11b3o19b3o53bobo3b2o3b2ob2o$39bobo
2b2ob2o5bo7bo22bo28b2o49b2o8bo3bo9bo$40bo4b4o27b2o7b2o3bo23bobo59b3o9b
3o7b2o$36b2o7b3o9b2o4bo11bo2bo10bobo3b2o19bo42bo27b2ob2o5bobo$37bo7bo
11b2o3bobo10bobo12bo4b2o19b2o40bobo27b3o6bo$37bobo4b2o17bo3b2o7bo36bo
45bo29bo5b3o$38b2o4bo23bo13b3o27bobo40b2o19b2o4bo11bo3b2o$65b3o14bobo
28bo42bo19b2o3bobo10b2obo2bo$46b3o16bo16b3o10bo60bobo23bo3b2o7bobob2o
$94bobo5bo3bo50b2o4bo23bo6b2obo$44bo48b2ob2o3bobo2b2o54b3o19b3o8bobo$
44bo33b2o21bo6bo3b2o47b2ob2o18bo8bobob2o$44bo3b2o27bobo22bo3b2o4b2o48b
3o28b2o$40b2o6bo28bo16bo11bo56bo$30bo8bo2bo6b3o24b2o15bo2bo$30b3o7bob
o8bo42b2o71b2o$33bo7bo117bo7bo$32b2o71b2o42bo8bobo7b3o$104bo2bo15b2o24b
3o9bo8bo$36bo57bo11bo16bo28bo3bo3bo$6b2o30bo48b2o4b2o3bo22bobo27b2o$2b
2obobo8bo16bo4bo48b2o3bo6bo21b2o33bobo$3bobo8b3o16bo4bo54b2o2bobo3b2o
b2o$3bob2o6bo21b2o5b2o50bo3bo5bobo47b2o$2obo2bo6b2o3bo23bobo60bo10b3o
16bo17b4o$o2b3o11bobo3b2o19bo42bo28bobo14b3o17bo2bo$b2o2bo12bo4b2o19b
2o40bobo27b3o13bo21b2o5b2o$3b2o36bo45bo36bo7b2o3bo23bobo$3bo6b3o27bob
o40b2o19b2o4bo12bobo10bobo3b2o19bo$bobo37bo42bo19b2o3bobo10bo14bo4b2o
19b2o$b2o6bo3bo9bo60bobo23bo3b2o7bo3bo32bo$13bo9bobo4bo54b2o28bo43bob
o$23bobo4bobo57b3o19b3o10bobo2b2o12b2o14bo$6b2o3b2o17bobob3o3b2o48bob
o19bo16b2obo10bo6b2o$5bobo14b3o7bo7b2o48b3o36b2obo10b3o3b3o$5bo28b2o94b
2o9bo10b2o$4b2o15b3o101b2o14b3o3b3ob2o6b2o$95b2o27bobo12b2ob2o3bobob2o
b2o3b2o$87bo7bo28bo14b2o13bobo$77bo8bobo7b3o24b2o15bob2o10bobo$33b3o15b
2o24b3o6bo2bo8bo43bo$21b2o28bo28bo6b2o53b2o7b2o$15b2o7bo7b3o14bobo27b
2o71bo$15b2o3b3obobo17b2o3b2o32b3o52bobo10b2obo15b2o$24bobo4bobo104bo
bo13b2o14bo$26bo4bobo9bo37bo52b2o3b2ob2obobo3b2ob2o12bobo$33bo9bo3bo15b
o17b2o51b2o6b2ob3o3b3o14b2o$15bo45b3o77b2o10bo9b2o$14bobo27b3o13bo21b
obo4b2o52b3o3b3o10bob2o$15bo36bo7b2o3bo19bo3bobo51b2o6bo10bob2o7b2o$11b
2o19b2o4bo12bobo10bobo3b2o11b2o6bo42bo14b2o12b2o2bobo2bobo$12bo19b2o3b
obo10bo2bo10b3o3b2o19b2o40bobo36bo$12bobo23bo3b2o7b2o12b2o20b2o45bo32b
o3b2o$13b2o5b2o21bo11bo5bo3b3o11bobo3b3obo40b2o19b2o4bo15b2o$18bo4bo16b
3o12bo4bobo3b2o9bo5b6o42bo19b2o3bobo10b4o2bo$18bo4bo16bo14bo6bo3b2o9b
o3b5o45bobo23bo3b2o9bob2o$18bo39bobo6bo5bobo4bo51b2o5b2o21bo6b2obo$20b
o36b2o6bobo5bo4b2o58bo2bo17b3o8bobo$53b2o13bo4bo13b2o49b4o17bo8bobob2o
$10b2o11b2o27bobo10bo3bo5bo11b2o50b2o27b2o$10bo2b2o8bo28bo16bo$11b3ob
2o7b3o24b2o13b2o12b3o53bobo$15bobo8bo115b2o$11b5ob3o48bo2bo7bo2bo51bo
3bo3bo$11bo4bo3bo103bo8bo9b3o$14bobo2b2o47b3o12b2o13b2o24b3o7bobo8bo$
14b2o65bo16bo28bo7bo$62b2o11bo5bo3bo10bobo27b2o$62b2o13bo4bo13b2o$71b
2o4bo5bobo6b2o$70bo4bobo5bo6bobo37bobo$65b5o3bo9b2o3bo6bo14bo18bo2bo$
62b6o5bo9b2o3bobo4bo12b3o19bobo$61bob3o3bobo11b3o3bo5bo11bo28b2o$62b2o
20b2o12b2o7b2o3bo23bobo$58b2o19b2o3b3o10bo2bo10bobo3b2o19bo$59bo6b2o11b
2o3bobo10bobo12bo4b2o19b2o$59bobo3bo19bo3b2o7bo36bo$60b2o4bobo21bo13b
3o27bobo$87b3o45bo$68b2o17bo16bobo$69bo35bo10b3o$116b3o4b2o3b2o$65b3o
32b2o22bobob2o4b2o$57b2o11b2o27bobo15bo7bo2b2o4b2o$57bo2bob2o6bo28bo18b
o$58b3obobo6b3o24b2o16b2o$62bobo8bo42bo$58b5ob3o$58bo4bo3bo60bo$61bob
o2b2o59b2o16b2o$61b2o63bo18bo$109b2o4b2o2bo7bo15bobo$109b2o4b2obobo22b
2o$115b2o3b2o4b3o$126b3o10bo$138bobo7b2o$109bo37bobo$108bobo27b3o6bo$
109bo35b3o$105b2o19b2o4bo11bo3b2o$106bo19b2o3bobo9bo2b2o2bo$106bobo23b
o3b2o5bobobob2o$107b2o28bo6b2obo$112bobo19b3o8bobo$112bo2bo18bo8bobob
2o$112bobo28b2o3$104b2o2b2o7b2o$104bo2bo2bo6bo$105b4o2bo6b3o$109bobo8b
o$105b5ob3o$105bo4bo3bo$108bobo2b2o$108b2o!

EDIT: Another p29 partial solution, missing F=20, F=19, and F=15

Code: Select all

x = 54, y = 33, rule = B3/S23
35bo7bo$34bobo5bobo$35bo7bo2$13b2o$13b2o$21bobo2bobo$20bo2bo2bo2bo$10b
2o9bobo2bobo20b2o$10bobo22b3o3b3o6bo$11bobo36bob2o$12bo22bobo3bobo5b2o
2bo$16b2o13b2o3bo5bo3bo4b2o$16bobo6b2o3bobo13b5o$2bo15bo6bo4bo13b2o4b
o$bobo6b3o5b2o6b3obo5b2o7bo2b2o$2bo7bobo15bob2o4b2o7bobo$10b3o27bo2bo
bobo$15b2o23b4ob2o$15bobo26bo$17bo24bobo$2o6b3o6b2o23b2o$2o6bobo$8b3o
$18b2o$15b2o2bo$11bo2bob3o$11b4o$8bo6b4o$8b6obo2bo$12bobo$10bo$10b2o!

Also the closest thing I could find for p31 (there are too few oscillators for this period)

Code: Select all

x = 116, y = 46, rule = B3/S23
104b2o7b2o$104b2o7b2o$64b2o7b2o$64b2o7b2o$29b2o$29b2o5b3o$35bo3bo64bo
9bo$34bo5bo62bobo7bobo$33bo3bo3bo22bo9bo20bo7bo2bo5bo2bo$36bobo2bo21b
obo7bobo6b2o10b2o8b2o7b2o$37bo3bo7bo13bo2bo5bo2bo5bo2bo6bo2bo8bo11bo$
31bo8bo7b2o14b2o7b2o8bo7bo2bo$30bob2obo3bo8bobo12bo11bo15bobo$30bo5b3o
46bobo15bo11bo$29b2o53bo2bo7bo8b2o7b2o$2o61bo11bo8bo2bo6bo2bo5bo2bo5b
o2bo$bo62b2o7b2o8b2o10b2o6bobo7bobo$bobo59bo2bo5bo2bo7bo20bo9bo$2b2o2b
2o48b2o5bobo7bobo$6b2o23bobo22bobo5bo9bo$31b2o23bo$2o30bo$o2bob2o4b2o
7b2o82b2o7b2o$2b2obobo3b2o7b2o82b2o7b2o$6b2o56b2o7b2o$64b2o7b2o$53bo$
29bo23b2o$11bo9bo5bobo22bobo$10bobo7bobo5b2o$10bo2bo5bo2bo$11b2o7b2o$
10bo11bo$55b2o$47b3o5bo$10bo11bo12bobo8bo3bob2obo$11b2o7b2o14b2o7bo8b
o$10bo2bo5bo2bo13bo7bo3bo$10bobo7bobo21bo2bobo$11bo9bo22bo3bo3bo$45bo
5bo$46bo3bo$47b3o5b2o$55b2o$11b2o7b2o$11b2o7b2o!

Lastly for now, p33 partial missing F=32, F=30, F=28, and F=27

Code: Select all

x = 137, y = 30, rule = B3/S23
123bo$12b3o107bobo$12b2o$11b3o108bo2bo$13bo109bobo3b2o$5b4o3bo111bo2b
4o$8b2obo29b2o9b2o29b2o9b2o30bo3bo$8b2o31bo11bo29bo11bo33bo$8b2o32b3o
5b3o31b3o5b3o31bo$9bo15bobo16bo5bo16bobo16bo5bo16bobo15b2o$4bo18b3ob3o
35b3ob3o35b3ob3o17b3o$3b3obo14bo7bo16b2o15bo7bo15b2o16bo7bo14bo$2bob4o
14b2o5b2o15bo2bo3bobo8b2o5bo15bo2bo15b2o5bobo13bo4bo$2b2o43b2o2b3ob3o
13bo3bo12b2o23b5o12b2o2bo$3bo7b2o38b3ob3o17bo39b3o7bo7bo$3o8b2o38b2o2b
2o5bo11bo7b3o19bo20bo8b3o$o10bobo4bo4bo7b3o17b6o3b2ob2o6bo23bo7bobo13b
obo3bo10bo$8bo3b2o5bo3bo7bobo6b3o8b2o2bo4b2ob2o6bo4b3obo5bo7bobo5bo3b
o5b3o3bo3bo$8bo3bo5b2o3bo7b3o6bobo8b2ob2o4bo2b2o6bo5bob3o4bo6bo3bo5bo
bo13bo3bo3b3o$8bo4bo4bobo19b3o8b2ob2o3b6o21bo7bobo7bo11bo3bobo$19b2o32b
o5b2o2b2o8b3o7bo11bo20bo$19b2o37b3ob3o17bo33bo7b3o$25b2o31b3ob3o2b2o13b
o3bo23b2o12b5o$8b2o14bo2bo15b2o5b2o8bobo3bo2bo16bo5b2o15bo2bo13bobo$9b
o15b2o16bo7bo15b2o16bo7bo16b2o15bo$6b3o35b3ob3o35b3ob3o35b3o$6bo16bo5b
o16bobo16bo5bo16bobo16bo5bo16bo$21b3o5b3o31b3o5b3o31b3o5b3o$20bo11bo29b
o11bo29bo11bo$20b2o9b2o29b2o9b2o29b2o9b2o!

EDIT 2: Omnifrequent p13 reduced by half exactly (52 cells)

Code: Select all

x = 16, y = 13, rule = B3/S23
12bo$10b3o$b2o6bo$bobo5b2o$2bo3bo$7bo5b2o$8o4bobo$o7b2o3bo$3bob2obo$3b
2obo2b7o$6bo8bo$6b2o3b2o$11b2o!

[WhiteHawk]

Solution for p36 in 473 (EDIT: 368 - EDIT 5: 234) cells

Code: Select all

x = 64, y = 35, rule = B3/S23
41b2o$41b2o2$41b4o$31b2o8bo3bo2b2o$31bobo10bo4bo$28b2obo3bo8bo$5bo23b
obo3bo12bo$5b3o20bo2bo3bo$8bo16bo3b2o18b2o$7b2o15bob3o2b4o13bo2bo2b2o
$24bo3bo2bo16bo2bo2b2o$10bo14bo2bo2bo5bo11b2o$9bobo10b3o11bobo$9bobo10b
o13bobo$10bo26bo11b2o7b2o$44b2o2bo2bo6b2o2b2o$8b2o28b2o4b2o2bo2bo4b2o
bo2b2o$8b2o28b2o9b2o5b3o$9bo28bo$51bo$51bo5b2o$13bo5b2o6b2o5bo15b3o4b
2o$13bo4bo2bo4bo2bo4bo15bobo$12bobo2b6o2b6o2bobo14bobo$13bo4bo2bo4bo2b
o4bo$13bo5b2o6b2o5bo$bo44bo6b4o$obo42bobo4bo4bo$obo5b2o5b2o14b2o5b2o5b
obo4bo3bobo$b2ob2o2b2o5b2o14b2o5b2o2b2ob2o6bo3bobo$4bo10bo16bo10bo15b
o$4bobo4bob5o12b5obo4bobo15bo$5b2o3bo3b3o14b3o3bo3b2o13bo2bo$11bo24bo
20b2o!

2nd reduction

Code: Select all

x = 85, y = 42, rule = B3/S23
67bo$57b2o3b4o3bo$56bobo6bo3bo$56bo12bo4bo5bo$53b2ob2o2b2o4bo6bobo3bo
bo$52bobo5b2o5b2o4bobo3bo2bo$52bobo17b2obob2obobo$41b2o10bo17bo3b2obo
b2o$41b2o29b2o$61bobo7bo3b3o2b2o$41b4o16bo2bo7bo3bo4bo$31b2o8bo3bo2b2o
11bobo8b3o2bo3bob2o$31bo12b2o3bo21bo2bob2ob2o2bo$28b2obo2bo36b2obo2bo
bo3bo$5bo23bob2ob3o11bo23bob2obob4o$5b3o20bo2bo40bo2bo2bo$8bo16b2o2b2o
2b2o14b2o10b2o10bobo4bo$7b2o15bob3o2b3o3bo10bo2bo2b2o5b2o11bo4b2o$24b
obob4ob6o9bo2bo2b2o$25bo9b3o11b2o$22b3o52bo$22bo52b3o$49b2o11b3o9bo$44b
2o2bo2bo9b6ob4obobo$9b2o26b2o5b2o2bo2bo10bo3b3o2b3obo$9b2o26b2o10b2o14b
2o2b2o2b2o$68bo2bo$51bo11b3ob2obo$65bo2bob2o$50bo3b2o12bo$9bobo6bo2bo
b2obo2bo6bobo11b2o2bo3bo8b2o$9bo2bo4b2o2bo4bo2b2o4bo2bo16b4o$9bobo6bo
2bob2obo2bo6bobo$57b2o$bo44bo10b2o$obo42bobo$obo5b2o5b2o14b2o5b2o5bob
o$b2ob2o2b2o4bo18bo4b2o2b2ob2o$4bo12bo12bo12bo$4bobo6bo3bo12bo3bo6bob
o$5b2o3b4o3bo12bo3b4o3b2o$15bo16bo!

(Original)

Code: Select all

x = 86, y = 54, rule = B3/S23
68bo$58b2o3b4o3bo$57bobo6bo3bo$57bo12bo4bo5bo$54b2ob2o2b2o4bo6bobo3bo
bo$53bobo5b2o5b2o4bobo3bo2bo$53bobo17b2obob2obobo$42b2o10bo17bo3b2obo
b2o$42b2o29b2o$62bobo7bo3b3o2b2o$42b4o16bo2bo7bo3bo4bo$32b2o8bo3bo2b2o
11bobo8b3o2bo3bob2o$32bo12b2o3bo21bo2bob2ob2o2bo$29b2obo2bo36b2obo2bo
bo3bo$30bob2ob3o11bo23bob2obob4o$29bo2bo40bo2bo2bo$26b2o2b2o2b2o14b2o
10b2o10bobo4bo$25bob3o2b3o3bo10bo2bo2b2o5b2o11bo4b2o$25bobob4ob6o9bo2b
o2b2o$26bo9b3o11b2o$23b3o52bo$16bo6bo52b3o$6b2o3b4o3bo31b2o11b3o9bo$5b
obo6bo3bo26b2o2bo2bo9b6ob4obobo$5bo12bo19b2o5b2o2bo2bo10bo3b3o2b3obo$
2b2ob2o2b2o4bo22b2o10b2o14b2o2b2o2b2o$bobo5b2o5b2o51bo2bo$bobo48bo11b
3ob2obo$2bo63bo2bob2o$51bo3b2o12bo$10bobo6bo2bob2obo2bo6bobo11b2o2bo3b
o8b2o$10bo2bo4b2o2bo4bo2b2o4bo2bo16b4o$10bobo6bo2bob2obo2bo6bobo$58b2o
$47bo10b2o$46bobo$32b2o5b2o5bobo$10b2o22bo4b2o2b2ob2o$10b2o19bo12bo$31b
o3bo6bobo$31bo3b4o3b2o$26bo6bo$24b3o$11b3o9bo$10b6ob4obobo$11bo3b3o2b
3obo$2o12b2o2b2o2b2o$o2bob2o10bo2bo$b3obobo4b3ob2obo$5bobo6bo2bob2o$b
5ob3o7bo$bo4bo3bo5b2o$4bobo2b2o$4b2o!

EDIT 2: An oh-so-close p31 oscillator once I found the p31 loop could support two pond two block (missing f=24 and f=21)

Code: Select all

x = 75, y = 89, rule = B3/S23
63b2o7b2o$63b2o7b2o$28b2o$28b2o5b3o$34bo3bo$33bo5bo$32bo3bo3bo22bo9bo
$35bobo2bo21bobo7bobo$36bo3bo7bo13bo2bo5bo2bo$30bo8bo7b2o14b2o7b2o$29b
ob2obo3bo8bobo12bo11bo$29bo5b3o$28b2o$62bo11bo$63b2o7b2o$62bo2bo5bo2b
o$55b2o5bobo7bobo$30bobo22bobo5bo9bo$30b2o23bo$31bo$10b2o7b2o$10b2o7b
2o$63b2o7b2o$63b2o7b2o$52bo$28bo23b2o$10bo9bo5bobo22bobo$9bobo7bobo5b
2o$9bo2bo5bo2bo$10b2o7b2o$9bo11bo$54b2o$2b2o42b3o5bo$bobo5bo11bo12bob
o8bo3bob2obo$bo8b2o7b2o14b2o7bo8bo$2o7bo2bo5bo2bo13bo7bo3bo$9bobo7bob
o21bo2bobo$10bo9bo22bo3bo3bo$44bo5bo$45bo3bo$35b2o9b3o5b2o$30b2o2bo2b
o16b2o$10b2o7b2o9b2o2bo2bo$10b2o7b2o14b2o3$35b2o$34bo2bo2b2o$16b2o16b
o2bo2b2o$16b2o5b3o9b2o$22bo3bo$21bo5bo$20bo3bo3bo$23bobo2bo13bo8b2o$24b
o3bo7bo5b3o6b2o$18bo8bo7b2o8bo$17bob2obo3bo8bobo6b2o$17bo5b3o$16b2o$49b
3o$42bob2obo4bo$42bo3bobo3bo$42bo4bo4bo$18bobo22b2o5b2o$18b2o25bo3bo$
19bo25bo3bo$46b3o4$16b3o$15bo3bo25bo$15bo3bo25b2o$13b2o5b2o22bobo$12b
o4bo4bo$12bo3bobo3bo$12bo4bob2obo$13b3o$47b2o$39b3o5bo$19b2o6bobo8bo3b
ob2obo$19bo8b2o7bo8bo$12b2o6b3o5bo7bo3bo$12b2o8bo13bo2bobo$36bo3bo3bo
$37bo5bo$38bo3bo$39b3o5b2o$47b2o!

EDIT 3: smaller p12 (74 cells)

Code: Select all

x = 18, y = 14, rule = B3/S23
5bo2b2ob2o$3b3o2b2ob2o$2bo$o2b10o$3o10bo$3b4ob2ob2obob2o$2bo4bob2obob
ob2o$bob5o4bobo$2bo3bob3obobo$3b2obo3bob2o$4bob4o$4bo$3b2o3b2o$8b2o!

EDIT 4: 63 cells

Code: Select all

x = 22, y = 21, rule = B3/S23
7bo$b2o4bobo$o5bobo$3bo4bo3b2o$b2o9b2o6b2o$20bo$7bo10bobo$4b2obo10b2o
$4b2o$4bo5b3ob2o$14b2o$18b3o$19b3o$2b2o$4bob2o4b2o$o2bo2b2o4b2o$obo$b
o2$b2o$b2o!

EDIT 5:
p26 only missing F=19

Code: Select all

x = 36, y = 41, rule = B3/S23
24bobobobo$23bob2ob2obo$21b3o7b3o$8b2o10bo4b2ob2o4bo$5b2o2bo10bo2b2ob
obob2o2bo$3b3ob2o10b2obobobobobobob2o$2bo17bobobo5bobobo$3b3ob2o11bob
o2bo3bo2bobo$5bob2o12bo4b3o4bo2$2b2o6b2o$2bobo4bobo$4bo4b2o$4b3o19b3o
$7bo8b2o$6b2o8b2o7bo3bo$25bo3bo2$16b2o4b2o2bo3bo$10bobo2bo2bo2bo2bo5b
o$7bobo5bo2bo2bo2bo4bo$2b2o2b3o4bo2b2o4b2o6b3o$2b2o2bo5bo19bo$8bo2bo$
22b2o$8bo2bo10b2o$2b2o2bo5bo$2b2o2b3o4bo$7bobo$10bobo3$3b2o$3bo2b2o$2o
bob2o2bo$2obo4b2o$4b3obo$7bo2bo$4b2obob2o$4bo2bo$6b2o!

[WhiteHawk]

Omnifrequent p26 (260 cells)

Code: Select all

x = 34, y = 44, rule = B3/S23
22bobobobo$21bob2ob2obo$4bo14b3o7b3o$3bobo12bo4b2ob2o4bo$3bobo12bo2b2o
bobob2o2bo$b3ob2o10b2obobobobobobob2o$o17bobobo5bobobo$b3ob2o11bobo2b
o3bo2bobo$3bob2o12bo4b3o4bo2$2o6b2o$obo4bobo$2bo4b2o$2b3o19b3o$5bo8b2o
$4b2o8b2o7bo3bo$23bo3bo2$14b2o4b2o2bo3bo$8bobo2bo2bo2bo2bo5bo$5bobo5b
o2bo2bo2bo4bo$2o2b3o4bo2b2o4b2o6b3o$2o2bo5bo19bo$6bo2bo$20b2o$6bo2bo10b
2o5bo$2o2bo5bo14b5o$2o2b3o4bo12bo5bo$5bobo5b2ob2o6b4o2bo$8bobo2b2ob2o
7bo2bob2o$25b4o3bo$24b2o3bobo$19bo3bo2bob2ob2o$4b2o13bo3bo2bo$5bo13bo
3bo2bob2ob2o$2b3o10b2o7b2o3bobo$2bo4b2o5bobo8b4o3bo$obo4bobo4bo10bo2b
ob2o$2o6b2o3b2o9b4o2bo$24bo5bo$5b2o18b5o$6bo20bo$3b3o$3bo!

Notably, this oscillator showcases a way to expose the spark of the p26 bi-block hassler.

EDIT: P32 solution (410 cells)

Code: Select all

x = 51, y = 81, rule = B3/S23
32b2o$32bob2o$33bo2bo$28bo4bo2bo$27bobo3bo2bo$15b2o11b2o3b3o$15b2o$15b
2o11b2o3b3o$14b3o4bobo3bobo3bo2bo$20bo7bo4bo2bo$13bo3bo2bo3bo8bo2bo$9b
2o2bo3bo2bo3bo7bob2o$9b2o6bo14b2o$14bobo4b3o16bobo3b2o$21b2o17bobo5bo
$9b2o10b2o14bob2o2bobo4bo$8bobo10b2o13b2o4b2obob4o$8bo27b2o5bobo$5b2o
bo24b2obobo4bo2b3o$5b2ob2o21b3o3bo4b2o4bo$22bo6bob2o$22b3o3b3o$16b2o7b
o13bo$16bobo5b2o12bobo6bo$16bo22bo6bobo$26b3o16bo3bo$25bo3bo6bo7bo3bo
$24bo5bo4bobo5bo3bo$24bo5bo3b2o2b2o2bo3bo$3b2o3b2o14bo5bo4b2ob2o3bobo
$3b2o3b2o15bo3bo5b3ob2o3bo$3b2o8b2o11b3o9b3o$3b3o6bo2b5o17bobo$3bobo7b
o2b4o17b2o$2bo2bo3b2o3b3o$2bobo4b2o$3bo$18b2o$5b2o6b2o3b2o$2o3b2o6b2o
$2o23b3o$16bo7bo3bo$9b2o4bobo5bo5bo$3b3o3b2o3bo2bo5bo5bo$4o2bo7bobo6b
o5bo$5o2bo6b3o7bo3bo$5b2o8b2o8b3o$10b2o3b2o20bo$10b2o3b2o11b2o5bobo$28b
o7b2o$23b3o3b3o$21b2obo6bo$5bo4b2o4bo3b3o22b2o$5b3o2bo4bobob2o23bo2bo
$8bobo5b2o18b3o5b2obo$3b4obob2o4b2o20bo8b2o$3bo4bobo2b2obo20bo6b2o3bo
$5bo5bobo13b2o14bo2b3o$6b2o3bobo24b2o2bob2o$26bo3bo7b2o3bo2bo$25bo4bo
14b2o$24bobobo7b2o$23bobobo7bo2bo$21bo4bo9bo2bo$21bo3bo13bo$36bo2bo$23b
2o11bobo$37bo2$39bo3bo$38bobobobo$39b2ob2o$37b3o3b3o$36b2o7b2o$35b3ob
o3bob3o$34b2o3b2ob2o3b2o$34b3o2b2ob2o2b3o$35b2o9b2o$36b4o3b4o$38bo5bo
$38bo5bo!

EDIT 2: P35 missing f=22

Code: Select all

x = 123, y = 93, rule = B3/S23
93b2o$94bo$92bo$92b5o$96bo$90b4o$90bo2bo2$97bo$96b3o3b2o$95bobob3o2bo
$94b3ob2o2b2o5b2o5bo$85b2o8bobobo7bo2bo4bo$81b2o2bobo8b3o17bo2b2o$81b
2o2bobo9bo15b2obobo2bo$86bo20bo4b2o2b2o4bo$89b2o17bo2bobob2o$89bo8bo10b
2o2bo$90b3o4bobo14bo4bo2bo$82b2o8bo5bo14bo5b2o$77b2o2bo2bo$77b2o2bo2b
o$82b2o3$82b2o$81bo2bo2b2o$81bo2bo2b2o$67bo5bo8b2o$66bobo4b3o$48b2o17b
o8bo$24b2o23bo25b2o$23bobo7bo13bo31bo$15b2o5bo2bob2o3bobo12b5o16bo9bo
bo2b2o$15bobo4bobobobo3bobo16bo15b3o8bobo2b2o$17bo3bo4bo4b2ob2o9b4o17b
obobo8b2o$17b2o2b4obo4bo13bo2bo13b2o2b2ob3o$14bo3bo2bo3bo6bob2o25bo2b
3obobo$11bo2b4ob2ob3o5bobob2o16bo9b2o3b3o$11b3o3bo4bo7b2o19b3o3b2o9bo
$14bo23bo11bobob3o2bo$13b2o3bo2bo15bobo9b3ob2o2b2o13bo2bo$bo2bo31b2ob
o10bobobo17b4o$b4o2bo30bo12b3o15bo$5b3o44bo16b5o$b3o8b3o9b3o13bo32bo$
o2bob3o6bo2b2ob2o2bo16b2o28bo$bob3o2bo8bo3bo18b2o11bo17b2o$2obo3b2o2b
o3b3o3b3o10bo17bobo$2bo2b2o2b3o22b2o17bo$2bobob2o25bobo21bo$b2o5b2o45b
3o$o2bobobo2bo43bo$2obobobob2o4b3o3b3o29bobo$2bobo2bo9bo3bo14bo13bob4o
$2bobob2o6bo2b2ob2o2bo9b3o14bo4b2o$2ob2o2bob2ob3o9b3o6bo15bo3b2obo$bo
bobobobo19bo3b2o12b3obobo2bo$bobobobobo18bobo15bo3bobo2bo$2bobob2ob2o
17b2obo14b2o2bo2b2o$3bo6bo2b2o13b2ob2o16b2o$7b3o4bo4bo9bo3bo$6b2obo2b
2o3b3o9b5o$4b2ob2obo3b2o5b3o7bo5bo$7bobo4b2o6bo12b3o$7bobo4bo2bo5bo10b
o$6b2ob2ob2o2bo2bo3b2o8bobo$3b2o4bo2bo7b2o3bo6b3obo$3b3obobo4b3obo4b2o
11b3o$5bo2bo3b2o2b7o4b2obob2obo3bo$3b3o2bo8bo6b4obo2b2o2bob2o$5bo11b2o
2b2obo4bobob4obo$3b2o9b2ob2obobobob2o10bo$bo3b2o2b2obob2o6bobobo5bo2b
2ob2o$b4o5bob7o3bobobo4bo4bo$5b5o5b2ob4obobo7bo2bo$3bobo9bo7bo6b2obob
2obo$b3o3b3o7bob5o7bobo3b2o$o4bo3bo7bobo9b3o2b2o$b8o6bo2bo2bo5b2o3bob
o$2bo6b3ob4obob2o6bo2b2o2bo$o3bo3bo3b2o3bobo6bobobo2b2o$5obo2b2o4b2o2b
o4b3obob3o$5bob2o2b4obobob2obo5b2obob3o$2b2obobo2bo2bo2bobo2bob2o7bob
o2bo$2bobo4b2o4b2ob2obo7b2obo3b2o$18bo2b2obo8bo$18bobo4bobob2ob2o$19b
2ob4obo2bobo$22bo2b2obobobo$22bobo2b2ob2o$23bobo$24bo!

EDIT 3: p40 missing f=27 and f=21

Code: Select all

x = 72, y = 78, rule = B3/S23
37b2o$30b2o5bo$31bo2b2obo$31bobo2bo$32bobo26b2o$34b2o2b2o22bo5b2o$33b
o5bo12bo9bob2obobo$34b5o13b3o8bobobo$55bo9bobo$34b2ob4o13b2o8bo3bo$34b
2obo2bo24b4o$20b2o44bo$20bo$21bo40bo5b2o$18b3o5b3o29bo4bo4bo$18bo6bo3b
o28bo3bo6b3o$24bo5bo28bo11bo$25bo3bo$21b2o3b3o11bo16b2o$20bobo16b2o6b
o9b2o$20bo18bobo5bobo13bo2bo$19b2o26b2o5b2o$55bo6bo4bo$52b3o5b3ob2ob3o
$52bo6bo3bo2bo3bo$43b2o13bob4o2b2ob2o$36b2o5bobo12bo4bo3bobo$20bo15b2o
5b3o10bobobobo4bobo$11b2o7bobo13b2o18b2obo2bo5bo$11b2o7b2o15bo21bobo$
36bobo9b2o9b2o$35b2obo9bo$49b3o$21b2o28bo$21b2o13b2o$11b3o22b2o$10bo3b
o$9bo5bo$3b2o4bo5bo34bo$3bo2bo2bo5bo32b2obo3b2o$4b2obo2bo3bo36bo3b2o$
b3o2bo4b3o35bobo$o3b2o44bo$b2o43bo2bo$2bob2o14b2o26bobo$2bo2bo14bo29b
o$3b2o16b3o22bo$23bo22bobo$7b2o6bo31bo2bo$8bo7bo29bo$5b3o6b3o28bobo$5b
o34b2o3bo$40b2o3bob2o$46bo4$42b2o$25bo11b2o2bo2bo$26bo10b2o2bo2bo$24b
3o15b2o3$42b2o$41bo2bo2b2o$41bo2bo2b2o$42b2o2$35bo$36bo$34bo7b2o$34bo
3bobo2bo2bo$38bob2obobobo$33bo2bobo4bo2bo$33b4ob4obo$37bo4bo$35bobo2b
o$35b2o3b2o!

[WhiteHawk]

P29 solved (probably overly large at EDIT: 319 cells)

Code: Select all

x = 94, y = 73, rule = B3/S23
10b2o$10b2o5bo$16bobo$17bo3$9b3o$10bo$3b2o10b3o4bo$3bo12bo3bo3bo$2obo
20bo$o2bob2o12bo4bo$2b2obo14bob2o$3bobo15b3o3b2o$2bo2bob2o18b2o9bo$3b
2o8b2o21b3o5bo13b2o$4bobobo5bo4b2o14bo6b3o13bo$4bobo4b3o6bo14b2o4bo8b
o9bobo$3b2obobo2bo5b3o7b2o12b2o5b3o5b6obo2bo$7b2o8bo8bo2bo3bo13bo8bo6b
4o$27b2o5bo12b2o10b4o$32bobo4bo19bo2bob3o$31bobo4b3o23bo2bo$31b2o12bo
20b2o$44b3o6b3o$36bo16bobo$36bo16b3o9b2o$65bo$63bobo$63b2o$38bo16b3o$
37bobo10bo4bobo$38bo5b2o3bobo3b3o8b2o$44b2o4bo15bo$64bobo$63b3o$61b3o
$60bob2o$58b3obo10b2o$58bob2o11b2o3$61b2o4b2o4b2o$61b2o3bo2bo2bo2bo$66b
o2bo2bo2bo3b2o$67b2o4b2o4b2o3$67b2o11b2obo$67b2o10bob3o$78b2obo$78b3o
$76b3o$75bobo$75bo15bo$74b2o8b3o3bobo$84bobo4bo$84b3o$77b2o$76bobo$76b
o$75b2o9b3o3b2o$86bobo3b2o$86b3o$74b2o$74bo2bo$75b3obo2bo$79b4o$75b4o
6bo$75bo2bob6o$79bobo$83bo$82b2o!

EDIT:

speaking of p33 heres a cool block/blinker hassler

Code: Select all

x = 65, y = 38, rule = B3/S23
4bobob2o10b2o$3bobob3o6b2o3bo41bo$bo3b2o2bo6bo2bo23bo18bobo$bo15b4o20b
3o19bo$2bo2b2o33bo$5bo9b6o19b2o$5b2o7bo2bo2bo36b2o4bo$5b3o6b2o19bo21b
2o3bobo$2ob2o29b2o17bobo3bo3b2o$ob2obo2bo24bob6obo10bobobobo$5bo3bo11b
o10b3o2bob2o2b2o5bobo4b2o$b4obob2o10b3o5b3o2bo4bo4bo4b3obo2bo$bo2b2o2b
2o9bo2bo11b2o5b2o3bo3bo$2b2o3b2o3b2o5b3o14bo3bo5b3o2bo$4b2obo4bo7bo15b
obobo5bo4bo$4bo2bo29b3o7b4o6b2o$5b2o4bo26bo8b2o6b4o$9bobo14b2o26bo4bo
$21bo2bo2bo26bo2b3o$11bo9b6o12b2o14bo3bo$10b2o26bo11bo2bob3o$10b5o6b4o
14b2o6b2o4bobo$10b2ob2o7bo2bo20bobobobo$11bo8bo3b2o20bo3bobo$20b2o25b
2o$47b2o$42bo$41bobo$41bob2o$38b2obo$38bo2bob2o$39b2o3b2obo$41b2o3bo3b
2o$41bo4bobo2bo$42b4o2b2o$48bo$42b2o5bo$42b2o4b2o!

Missing f=28 to solve p33

[qqd]

...
EDIT:

speaking of p33 heres a cool block/blinker hassler

Code: Select all

x = 65, y = 38, rule = B3/S23
4bobob2o10b2o$3bobob3o6b2o3bo41bo$bo3b2o2bo6bo2bo23bo18bobo$bo15b4o20b
3o19bo$2bo2b2o33bo$5bo9b6o19b2o$5b2o7bo2bo2bo36b2o4bo$5b3o6b2o19bo21b
2o3bobo$2ob2o29b2o17bobo3bo3b2o$ob2obo2bo24bob6obo10bobobobo$5bo3bo11b
o10b3o2bob2o2b2o5bobo4b2o$b4obob2o10b3o5b3o2bo4bo4bo4b3obo2bo$bo2b2o2b
2o9bo2bo11b2o5b2o3bo3bo$2b2o3b2o3b2o5b3o14bo3bo5b3o2bo$4b2obo4bo7bo15b
obobo5bo4bo$4bo2bo29b3o7b4o6b2o$5b2o4bo26bo8b2o6b4o$9bobo14b2o26bo4bo
$21bo2bo2bo26bo2b3o$11bo9b6o12b2o14bo3bo$10b2o26bo11bo2bob3o$10b5o6b4o
14b2o6b2o4bobo$10b2ob2o7bo2bo20bobobobo$11bo8bo3b2o20bo3bobo$20b2o25b
2o$47b2o$42bo$41bobo$41bob2o$38b2obo$38bo2bob2o$39b2o3b2obo$41b2o3bo3b
2o$41bo4bobo2bo$42b4o2b2o$48bo$42b2o5bo$42b2o4b2o!

Missing f=28 to solve p33

Omnifrequent p33:

Code: Select all

x = 107, y = 57, rule = B3/S23
4b3o2bo10b2o$10bo5b2o3bo$2bob4obo6bo2bo23bo$b2o14b4o20b3o$5b2o33bo12bo
bo$4bo10b3ob2o19b2o10bo2bo$4bo2bo6bo2bob2o32b2o$7bo6b2o2bo$2obo3bo26bo
$ob2obo17b2o8bobo$5b3obo12bo5b2o3bobo4bo12b3o$b3o2b2o2bo14bo2b2o4bo5bo
11bo2bo11b3o$bo3b2o11b2o2b2o11bo4bo10bo15bo2bo$2b2o3bobo2b2o2bo18b2o
15bo2bo15bo$4b2obo4b2o5bo14b2o17b3o11bo2bo$4bo2bo9b2o36bo11b3o$5b2o3bo
28b3o8bo16bo$10bo12bo2b2o10bo2bo8b3o19bo$10bo10b2obo2bo10b3o9bo2bo16b
3o$10b2o9b2ob3o27bo14bo2bo9b2o$13bo36bo2bo14bo13bo$9bo4bo6b4o25b3o16bo
2bo7bobo$14bo7bo2bo44b3o7b2o$10b3o7bo3b2o$20b2o$51b2o6bo4b2o12bo$42b2o
6bo2bo4bobo4bo13bo$41bo2bo5bobo6bo2bo14b3o$41bob2o18bo$38b2obo3bo17bob
3o$38bo2b3o2bo19b2o$39b2o5bo$41b4obo3b2o$41bo2bobobo2bo17b2o$42b4o2b2o
13bo4b4o13bobo$48bo12b2o4bo3bo14b2o$42b2o5bo12bobo3b3o5bo9bo$42b2o4b2o
13bo5bo5b3o3b2o$74bo3bo$74b4o$75b2o2$85b2o8bo$87bo5bobo$88b2o4b2o$86b
5o$86b3obo14b2o$77b2o5bo15b2obo2bo$78bo4bobo13bobob3o$75b3o3b3obo2b2o
9bobo$75bo4bo9bo6b3ob5o$80bob2ob2o2bobo4bo3bo4bo$79b2obo2bo4bo5b2o2bob
o$78bo4b2ob4o11b2o$79b3obo3bo$81bobobo$82b2ob2o!

EDIT:

...
The conjecture can be stated as follows

"In B3/S23, there exists a non-welded & nontrivial oscillator for every period n where every possible instance of cells oscillating at any given frequency value between n and 1 inclusive can be found in said oscillator"
...

Would like to clarify exactly what a non-trivial oscillator is in this setting:
A non-trivial oscillator of a specific period is an oscillator where at least one cell oscillates at the full period, and there does not exist any collection of live cells, which, if converted to dead cells, results in an oscillator oscillating at the same period that has at least one cell oscillating at the full period.

This definition also takes care of welded oscillators as well (Which, I assume, means that you weld the catalysts of two different oscillators in such a way that they do not interact in any way.)

But this also implies that the omnifrequent p26 is trivial (you can remove the bi-block and still end up with a period 26 oscillator.)

[WhiteHawk]

p6 reduced by 3 cells, now down to 20 cells

Code: Select all

x = 12, y = 8, rule = B3/S23
o2b2o4bo$2o2bob2obo$4bobo$5b2o$7bo$7bo3bo$9bobo$10bo!

[Sokwe]

5 - 16 cells

The RLE of the smallest known examples contains fumarole, which has 18 cells, not 16. However, the 17-cell Silver's p5 is the actual smallest known, as the two known smaller p5 oscillators, pseudo-barberpole and octagon 2, do not have frequency-4 cells.