The Omnifrequency Project

[ElijahKen]

Omnifrequent p46:

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x = 129, y = 116, rule = B3/S23
94b2o19b2o$94bobo18b2o$83bo12bo30bo$83b3o8bo30b3o$86bo6bo3bo3bo2b2o10b
2o6bo$85b2o6b2o7b2obo10b2o6b2o$104bo$96b2o4b3o17bo$121b3o$96b2o4b3o15b
5o$84b3o3b3o2bobo6bo$94b2o6b2obo$88bo6b2o4bo2b2o$88bo$88bo$117bobo$
118b2o$118bo3$36b2o5b2o41bo$36b2o5b2o40bo$85b3o2$88b3o$88bo$89bo2$58b
2o$59bo6bo50bo$59bobo4bo22bo27b2o$36b3o3b3o15b2o4bo9b2o11bo11b4o11bobo
$35bo9bo29bobo11bo10b2o2bo17bob2o$35bo3bobo3bo17bo4b3o6bo21b2o2bo18bo
3bo$2b2o32b3o3b3o18bo21b3o3b3o6bo2bo18b3o$3bo33bo5bo22bo34b2o$3bobo60b
o22bo$4b2o4bo55bo22bo11b2o$9bobo14b2o32b2o25b3o10bo2bo$8bo3bo5bo7bobo
27b2o2b2o24b2o6b2o3b2o2bo13b2o6b2o$9bobo6b2o6bo29b2o29bo6b2o4b2o2bo12b
2o6bo$10bo6bobo41bo5bo16b3o14b4o21b3o$60b3o3b3o15bo43bo$59b2o2bobo2b2o
25b2o19b2o$4b2o53b2ob2ob2ob2o25b2o19b2o$2o2b2o43b2o11b2ob2o$2o46bobo9b
obo3bobo$49bo9bo2bo3bo2bo$62bo3bo$46b2o11bobo5bobo$45bo14bo7bo32b2o$
48bo52bo$4b3o3b3o33b2o51bobo$4bo2bobo2bo86b2o$4bo7bo20bo5bo54bo$32b3o
3b3o51b3o$5bo5bo19bo3bobo3bo33b3o16bo$6b2ob2o20bo9bo35bo9b2o$32b3o3b3o
35bo9b2o$53b2o33bo$53bobo43b2o$55bo43b2o2b2o$55b3o45b2o$34b2o17b2o3bo$
35bo16bo2b4o$13bo17b2ob2o8bo7b2obo$2o9bobo18bobo4b2o2b2o10bob2o$2o2b2o
6b2o19bo5b2o14bobo$4b2o28bo19b2obobo$34bo23b2o$34bo58bo5bo$12bo51bo7bo
19bobo3bobo$11bo2bo15b3o30bobo5bobo17bo3bobo3bo$12bobo51bo3bo20bo3bobo
3bo$13bo20bo4b2o22bo2bo3bo2bo17bo9bo$4b2o4bo11b2o10bo4bobo22bobo3bobo$
3bobo4bo10bo2bo9bo6bo24b2ob2o21b2o5b2o$3bo6bo11b2o17b2o20b2ob2ob2ob2o$
2b2o59b2o2bobo2b2o$64b3o3b3o$65bo5bo22b2o$60b2o30b2o2bo$60b2o2b2o25bo
4bo6b2o$31b2o31b2o25bo7b2o2b2o$31bobo36bo28b2o$31bo38bo21bo$70bo22bobo
$67bo26bo$67bo4b3o$90b3o$64b2o4bo$63bobo4bo10b2o11bo4b2o$63bo6bo10b2o
11bo4bobo$62b2o17b2o11bo6bo$101b2o$42b3o$42bo$43bo3$71bo$43bo27b2o$43b
o11b4o11bobo$43bo10b2o2bo17bob2o$53b2o2bo18bo3bo$39b3o3b3o6bo2bo18b3o$
55b2o$43bo$43bo11b2o$41b3o10bo2bo$40b2o6b2o3b2o2bo13b2o6b2o$41bo6b2o4b
2o2bo12b2o6bo$38b3o14b4o21b3o$38bo43bo$49b2o19b2o$49b2o19b2o!

Can likely be reduced.

I think the prior definition is problematic. It does not forbid all welds, and disallows many helpful things, like a number of the pond and block reactions (they can be removed when not period multiplying and still satisfy the definition, thus the p29 is invalid).
This is also not allowed, because the twin bees shuttle can be removed without changing the period or "pseudo" status of the oscillator.

Code: Select all

x = 43, y = 54, rule = B3/S23
5$21b2o5b2o$21b2o5b2o11$21bo7bo$19bob2o5b2obo$19bo3b2ob2o3bo$20bo3bob
o3bo$21b3o3b3o10$18bo14bo$17b3o14bo$16bobobo11b3o$16bobobo$14b2ob3ob2o
12b2o$13bob2obob2obo11bo$7b2o3b2obo5bob2o11b3o$7b2o4b2obo3bob2o2bob2o
8bo$14b3o3b3o3b2obo2$6b2o$7bo$4b3o$4bo13bo$17bobobob2o$16bob2ob2obo$16b
o$15b2o!

The latest definition also allows this, in the event you want to add p2 cells (which I did in the above p46):

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x = 43, y = 31, rule = B3/S23
17b2o$17b2o$6bo$6b3o$9bo6b2o12b3o8b2o$8b2o6b2o10bo3bo8b2o$27bo4bo$27bo
3bo2$27bo3bo$7b3o17bo4bo$12bo5bo9bo3bo8b2o$11bobo3bo12b3o8b2o$10bo6b3o
$11b2o4$5b2o$5bo2bob2o$6b3obobo$10bobo$4b7ob3o$2obobo5bo3bo$bobo4b2obo
2b2o$bob2o4bob2o$2o4bo$3b2ob2o$4bo$2bobo$2b2o!

It is (I think) impossible to remove the beacon (by turning cells off) without destroying the integrity of the eater, yet the beacon clearly is just welded on.
I am not sure how it needs to be changed. When it is, the above p46 can easily be reduced

[qqd]

Omnifrequent p46:

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snip

Can likely be reduced.

I think the prior definition is problematic. It does not forbid all welds, and disallows many helpful things, like a number of the pond and block reactions (they can be removed when not period multiplying and still satisfy the definition, thus the p29 is invalid).
This is also not allowed, because the twin bees shuttle can be removed without changing the period or "pseudo" status of the oscillator.

Code: Select all

snip

The latest definition also allows this, in the event you want to add p2 cells (which I did in the above p46):

Code: Select all

snip

It is (I think) impossible to remove the beacon (by turning cells off) without destroying the integrity of the eater, yet the beacon clearly is just welded on.
I am not sure how it needs to be changed. When it is, the above p46 can easily be reduced.

Yes, I did realize a while ago that that definition was quite strict, ruling out most of the omnifrequent oscillators on this thread, except for a few. The generalized p61+ omnifrequent oscillators using double-barreled guns still work though, so I think there is potential to work around this definition. I was referring to stable welds when I framed the definition of a 'non-trivial oscillator' in the context of omnifrequent oscillators, and I admit I did not think of periodic welds like the one you highlighted in a similar manner to stable welds.

With that being said, I still do think that omnifrequent oscillators constructed using the two pond and two block reaction (or the two beehive and two block reaction for domino sparks Could not find the source of this reaction but it exists) cannot be considered non-trivial, since they just utilize the sparks of already independent oscillators to get a few more frequencies. The long boat spin reaction, on the other hand, is a dependent (in the sense of a 'dependent conduit') mechanism, meaning that it cannot be simply removed without destroying the oscillator. (This also applies to other dependent or independent reactions used in this project.)

There are a few flaws to this definition though, such as being able to construct a seemingly trivial oscillator which is in fact non-trivial by this definition solely because the non-interacting components like the beacon can be used as inductors to stabilize otherwise unstable catalysts.

Also, in some extremely rare cases, a seemingly non-trivial oscillator by this definition actually turns out to be trivial because there is a collection of live cells which if turned off result in a different non-trivial oscillator of the same period by mere chance.

For example, you can have an even period gun firing gliders at a stable glider eater, like the drifty eater 3. You may be able to turn off a particular collection of live cells in the eater in such a way that the ash produced by the resulting unstable pattern just happens to form a natural eater 1 on the correct glider lane. If no gliders or other spaceships are produced, and no oscillators with period greater than 2 are produced in the final ash, and there is no ash on the glider lane before the eater 1 once the pattern stabilizes, the result is a technically different non-trivial oscillator of the same period.

The sole reason of providing a definition for a non-trivial oscillator is to make the omnifrequent conjecture sound. Up until then, deciding whether an oscillator was non-trivial or not could only be ascertained in a subjective manner, and while this definition is not without its problems, it is at least a foundation that can be worked upon to formulate a more useful one.

[WhiteHawk]

I think there is a misunderstanding, because these examples are inversely permitted/not permitted based on what I am pretty sure "nontrivial" actually means.

As an example, this hassler would 100% be allowed if it was part of a pattern that proved the conjecture for it's period since there are no non-interacting stators (additionally, the idea of the self-supporting nature of this oscillator only holds up if the twin bee shuttle were removed, as removing the tanner's p46 causes the the whole thing to collapse).

Code: Select all

x = 43, y = 54, rule = B3/S23
5$21b2o5b2o$21b2o5b2o11$21bo7bo$19bob2o5b2obo$19bo3b2ob2o3bo$20bo3bob
o3bo$21b3o3b3o10$18bo14bo$17b3o14bo$16bobobo11b3o$16bobobo$14b2ob3ob2o
12b2o$13bob2obob2obo11bo$7b2o3b2obo5bob2o11b3o$7b2o4b2obo3bob2o2bob2o
8bo$14b3o3b3o3b2obo2$6b2o$7bo$4b3o$4bo13bo$17bobobob2o$16bob2ob2obo$16b
o$15b2o!

This one is not allowed since there are 2 stators which are completely non-interacting

Code: Select all

x = 43, y = 31, rule = B3/S23
17b2o$17b2o$6bo$6b3o$9bo6b2o12b3o8b2o$8b2o6b2o10bo3bo8b2o$27bo4bo$27bo
3bo2$27bo3bo$7b3o17bo4bo$12bo5bo9bo3bo8b2o$11bobo3bo12b3o8b2o$10bo6b3o
$11b2o4$5b2o$5bo2bob2o$6b3obobo$10bobo$4b7ob3o$2obobo5bo3bo$bobo4b2obo
2b2o$bob2o4bob2o$2o4bo$3b2ob2o$4bo$2bobo$2b2o!

There is this small change which permits it to be allowed in a solution (assuming the weld is optimal and the reaction which required the SL welding the eater is connected to the other p46 part externally)

Code: Select all

x = 43, y = 31, rule = B3/S23
17b2o$17b2o$6bo$6b3o$9bo6b2o12b3o8b2o$8b2o6b2o10bo3bo8b2o$27bo4bo$27b
o3bo2$27bo3bo$7b3o17bo4bo$12bo5bo9bo3bo8b2o$11bobo3bo12b3o8b2o$10bo6b
3o$11b2o4$5b2o$5bo2bob2o$6b3obobo$10bobo$4b7ob3o$2obobo5bo3bo$bobo4b2o
bo2b2o$bob2o4bob2o$2o4b3o$3b2obo$4bo$2bobo$2b2o!

Two pond and two block is also not trivial (akin to any other object hassler, it can't be hassle/be hassled on it's own), nor is period-multiplying. Trivial oscillators would be akin to a stable weld which puts cribbage and goban together without them interacting otherwise.

For more examples of what I would consider trivial vs non-trivial, see the page on Trivial

[ElijahKen]

Those two examples I provided were examples of where qqd's proposed formal definition disagreed with what one would expect.
A better definition would likely be something like: All omnifrequent oscillators must be non-trivial, and each rotor must have a purpose, i.e. there must not be an "interaction" between rotors where either could be removed without altering the other one. Removing a rotor simply means turning on cells off or off cells on such that none of the targeted rotor's cells remain periodic.
This definition may be insufficient, but it could help with a formal definition.
Also, smaller omnifrequent p46:

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x = 105, y = 105, rule = B3/S23
48b2o19b2o$48bobo18b2o$37bo43bo$37b3o39b3o$40bo6bo8b4o10b2o6bo$39b2o6b
2o7b2obo10b2o6b2o$59bo$57b2o16b3o$74bo3bo$39bo5bo4b2o5b2o15bo3bo$39bo
5bo2b2obo7bo15b3o$39bo5bo2bo7b2obo$48b3o5b4o$41b3o2$73bo$71bobo$72b2o
4bo$77bo2bo$77bo2bo$74bo4bo$39bobo31bobo$39b2o32b2o$40b4o$42b2o$42bobo
3$70b2o$70b2o$56b2o24bo$30b2o10b3o9b5o21b3o$31b2o20bo4bo12b2o6bo$30bo
9bo5bo6bo2b3o12b2o6b2o$40bo5bo6b2o2bo$40bo5bo8b2o2$43b2o10b2o20bo$17b
2o11b3o7b2obo9b2o2bo18b2o$2o14b2ob2o19bo7b2o3bo2b3o16b2o$2o15bo2bo7bo
5bo6bo6b2o3bo4bo18bobo$17bo2bo7bo5bo3b3o13b5o13bo$18b2o8bo5bo3bo17b2o
12bobo$49b2o20b2o$18b2o10b3o16b2o$17bo2bo$2o15bo2bo4b2o6b2o$2o14b2ob2o
4b2o6bo$17b2o15b3o$36bo43bo$24b2o53bobo$24b2o53bobo19b2o$80bo20bo$99bo
bo$24b2o73b2o$25bo11b2o54bobo$36bobo9b2o43bo2bo$15b2o17b3o11b2o36b2o5b
obo$2o12bo2bo7b2o6bo3bo38bo9bobo$2o11b2o2bo7b2o6b2o2b3o17bo3bo6b2o5b2o
9bo$14bo2bo22bo6b2o7bo5bo4bobo$15bo23b2o6b2o7bo12bo3bobo23b2o$56b2o3bo
11bobo2b3o18b2o2b2o$15bo6b3o33b3o42b2o$14bo2bo4bob2ob3o3b3o6bo$2o11b2o
2bo8bo15bo15b3o$2o12bo2bo6b2o5bo9bobo12b2o3bo$15b2o7bo6bo10bo13bo13b2o
6b2o$31bo10bo13bo5bo7b2o6bo$57bo3bo17b3o$81bo11bo5bo$69b2o21b3o3b3o$
69b2o20b2o2bobo2b2o$43bobo44bob4ob4obo$43b2o47b3o3b3o$44bo46b3o5b3o5$
36b2o$74b2o$69b2o2bobo$41bo27bo3bo4bo$40b2o28b3ob5o$40bobo29bobo$72bob
ob3o13b2o5b2o$73b2obo2bo12b2o5b2o$78b2o$69b2o$54b2o12bobo$40b3o9b5o13b
o$51bo4bo18bobo$38bo5bo6bo2b3o16b2o$38bo5bo6b2o2bo18b2o$38bo5bo8b2o20b
o2$41b2o10b2o$38b2obo9b2o2bo$38bo7b2o3bo2b3o12b2o6b2o$39bo6b2o3bo4bo
12b2o6bo$36b3o13b5o21b3o$36bo17b2o24bo$47b2o19b2o$47b2o19b2o!

[qqd]

Those two examples I provided were examples of where qqd's proposed formal definition disagreed with what one would expect.
A better definition would likely be something like: All omnifrequent oscillators must be non-trivial, and each rotor must have a purpose, i.e. there must not be an "interaction" between rotors where either could be removed without altering the other one. Removing a rotor simply means turning on cells off or off cells on such that none of the targeted rotor's cells remain periodic.
This definition may be insufficient, but it could help with a formal definition.
...

I found one way to formalize that idea, though it may not be exactly equivalent, but at least it takes care of the two problematic cases we encountered earlier, resulting in a much more promising definition:

An oscillator of a specific period, is considered to be trivial, if no cell of the oscillator oscillates at the full period, and if either of the following conditions hold for all of its phases:

1. There exists a division of its rotor cells into two types, Type 1 and Type 2, such that no 2x2 block of cells exist where at least 1 cell is of Type 1 and at least 1 cell is of Type 2.

2. There exists a division of the combination of rotor and stator cells into two types, Type A and Type B, such that both of these conditions hold:
2a. the pattern made of the cells of Type A evolves in the same way whether the Type B cells which are on in the original oscillator are turned off or not.
2b. the pattern made of the cells of Type B evolves in the same way whether the Type A cells which are on in the original oscillator are turned off or not.

Condition 1 ensures that the rotor cells of a non-trivial oscillator are all 'connected' , i.e. that none of the rotor cells are separated from the rest of the oscillator rotor, which takes care of this example, where the beacon's rotor cells (taken as Type 1, in pink and purple) are completely separated from the other rotor cells (taken as Type 2, in green and blue) below (the stator cells are in yellow):

Code: Select all

x = 43, y = 31, rule = LifeSuper
17.2E$17.EAB$6.E12.B2.B.9B.B3.4B$6.3E8.20B.4B$9.E6.EA12B3A8BAE$8.EAB
5.EA10BA3BA8BAE$8.5B4.B.8BA4BA7B.B$10.3B6.8BA3BA8B$9.5B4.2B$8.7B2.10B
A3BA8B$7.3A17BA4BA7B.B$8.4BA5BA9BA3BA8BAE$9.2BABA.B.A12B3A8BAE$10.A2B
3.B3A17B.4B$11.2A2.4B3.B.9B.B3.4B$14.4B$13.4B$12.4B$5.2E2.2B.3B$5.E2.
AB2A3B$6.3EBABA$10.A.E$4.7E.3E$2E.E.E5.E3.E$.E.E4.2E.E2.2E$.E.2E3.HE.
2E$2E4.EH$3.2E.2E$4.E$2.E.E$2.2E!

There is no 2x2 block of cells in the above pattern which contain both Type 1 and Type 2, satisfying condition 1 and therefore rendering this oscillator trivial.

Condition 2 ensures that different parts of the rotor actually interact, even if they are connected, like in this example where Type A cells (in pink and purple) do not interact with Type B cells (green and blue) and evolve independently of each other:

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x = 71, y = 64, rule = LifeSuper
44.A$39.2A3.3A$39.A2.2A3.A$40.2A2.B2A$42.2A.B$40.2A.2AB$39.A2.A2B$39.
BAB2.BA.A$39.ABA.B4AB$39.2B.B2A.2A$39.A2BA.B$38.BA.3A3.B$39.AB.A3.3A$
40.2BAB2.2A$39.A2B2.AB2AB$40.2A2.2B.A$7.2G3.2G21.A6.BA2BA$7.G3.G.G21.
3A5.ABA$4.2G.G2.GH.G.G22.A5.3B.2B9.2A$4.G2.2GH.HGH.3G19.2A6.6B8.A$6.G
3.GH.G4.G18.15B4.BA.A$7.3G.GH2GH3G11.2A7.16B.B2A$9.G.3H.G15.A6.19B$9.
HG2H2.G.2G11.A7.19B$4.2G4.H2G.2G.2G11.2A7.18B$2G.G.GH.HG2.G.G17.AB6.
4BABA9B$2G.G.3G.2G.G.G15.3A11BABA8B$3.G2.2G3.G.G15.A2.B.B2A7B3A8B$3.G
.G.H2G2.G16.2A4.2A18B$4.G.G.H.2G24.19B$6.G.G.H25.20B$6.G.GH2G2H3.H.3H
G5H.3H.H.3H2B2.14B$7.2G.2G2H.7H2G14H6.14B2.2B$11.9HGH3G15H4.20B$11.2H
2G9H2G15H4.19B$10.H.3HG7H2G15H5.18B2A4.2A$12.11HG14H7.8B3A7B2AB.B2.A$
29.3H.H.3H7.8BABA11B3A$12.11HG11H9.9BABA4B6.BA$10.H.3HG7H2G10H.H6.18B
7.2A$11.2H2G9H2G10H2G5.19B7.A$11.9HGH3G11H2G5.19B6.A$10.2G2H.7H2G8H.
4H4.2AB.16B7.2A$9.GHG2H3.H.3HG5H.H3.4H3.A.AB4.15B$9.G30.A8.6B6.2A$8.
2G29.2A9.2B.3B5.A$54.ABA5.3A$53.A2BAB6.A$52.A.2B2.2A$51.B2ABA2.2BA$
52.2A2.BA2B$51.3A3.A.BA$52.B3.3A.AB$55.B.A2BA$52.2A.2AB.2B$51.B4AB.AB
A$52.A.AB2.BAB$55.2BA2.A$54.B2A.2A$54.B.2A$53.2AB2.2A$52.A3.2A2.A$53.
3A3.2A$55.A!

This is a non-trivial (in the regular sense) p138 (Type A cells) with the p69 pi-heptomino hassler (Type B cells).

[WhiteHawk]

A first pass at p48. A lot of frequencies missing.

Code: Select all

x = 64, y = 64, rule = B3/S23
47bo$46bobo$45bo3bo$44bo3bo$43bo3bo$42bo3bo$43bobo$44bo3$34b2o5b2o$33b
o2bo4bobo$33bob2o4bo$32b2o8bo$31bo3b2o6b2o4bo$32b3o2bo4bo5bob2o10b2o$
35b2obo4b2o3bob2o6bob4o$34bo2bo11bo2bo3b3o2bobo$34b2o14b2o$44b3o3b2o6b
2o$43bo3bo11bo$42bo5bo$48bo$41bo3b2obo$45bo$42bobo$49b2o$40b2o7bo$35b
2o2bo2bo7b3o$35b2o2bo2bo9bo$40b2o3$40b2o$29bo9bo2bo2b2o$13b2o14b3o7bo
2bo2b2o$7b2o5bo17bo7b2o$7b2o5bob2o13b2o$15bobo19bobo$20b2obo12bo$6b3o
11bob2o9bob2o3bo$6bobo3b3o18bo$4bo7b2o19bo5bo$4bo5bob2o20bo3bo$4bo3bo
b2o18b2o3b3o$6b5o6bob2obo7b2o14b2o$17bo4bo6bo2bo11bo2bo$bob2obo10bob2o
bo7b2obo3b2o4bob2o$bo4bo23b2obo5bo4bo2b3o$bob2obo6b5o14bo4b2o6b2o3bo$
12b2obo3bo19bo8b2o$10b2obo5bo20bo4b2obo$10b2o7bo18bobo4bo2bo$9b3o3bob
o21b2o5b2o$2obo11b3o$ob2o$6bobo28bo$6b2obo5b2o19bobo$9bo5b2o18bo3bo$9b
2o23bo3bo$33bo3bo$32bo3bo$33bobo$34bo!

[ElijahKen]

Completed (by P1GG):

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x = 36, y = 44, rule = B3/S23
11b2o$12bo$12bob2obo$11b2obob2o$5bo$4b2o5b3o$3b2obo4bo2bo$13b2o$4bobo$
4b2obo$7bo$4b2o$5bo2b2o$5bo$2bo2bo3bo$bobo2bo8bo$2bo8bo2bobo11bo$8bo3b
o2bo10b3o$12bo12bo$8b2o2bo13bo$12b2o8bo3bo$10bo10bo$10bob2o7bo3bo$11bo
bo6b2obobo$3b2o15b2ob2o$3bo2bo4bob2o6b3o$4b3o5b2o3b2o$12bo4b2o4bo$2obo
b2o16bo$ob2obo17bo$5bo11b2o$5b2o6b2o2b2o$12bobo8bo5bo$12bo10b2o2b2o$
11b2o13bo7b2o$34b2o2$22bobo5bo$20b3obobo2b2o$19bo$20b3ob2o$22bobo$22bo
bo$23bo!

This is a smaller omnifrequent p21 (139 cells, down from 287).

[KtT]

901-cell omnifrequent p35:

Code: Select all

x = 84, y = 109, rule = B3/S23
b2o4b2ob2o$2bo4bob2obo$2bob2obo4bo14bo$2o2bobob4ob2o10b3o$bobo2bo4bo3b
o8bo$o2b2obo3bo2bobo8b2o$b2o3bo4bo3b2o$3b2o2bo4b2o8bo$3bo5bo4b2o2b2ob
obo22b2o$4bo5b4o8b2o2b2o18bobo$3b2o8bob2o9b2o15b2obo2bo5b2o$10b2obobo
27bobobobo4bobo$10b2obobo29bo4bo3bo10b2o$14bo30bob4o2b2o11bo$25b2o19b
o3bo2bo3bo6bo$25bobo19b3ob2ob4o2bo3b5obo$4b2o5b2o4bo7bo23bo4bo3b3o7bo
b3o$5bo5b2o3bo40bo6b3o6bo$5bobo8b3o31bo2bo3b2o4bo2b7o$6b2o56bobob2o$10b
2o51b2obo4b2o$9bobo54bo2b2o2bo$10bo55bobo2b2obo$34b2o27b2obobo4bobo$10b
o22b2o14bo5bo7bob2obob3o2bo$10bo9bo14bo13b2o3b2o14bo2b2o$5b2o11bobo28b
o5bo8b2obobob2o4bo$5bo2bo3bo6b2o42bob2o2b2obob4o$7b2obob3o46b3o3bobo2b
obo$10bo4bo33bo5bo4bo3b2o6bobo2b3o2b2o$6bob2obobobo2bo30b2o3b2o5b3o2b
o4b2obobobobo2bo$6b2obobo4b3o16bo13bo5bo7bobob4obobo2bob2obo$9bo2bob2o
19b3o4b3o20b3o3bo2bobobo2bo$9bo3bobob4o17bo3bo21bo6bob2obo2b2o$10bo4b
obo2bo6bobo7b2o4bo20b4obobo3bo$15bo12b2o39bob3obobo2b3o$11bo4bo11bo33b
5o3bo3b2obobo2bo$12b5o25bo14b2o2bo4bo5bo4b3obo$41b2o10bo3bo4b2o3b10o2b
2o$8bo2bobob2o25bo6b2ob2o4b3obo5bo$8b4ob2obo32bo12bob2o3b5o2b2ob2o$12b
o35bo4bobobob4o2bo2bo5bo5bo$10bobo24bo9bo3bobobo5b2o4b2obo3bo5bobo$10b
2o26bo7bo2bobobobo2bo4bobo2bo5bo2bo3b2o$36b3o7b2o3bobo4b2ob2ob2obob2o
2bo2bobo$45bo2b3obobobo2bobobobobobobo2bobobo$46bobo3bobob2ob2o5bo2bo
2b3obob2o$48b3obob2o10b6o3bo$49bo2bo4bob4ob2o6b3o$49b2obob2ob2o3b2o3b
5o$52bo2bo4bo4b2o5bo$40b3o8b2obo2b5ob2o2b2o2bobo$39bo3bo8bob3o7bo2bob
o2bo$38bo5bo7bo5b5o6b3o$32bo5bo5bo8bob3obo3b6o3b3o$31bobo4bo5bo12bo2b
2o3bo2bo2bo3bo$32bo6bo3bo10bo2b2o5bo2bo4bob2o$40b3o12bo9bob2o2b2o$58b
o2bobo4bo2bob3o$43b2o6bobo3bobo3bob2obobobo2bo$43bo8b2o4bo2bobobo2bo2b
4o$44b3o5bo6b3obo3b2o$46bo15bobo4b4o$61bo2bo4bo3bo$62b2o8b2o$72bo$70b
obo$61bo8b2o$62bo$60b3o$67bo$66b2o$50bo14b2o$50b3o$53bo4b2o$52bo2b2o4b
o$52b3o5bo$50b2o4bo15b2o$51bob2obobo14bo$51bo2bobob3o12bob2o$52bo2bob
o3bo4b2o4b2obo2bo$53b2o2bo2b2o3bobo7bob2o$57b2o6bo9bo$64b2o8b2o$60bo6b
o$59bobo3b2o$60bo4bo$68b3o$67bo$65b2o3bo$65bob3o$66bo4$61b2o$63bo2b2o
$63bo2b2o$62b2o$60bo$60bobobo$60bo3b2o$61b2o3bo$62bobobo$66bo$63b2o$59b
2o2bo$59b2o2bo$64b2o!

[WhiteHawk]

Over 100-cell reduction of omnifrequent p28 (171 cells)

Code: Select all

x = 40, y = 51, rule = B3/S23
33b2o$25bo6bobo3b2o$25b2o4bo2bo3b2o$29bo3bo$29bobo2$29bobo$29bo3bo$25b
2o4bo2bo3b2o$25bo6bobo3b2o$33b2o3$28b2o$28b3o$23b2o2bo2bo$23b2o2bo2bo
$28b2o3$28b2o$27bo2bo2b2o$7b2o8bo9bo2bo2b2o$3b2obobo2bo5b3o7b3o$4bobo
4b3o6bo7b2o$4bob2o6bo4b2o$3b2o2bo5b2o$2bo2b2o15bo4b2o$3bobo15bobo3b2o
$2b2obo15bo$o2bob2o8b3o4bobo$2obo12bo6b2o$3bo5b3o$3b2o5bo3$5bo$4bobo15b
o$4bo2bo9b2o3b2o$11bo5b2o3b2o$11bo10bo$5bo2bo2bo8bo2bo$6b2o12bob3o$19b
2o3bo$18bo3b2o$18b3obo$19bo2bo$20bo$19b2o3b2o$19b2o3b2o$20bo!

EDIT:
Reduction of omnifrequent p46

Code: Select all

x = 103, y = 105, rule = B3/S23
48b2o19b2o$48bobo18b2o$37bo43bo$37b3o39b3o$40bo6bo8b4o10b2o6bo$39b2o6b
2o7b2obo10b2o6b2o$59bo$57b2o16b3o$74bo3bo$39bo5bo4b2o5b2o15bo3bo$39bo
5bo2b2obo7bo15b3o$39bo5bo2bo7b2obo$48b3o5b4o$41b3o2$73bo$71bobo$72b2o
4bo$77bo2bo$77bo2bo$74bo4bo$39bobo31bobo$39b2o32b2o$40b4o$42b2o$42bob
o3$70b2o$70b2o$56b2o24bo$30b2o10b3o9b5o21b3o$31b2o20bo4bo12b2o6bo$30b
o9bo5bo6bo2b3o12b2o6b2o$40bo5bo6b2o2bo$40bo5bo8b2o2$43b2o10b2o20bo$17b
2o11b3o7b2obo9b2o2bo18b2o$2o14b2ob2o19bo7b2o3bo2b3o16b2o$2o15bo2bo7bo
5bo6bo6b2o3bo4bo18bobo$17bo2bo7bo5bo3b3o13b5o13bo$18b2o8bo5bo3bo17b2o
12bobo$49b2o20b2o$18b2o10b3o16b2o$17bo2bo$2o15bo2bo4b2o6b2o$2o14b2ob2o
4b2o6bo$17b2o15b3o$36bo43bo18b2o$24b2o53bobo17bo$24b2o53bobo15bobo$80b
o11b2o3b2o$94bo$24b2o69bo$25bo11b2o53bobo$36bobo9b2o43bo$15b2o17b3o11b
2o36b2o$2o12bo2bo7b2o6bo3bo38bo9bobo$2o11b2o2bo7b2o6b2o2b3o17bo3bo6b2o
5b2o9bo10b2o$14bo2bo22bo6b2o7bo5bo4bobo27b2o2b2o$15bo23b2o6b2o7bo12bo
3bobo25b2o$56b2o3bo11bobo2b3o$15bo6b3o33b3o$14bo2bo4bob2ob3o3b3o6bo$2o
11b2o2bo8bo15bo15b3o$2o12bo2bo6b2o5bo9bobo12b2o3bo$15b2o7bo6bo10bo13b
o13b2o6b2o$31bo10bo13bo5bo7b2o6bo$57bo3bo17b3o$81bo$69b2o19b2o5b2o$69b
2o18bo2bo3bo2bo$43bobo46b2ob2o$43b2o46bobobobo$34bo9bo46bobobobo$32bo
bo54bo9bo$33b2o53bo11bo$36bo$35bobo54b2ob2o$35bobo52bo2bobo2bo$36bo37b
2o14b3o3b3o$69b2o2bobo$41bo27bo3bo4bo$40b2o28b3ob5o11b2o5b2o$40bobo29b
obo15b2o5b2o$72bobob3o$73b2obo2bo$78b2o$69b2o$54b2o12bobo$40b3o9b5o13b
o$51bo4bo18bobo$38bo5bo6bo2b3o16b2o$38bo5bo6b2o2bo18b2o$38bo5bo8b2o20b
o2$41b2o10b2o$38b2obo9b2o2bo$38bo7b2o3bo2b3o12b2o6b2o$39bo6b2o3bo4bo12b
2o6bo$36b3o13b5o21b3o$36bo17b2o24bo$47b2o19b2o$47b2o19b2o!

[Sokwe]

901-cell omnifrequent p35:

Here is a smaller example (810 cells) that uses the same basic components, but utilizes the smaller form of the p35 gun:

Code: Select all

x = 104, y = 63, rule = B3/S23
53b2ob2o4b2o$24b2o26bob2obo4bo$23bobo11bo14bo4bob2obo$15b2o5bo2bob2o8b
3o10b2ob4obobo2b2o$15bobo4bobobobo11bo8bo3bo4bo2bobo$17bo3bo4bo12b2o8b
obo2bo3bob2o2bo$17b2o2b4obo21b2o3bo4bo3b2o$14bo3bo2bo3bo16bo8b2o4bo2b
2o$11bo2b4ob2ob3o16bobob2o2b2o4bo5bo$11b3o3bo4bo14b2o2b2o8b4o5bo$14bo
22b2o9b2obo8b2o$13b2o3bo2bo27bobob2o$bo2bo44bobob2o10b2o$b4o2bo42bo11b
2o2bo2b2o$5b3o54bo3bobo2bo$b3o40bobo16b3obobo2bo$o2bob3o28b2o7b2o9bo8b
obob2obo$bob3o2bo7bo5bo14b2o6bo10b3o6bobo4b2o$2obo3b2o2bo4b2o3b2o13bo
22bo6bo2b3o$2bo2b2o2b3o4bo5bo35b2o7b2o2bo$2bobob2o54b3o5bo$b2o5b2o61b
3o$o2bobobo2bo5bo5bo37bo12bo$2obobobob2o5b2o3b2o31bo5b2o$2bobo2bo8bo5b
o13bo18bo$2bobob2o19b3o4b3o16b3o5bobo3b2o$2ob2o2bob2o18bo3bo27bobo3bob
o$bobobobobo18bo4b2o34bo$bobobobobo59b2o$2bobob2ob2o$3bo6bo2b2o14bo$7b
3o4bo4bo9b2o$6b2obo2b2o3b3o9bo32b3o$4b2ob2obo3b2o5b3o13bo$7bobo4b2o6bo
12b3o24bo17bo20b2o$7bobo4bo2bo5bo10bo26bobo15bobo13b2o4b2o$6b2ob2ob2o
2bo2bo3b2o6b2o2bo25bobo16bo10b2ob2obo$3b2o4bo2bo7b2o3bo4bo2b2obo24b3o
26b4obob3o$3b3obobo4b3obo4b2o3b2o6b3o$5bo2bo3b2o2b7o4bobo3b3o3bo13bo4b
2o10bo23b3obob4o$3b3o2bo8bo6b4obobo4bob2o12bobo3b2o10b2o24bob2ob2o$5bo
11b2o2b2obo3bo2bo2b3obo14bo16bobo5b3o10b2o4b2o$3b2o9b2ob2obobobob2o3bo
6bo30bo14b2o5b2o$bo3b2o2b2obob2o6bobobo4bob4ob2o38bobo2bo2bo$b4o5bob7o
3bobobo4bo4bo27b2o8b2o3bo4b2o$5b5o5b2ob4obobo4b2ob2obo27bo$3bobo9bo7bo
5b2o2bob2obo26b3o5bo$b3o3b3o7bob5o4b2o3bo3b2o28bo4bo$o4bo3bo7bobo7b2o
2b2ob2o36b5o$b8o6bo2bo2bo5b2obo3bo43bo$2bo6b3ob4obob2o6bo2b2o2bo38b5o$
o3bo3bo3b2o3bobo6bobo4b2o39bo$5obo2b2o4b2o2bo4b3obo2b2o43bo$5bob2o2b4o
bobob2obo5b2obob3o38b2o$2b2obobo2bo2bo2bobo2bob2o5bobobo2bo$2bobo4b2o
4b2ob2obo2bo4b2obo3b2o$18bo2b3o3b2obo2bo$18bobo2bo3b2obob2o$19b2ob2o3b
o2bobo$22bo5bobobo$22bobo2b2ob2o$23bobo$24bo!

I made no attempt to reorder, reorient, or rephase the components to minimize the population, so this can certainly be reduced further.

[WhiteHawk]

Omnifrequent p39 - 100% reducible (EDIT: Removed one column of p39 hasslers, but still probably reducible)

Code: Select all

x = 154, y = 176, rule = B3/S23
89b2o$86b2o2bo2b2o$86bo3bobo2bo$87b3obobo2bo$80bo8bobob2obo$80b3o6bob
o4b2o$83bo6bo2b3o$82b2o7b2o2bo$86b3o5bo$95b3o$56b2o26bo12bo$52b2obobo
8bo17bo$53bobo8b3o17bo$53bob2o6bo28b2o$50b2obo9b2o3bo17b3o3bobo$50bo2b
4o10bobo3b2o11bo7bo$51b2o3bo11bo4b2o9b2o8b2o$53b3o28bo2bo3bo$53bo4bo5b
o4bo7bo5bo3bo2bobo$51bobo4bo5bo2b3o7b3o4bo2b2o2bo$51b2o5bo5b2o4bo5bo3b
o5bo$66bo4bo3bo4bo3b2o$60b3o3b2obobo3bobob2o$56b2o10bo9bo11b2o$55bobo
32b2o$55bo28b2o52b2o$54b2o14b3o13bo46b2o2bobo$69bo2bo11bo2b2o44bo3bo4b
o$69bo3bo9bo3bo46b3ob5o$68b2o2bo11bo2bo39bo8bo$70bo13b3o14b2o24b3o6bo
b5o$71b2o28bo28bo6b2obo2bo$65b2o32bobo27b2o11b2o$65b2o11bo9bo10b2o$76b
2obobo3bobob2o3b3o37bo$71b2o3bo4bo3bo4bo42b3o$70bo5bo3bo5bo4b2o5bo14b
o18b2ob2o$65bo2b2o2bo4b3o7b3o2bo5bo12b3o19b3o$64bobo2bo3bo5bo7bo4bo5b
o11bo23bo4b2o$65bo3bo2bo28b2o7b2o3bo23bobo$61b2o8b2o9b2o4bo11bo2bo10b
obo3b2o19bo$62bo7bo11b2o3bobo10bobo12bo4b2o19b2o$62bobo3b3o17bo3b2o7b
o6bo29bo$63b2o28bo13b3o27bobo$72bo17b3o13b2ob2o27bo$72bo17bo16b3o9b3o
$72bo35bo9bo3bo8b2o$118b2ob2o3b2o3bobo$68b3o32b2o28bo3b2o$73b2o27bobo
26bobo3b2o$65b2o6bo28bo28b2o$55bo8bo2bo6b3o24b2o16bo$55b3o7bobo8bo42b
o$58bo7bo$57b2o72bo$131bo16b2o$118b2o28bo$31b2o28b3o48b2o3bobo26bobo$
27b2obobo8bo19bobo48b2o3bo28b2o$28bobo8b3o19b3o53bobo3b2o3b2ob2o$28bo
b2o6bo28b2o49b2o8bo3bo9bo$25b2obo9b2o3bo23bobo59b3o9b3o7b2o$25bo2b4o10b
obo3b2o19bo42bo27b2ob2o5bobo$26b2o3bo11bo4b2o19b2o40bobo27b3o6bo$28b3o
35bo45bo29bo5b3o$28bo6b3o27bobo40b2o19b2o4bo11bo3b2o$26bobo6bobo28bo42b
o19b2o3bobo10b2obo2bo$26b2o7b3o10bo60bobo23bo3b2o7bobob2o$47bobo5bo3b
o50b2o4bo23bo6b2obo$46b2ob2o3bobo2b2o54b3o19b3o8bobo$31b2o21bo6bo3b2o
47b2ob2o18bo8bobob2o$30bobo22bo3b2o4b2o48b3o28b2o$30bo16bo11bo56bo$29b
2o15bo2bo$47b2o71b2o$112bo7bo$58b2o42bo8bobo7b3o$57bo2bo15b2o24b3o9bo
8bo$47bo11bo16bo28bo3bo3bo$40b2o4b2o3bo22bobo27b2o$40b2o3bo6bo21b2o33b
obo$46b2o2bobo3b2ob2o$47bo3bo5bobo47b2o$58bo10b3o16bo17b4o$40bo28bobo
14b3o17bo2bo$39bobo27b3o13bo21b2o5b2o$40bo36bo7b2o3bo23bobo$36b2o19b2o
4bo12bobo10bobo3b2o19bo$37bo19b2o3bobo10bo14bo4b2o19b2o$37bobo23bo3b2o
7bo3bo32bo$38b2o28bo43bobo$43b3o19b3o10bobo2b2o12b2o14bo$43bobo19bo16b
2obo10bo6b2o$43b3o36b2obo10b3o3b3o$83b2o9bo10b2o$78b2o14b3o3b3ob2o6b2o
$48b2o27bobo12b2ob2o3bobob2ob2o3b2o$40bo7bo28bo14b2o13bobo$30bo8bobo7b
3o24b2o15bob2o10bobo$30b3o6bo2bo8bo43bo$33bo6b2o53b2o7b2o$32b2o71bo$36b
3o52bobo10b2obo15b2o$91bobo13b2o14bo$6b2o26bo52b2o3b2ob2obobo3b2ob2o12b
obo$2b2obobo8bo17b2o51b2o6b2ob3o3b3o14b2o$3bobo8b3o77b2o10bo9b2o$3bob
2o6bo21bobo4b2o52b3o3b3o10bob2o$2obo9b2o3bo19bo3bobo51b2o6bo10bob2o7b
2o$o2b4o10bobo3b2o11b2o6bo42bo14b2o12b2o2bobo2bobo$b2o3bo10b3o3b2o19b
2o40bobo36bo$3b3o12b2o20b2o45bo32bo3b2o$3bo4bo5bo3b3o11bobo3b3obo40b2o
19b2o4bo15b2o$bobo4bo4bobo3b2o9bo5b6o42bo19b2o3bobo10b4o2bo$b2o5bo6bo
3b2o9bo3b5o45bobo23bo3b2o9bob2o$11bobo6bo5bobo4bo51b2o5b2o21bo6b2obo$
10b2o6bobo5bo4b2o58bo2bo17b3o8bobo$6b2o13bo4bo13b2o49b4o17bo8bobob2o$
5bobo10bo3bo5bo11b2o50b2o27b2o$5bo16bo$4b2o13b2o12b3o53bobo$95b2o$21b
o2bo7bo2bo51bo3bo3bo$77bo8bo9b3o$21b3o12b2o13b2o24b3o7bobo8bo$34bo16b
o28bo7bo$15b2o11bo5bo3bo10bobo27b2o$15b2o13bo4bo13b2o$24b2o4bo5bobo6b
2o$23bo4bobo5bo6bobo37bobo$18b5o3bo9b2o3bo6bo14bo18bo2bo$15b6o5bo9b2o
3bobo4bo12b3o19bobo$14bob3o3bobo11b3o3bo5bo11bo28b2o$15b2o20b2o12b2o7b
2o3bo23bobo$11b2o19b2o3b3o10bo2bo10bobo3b2o19bo$12bo6b2o11b2o3bobo10b
obo12bo4b2o19b2o$12bobo3bo19bo3b2o7bo36bo$13b2o4bobo21bo13b3o27bobo$40b
3o45bo$21b2o17bo16bobo$22bo35bo10b3o$69b3o4b2o3b2o$18b3o32b2o22bobob2o
4b2o$10b2o11b2o27bobo15bo7bo2b2o4b2o$10bo2bob2o6bo28bo18bo$11b3obobo6b
3o24b2o16b2o$15bobo8bo42bo$11b5ob3o$11bo4bo3bo60bo$14bobo2b2o59b2o16b
2o$14b2o63bo18bo$62b2o4b2o2bo7bo15bobo$62b2o4b2obobo22b2o$68b2o3b2o4b
3o$79b3o10bo$91bobo7b2o$62bo37bobo$61bobo27b3o6bo$62bo35b3o$58b2o19b2o
4bo11bo3b2o$59bo19b2o3bobo9bo2b2o2bo$59bobo23bo3b2o5bobobob2o$60b2o28b
o6b2obo$65bobo19b3o8bobo$65bo2bo18bo8bobob2o$65bobo28b2o3$57b2o2b2o7b
2o$57bo2bo2bo6bo$58b4o2bo6b3o$62bobo8bo$58b5ob3o$58bo4bo3bo$61bobo2b2o
$61b2o!

EDIT: even more almost p40, missing F=27

Code: Select all

x = 80, y = 82, 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$3b2o4bo5bo$3bo2bo2bo5bo$4b2obo2bo3bo14b2o$b3o2bo4b3o15b2o$o3b
2o$b2o$2bob2o14b2o$2bo2bo14bo6b4o11b2o$3b2o16b3o2b2ob4o6b2o2bo$23bo3b
o4bo6bo3b2o$7b2o6bo11b4o2bo4bo2b4o$8bo7bo10b2o3bo6bo4bo$5b3o6b3o11bo2b
2o6b4ob2o$5bo22b2o11b4o$48b3o$47bob2o6bo5b2o$46b2o9b2o4b2o$41b2o4b2o9b
2o$41b2o5bo6b2obo$55b3o$25bo35b4o11b2o$26bo33b2ob4o6b2o2bo$24b3o16bo17b
o4bo6bo3b2o$42b2o17b4o2bo4bo2b4o$41bob3o15b2o3bo6bo4bo$41b2o19bo2b2o6b
4ob2o$42b3o17b2o11b4o$43b2o4bo$44bo4b2o$49b3o$35bo15b2o22b2o$36bo11b3o
bo22b2o$34b3o13b2o$50bo3$46b2o$41b2obo2bo2bo$40bobob2obobobo$37bo2bob
o4bo2bo$37b4ob4obo$41bo4bo$39bobo2bo$39b2o3b2o!

EDIT 2: reduced p30, 134 cells

Code: Select all

x = 39, y = 39, rule = B3/S23
13b2o$13bo$14b3ob2o$16bobo3b2o$18bo4bo$18bob3o$12b2o3b2obo$12bobo11bo
$13bo11bobo$10bo7b2o4bob2o6b2o$10b6o2b2o3b2ob2o5bo2bo$15bo8bob2o6b2o$
12b2o11bobo$12bo13bo$14bo20bo$13b2o19b3o$33bo3bo$35bo$32bo5bo$32bo5bo
$33bo3bo$34b3o$8bo$7bobo$2o4bob2o15b2o$2o3b2ob2o14bobo8bo$6bob2o13bo6b
2o2bobo$7bobo13bo2bo2bo2bobobo$8bo5bo8bo6b2o3bo$14bobo7bobo$14b2o9b2o
$5b2o$5bo2bob2o$6b3obobo$10bobo$6b5ob3o$6bo4bo3bo$9bobo2b2o$9b2o!

Reduced p35, 807 cells

Code: Select all

x = 100, y = 62, rule = B3/S23
24b2o$23bobo$15b2o5bo2bob2o$15bobo4bobobobo20b2ob2o4b2o$17bo3bo4bo21b
ob2obo4bo$17b2o2b4obo6bo14bo4bob2obo$14bo3bo2bo3bo7b3o10b2ob4obobo2b2o
$11bo2b4ob2ob3o11bo8bobo4bobo2bobo$11b3o3bo4bo12b2o8bobo2bo5b2o2bo$14b
o29b2obo2bo2b2o3b2o$13b2o3bo2bo16bo5bo2b3o6b2o$bo2bo32bobo5b2o3bo6bo$
b4o2bo25b2o2b2o5bo2b4o5bo$5b3o25b2o9b2obo8b2o$b3o41bobob2o$o2bob3o28b
2o7bobob2o10b2o$bob3o2bo7bo5bo14b2o7bo11b2o2bo2b2o$2obo3b2o2bo4b2o3b2o
13bo21bo3bobo2bo$2bo2b2o2b3o4bo5bo36b3obobo2bo$2bobob2o44bo8bobob2obo
$b2o5b2o42b3o7bo5b2o$o2bobobo2bo5bo5bo32bo6bo3b2o$2obobobob2o5b2o3b2o
21bobo7b2o7bo3bo$2bobo2bo8bo5bo13bo8b2o19bo$2bobob2o19b3o4b3o8bo21b3o
$2ob2o2bob2o18bo3bo25bo9bo$bobobobobo18bo4b2o23b2o$bobobobobo49bo$2bo
bob2ob2o52b2o$3bo6bo2b2o14bo33bobo$7b3o4bo4bo9b2o23bo10bo$6b2obo2b2o3b
3o9bo25bo9b2o$4b2ob2obo3b2o5b3o13bo15b3o$7bobo4b2o6bo12b3o$7bobo4bo2b
o5bo10bo$6b2ob2ob2o2bo2bo3b2o6b2o2bo$3b2o4bo2bo7b2o3bo4bo2b2obo$3b3ob
obo4b3obo4b2o3b2o6b3o37bo14bo5b2o$5bo2bo3b2o2b7o4bobo3b3o3bo35bobo13b
2o4b2o$3b3o2bo8bo6b4obobo4bob2o17b3o16bo16b2o$5bo11b2o2b2obo3bo2bo2b3o
bo17bo3bo25bo2b2ob3o2bo$3b2o9b2ob2obobobob2o3bo6bo16bo5bo25b3obo2bob3o
$bo3b2o2b2obob2o6bobobo4bob4ob2o9bo5bo5bo12b2o12bo2b3ob2o2bo$b4o5bob7o
3bobobo4bo4bo11bobo4bo5bo10b3ob2o2b2o9b2o$5b5o5b2ob4obobo4b2ob2obo12b
o6bo3bo10bo2bob2obo2bo4b2o4b2o$3bobo9bo7bo5b2o2bob2obo18b3o11b2o6bob2o
4b2o5bo$b3o3b3o7bob5o4b2o3bo3b2o39b2ob2o$o4bo3bo7bobo7b2o2b2ob2o24b2o
15b2ob2o$b8o6bo2bo2bo5b2obo3bo25bo18bo$2bo6b3ob4obob2o6bo2b2o2bo25b3o
$o3bo3bo3b2o3bobo6bobo4b2o28bo4bo2bo$5obo2b2o4b2o2bo4b3obo2b2o35b4o$5b
ob2o2b4obobob2obo5b2obob3o37bo$2b2obobo2bo2bo2bobo2bob2o5bobobo2bo32b
5o$2bobo4b2o4b2ob2obo2bo4b2obo3b2o32bo$18bo2b3o3b2obo2bo38bo$18bobo2b
o3b2obob2o37b2o$19b2ob2o3bo2bobo$22bo5bobobo$22bobo2b2ob2o$23bobo$24b
o!

EDIT 3: Close attempt at p43, only missing F=33 and F=30

Code: Select all

x = 115, y = 87, rule = B3/S23
69b2o3b2o$70bo2bobo$68bo4bo$67bob4ob4o$54b2o8bo2bo4bobo2bo$52b3o8bobo
bob2obobo6bo$47b2o2bo4bo7bo2bo2bob2o7b3o$47bo3bob2ob3o8b2o15bo$48b3ob
obo4bo23b2o$50bobo3b3o$50bobobobo$45bo5b2ob2o11bo12bo14bo$45b3o18b2o11b
2o8b2o3bobo$48bo16b3o11bobo7b2o4bo$47b2o6b2o4b2o3b2o$55b2o4bo2bo2bo6b
2o$51b2o21bo2b2o4b3o$23bo27b2o22b2obo4bo$22bobo19b2o13bo4bo18bob2o$20b
3obo19b2o13bo2b2o11b3o8bo8bo$19bo4bob2o23b2o6b2o14bo2bo5b2ob3o4bobo$19b
obobobobo9b2o9b2o2bo13b2o8bobo4b3ob2o5bo2bo$20b2obobo11b2o8bo4bo13b2o
9bo8bo8b3o$24bobo32b2o25b2obo$25bo33b2o28bo4bob2o$37b2o4b2o2bo2bo4b2o
30b3o4b2o2bo$2o10bo23bo2bo2bo2bo3b2o4b2o6b2o32b2o$bo8b2ob2o4b3o10bo3b
o2bo2bo2bo17bo$bobo6b2ob2o4bo2bobo5bo3bo2b2o4b2o19b3o10bo4b2o7bobo13b
2o$2b2o8bo2bo4bo2bobo3bo26b2ob2o5bo9bobo3b2o8b2o13bo$6b3o4b2o8bobo2bo
5bo20bobobobo15bo14bo12bobo$9bo18bo3b2o9b2o8b3o3bobo43b2o$6bo3bo17bo3b
o10b2o7bo4bobob3o36bobo$5b2o3bo18bo23b3ob2obo3bo23b2o10bo2bo$4bo5bo2b
obo8b2o4b3o22bo4bo2b2o23bo11bo2bo$9bo3bobo2bo4bo2bo8b2o20b3o29b3o9b2o
$4bo3bo5bobo2bo4b2ob2o6bobo18b2o33bo5bo10bo$6bo10b3o4b2ob2o8bo57b2o9b
3o$26bo10b2o57b2o7bo$105b2o$13bo78b2o$12bobo76bobo9bo$13bobob2o72bo11b
o$11bobobobobo70b2o11bo$11b2obo4bo$14bob3o$14bobo73b2o16b2o$15bo75bo16b
2o$91bobo$92b2o3$101bo$100b3o$100bob2o$103b2o$100bob2o$100b3o8b2o$101b
o9bobo$113bo$113b2o2$88b2o$89bo$89bobo9bo$90b2o8b3o$99b2obo$98b2o$99b
2obo$100b3o$101bo3$109b2o$109bobo$93b2o16bo$93b2o16b2o3$99bo$99bo$99b
o2$96b2o$97bo$94b3o$94bo!

EDIT 4: Surprise reduction to p10 (39 cells) and p15 (79 cells)

Code: Select all

x = 15, y = 14, rule = B3/S23
2b2o$3bo2b2o$3bobobo$2b2obo$o2bo2bo$2o3bo$9b2o$8bobo2bo$6bobobobobo$5b
o4bo2bo$5b4obo$9bo$7bo$7b2o!

Code: Select all

x = 25, y = 20, rule = B3/S23
23bo$8bo14bo$8b3o11b3o$11bo$4b2o4b2o$5bo16b3o$5bobo15bo$6b2o4b2o9bo$11b
o2bo2bo5bo$17bo5bo$9bo12b3o$2b2o8b3obo$2bo6b2o$7bo14b3o$6obo7b2o6bo$o
14bo7bo$b2ob2o3b2o5b3o$2bobo4bobo6bo$2bobo6bo$3bo7b2o!

EDIT 5: P40 improved, missing only F=27

Code: Select all

x = 77, y = 82, rule = B3/S23
37b2o$30b2o5bo$31bo2b2obo21b2o$31bobo2bo23bo5b2o$32bobo15bo9bob2obobo
$34b2o2b2o10b3o8bobobo$33bo5bo13bo9bobobo$34b5o13b2o8bobo2bo$62bo3b2o
$34b2ob4o$34b2obo2bo22bo3bo$20b2o45bo$20bo5b3o37bo$21bo3bo3bo27b5o5b3o
$18b3o3bo5bo25bo2b3o7bo$18bo4bo3bo3bo23bo3bo$26bobo2bo14bo8bo$27bo3bo
7bo6bobo7bobo$21bo8bo7b2o6b2o8bobo$20bob2obo3bo8bobo11b2o$20bo5b3o24b
o6b2o2b2o$19b2o29b3o5b3ob2ob3o$44bo5bo6bo10bo$42b5o9bob2ob2ob2ob2o$34b
2o5b3ob2o9bobo2bo3bobo$34b2o6bo2b2o7bobo2b3o3bobo$43b3o8b2obo2bo5bo$44b
3o10bobo$11b2o6bo13bob2o9b2o9b2o$11b2o6bobo11bobo10bo$19b2o13bo12b3o$
34b2o13bo$34b2o$11b3o7b2o11b2o$10bo3bo6b2o$10bo3bo$9b2o4b2o$8bo3bo4bo
$3b2o2b2o2bobo3bo$3bo2bobo3bo4bo$4b2o2bo2bo3b2o12b2o$b3o3bo3bo2bo14b2o
$o3b3o7bo$b2o8b3o$2bob2o14b2o18bo$2bo2bo14bo18bo2bo$3b2o16b3o18bo$23b
o14b2obo$7b2o23b2o4b2o$8bo7bo13bob2o$5b3o9bo11bo18bo$5bo9b3o11bo2bo11b
o3b2o$31bo16bobo6bo$49b3o5b3o3b2o$45b2o9b5o2b2o$41b2o2b5o9b2o$41b2o3b
3o5b3o$48bo6bobo16bo$56b2o3bo11bo2bo$26bo30bo18bo$27bo44b2obo$25b3o38b
2o4b2o$43b3o18bob2o$41bob3o17bo$40bob3obo16bo2bo$41b5o3b3o13bo$42b3o3b
5o$47bob3obo$48b3obo22b2o$36bo11b3o24b2o$37bo$35b3o3$46b2o$41b2obo2bo
2bo$40bobob2obobobo$37bo2bobo4bo2bo$37b4ob4obo$41bo4bo$39bobo2bo$39b2o
3b2o!

[KtT]

EDIT 5: P40 improved, missing only F=27

Code: Select all

x = 77, y = 82, rule = B3/S23
37b2o$30b2o5bo$31bo2b2obo21b2o$31bobo2bo23bo5b2o$32bobo15bo9bob2obobo
$34b2o2b2o10b3o8bobobo$33bo5bo13bo9bobobo$34b5o13b2o8bobo2bo$62bo3b2o
$34b2ob4o$34b2obo2bo22bo3bo$20b2o45bo$20bo5b3o37bo$21bo3bo3bo27b5o5b3o
$18b3o3bo5bo25bo2b3o7bo$18bo4bo3bo3bo23bo3bo$26bobo2bo14bo8bo$27bo3bo
7bo6bobo7bobo$21bo8bo7b2o6b2o8bobo$20bob2obo3bo8bobo11b2o$20bo5b3o24b
o6b2o2b2o$19b2o29b3o5b3ob2ob3o$44bo5bo6bo10bo$42b5o9bob2ob2ob2ob2o$34b
2o5b3ob2o9bobo2bo3bobo$34b2o6bo2b2o7bobo2b3o3bobo$43b3o8b2obo2bo5bo$44b
3o10bobo$11b2o6bo13bob2o9b2o9b2o$11b2o6bobo11bobo10bo$19b2o13bo12b3o$
34b2o13bo$34b2o$11b3o7b2o11b2o$10bo3bo6b2o$10bo3bo$9b2o4b2o$8bo3bo4bo
$3b2o2b2o2bobo3bo$3bo2bobo3bo4bo$4b2o2bo2bo3b2o12b2o$b3o3bo3bo2bo14b2o
$o3b3o7bo$b2o8b3o$2bob2o14b2o18bo$2bo2bo14bo18bo2bo$3b2o16b3o18bo$23b
o14b2obo$7b2o23b2o4b2o$8bo7bo13bob2o$5b3o9bo11bo18bo$5bo9b3o11bo2bo11b
o3b2o$31bo16bobo6bo$49b3o5b3o3b2o$45b2o9b5o2b2o$41b2o2b5o9b2o$41b2o3b
3o5b3o$48bo6bobo16bo$56b2o3bo11bo2bo$26bo30bo18bo$27bo44b2obo$25b3o38b
2o4b2o$43b3o18bob2o$41bob3o17bo$40bob3obo16bo2bo$41b5o3b3o13bo$42b3o3b
5o$47bob3obo$48b3obo22b2o$36bo11b3o24b2o$37bo$35b3o3$46b2o$41b2obo2bo
2bo$40bobob2obobobo$37bo2bobo4bo2bo$37b4ob4obo$41bo4bo$39bobo2bo$39b2o
3b2o!

466-cell omnifrequent p40:

Code: Select all

x = 74, y = 117, rule = B3/S23
48b2o$41b2o5bo$42bo2b2obo$42bobo2bo$43bobo$45b2o2b2o$44bo5bo$45b5o$39b
2o$36b2o7b2ob4o19b2o$39bob2o2b2obo2bo9bo8bobo$31b2ob2ob2ob3o17bobob2o
4bo$31bob3o2bo3b2o8bo8bob3ob2o$32bob2obob2o2b2o7b3o8bo3b2o$29b3o7b3o2b
o10bo7b4o4b3o$29bo6b3o2bo12b2o8bob3o$43b3o20bobo$67bo$32b2o24bo$31bob
o22b2obo$31bo24bo2bo11bo$30b2o24b3o10b3o$36bo31bo$27b2o7bobo29b2o$27b
2o7b2o2$65b3o2bo$54b2o8bo2b2o$37b2o16bo9bobo$37b2o13b3o8bobobo$27b3o22b
o9bob2obobo$26bo3bo31bo5b2o$25bo5bo29b2o$19b2o4bo5bo$19bo2bo2bo5bo$20b
2obo2bo3bo$17b3o2bo4b3o$2o8b2o4bo3b2o$2o9bo5b2o$8bo9bob2o14b2o$7bo3bo
6bo2bo14bo$8bobo8b2o16b3o$9bo29bo$23b2o6bo$24bo7bo$7bo13b3o6b3o4b2o$6b
obo12bo16bo$5bo3bo28bob2o$8bo27b3o2bo$5bo9b2o6bo11bo3b2o$5b2o8b2o5b2o
11b4o$21b2o15bo$21b2o12b2obob2o$22b2o12bobo2bo$23bo3bo6bo4bo$10b3o11b
o3bo5b5o$10bobo15b2o$10bo2b2o14b2o5bo$13bo15b2o4bobo$12b2o14b2o6bo$28b
o2$16b2o$16bo$15b2o2bo$17bobo$17b3o5$13b2o8b2o$13b2o9bo$21bo$20bo3bo$
21bobo$22bo3$20bo$19bobo$18bo3bo$21bo$18bo9b2o$18b2o8b2o3$8b2o$8bobo$
10bo12bobo$10b2o11bobo$12bo11bo$10b2obo$9bo2bo5b3o$9b2o6bo2bo$16b2ob2o
5bo4b2o$17bobo6bo4b2o5$15b2o4bo6bobo$15b2o4bo5b2ob2o$27bo2bo6b2o$27b3o
5bo2bo$34bob2o$35bo$23bo12b2o$23bo13bo$37bobo$38b2o$19b3o$19b3o$19b3o
$16b3o$16b3o$16b3o!

EDIT:440-cells:

Code: Select all

x = 88, y = 80, rule = B3/S23
22b2o$20bob2o$19bo$22bo40b2o$18b2obo34b2o5bo$18b2o37bo2b2obo$2o55bobo
2bo$obo55bobo$2bo57b2o2b2o$2b2o55bo5bo$4bo55b5o$2b2obo3b2ob2o$bo2bo4b
o4b2o44b2ob4o19b2o$b2o7bobob2o44b2obo2bo9bo8bobo$12bob2o7b2o21b2o27bo
bo2b2o2bobo$13bo9b2o21bo20bo8bo3bob3o$47bo19b3o13bo3bo$44b3o23bo7bo8b
o$44bo8bo15b2o7b2o3bo3bo$52b3o25b2obo$7b2o9bo33bobo27bo$7b2o7b2obo27b
2o4b2o$16b2obobo7b2o15bobo18bo7b3o$16b2o4bo4bo2bo15bo19b2o7bo2bo7bo$18b
2ob2o3bob2o15b2o19bobo7b3o5b3o$27bo55bo$28b2o12b2o39b2o$29bo12b2o$29b
obo$30b2o14b2o32b3o2bo$49bo19b2o8bo2b2o$44bo3bo3b2o16bo9bobo$10b2o31b
o8b2o13b3o8bobobo$10b2o31b2ob2o19bo9bob2obobo$18bobo23bobo30bo5b2o$16b
3ob2o23bo30b2o$20b3o11b2o13b3o$34bo2bo13bo$35b2obo4bo4bob2o$32b3o2bo5b
2o3b2o$31bo3b2o4bobo$14b3o15b2o9bo$15b2ob3o12bob2o4bo9b2o$16bobo14bo2b
o4b3o7bo$25b2o7b2o16b3o$25b2o27bo$38b2o$39bo$36b3o13b2o$22bo13bo16bo$
21bo2bo28bob2o$19b2o3bo26b3o2bo$19bo5bo11b2o11bo3b2o$19b3o2bo12b2o10b
obobo$49bo3bo$50b2obob2o$37b2o4b2o6bobo2bo$36bo2bo2bo2bo3bo4bo$25bo2b
3o5bo2bo2bo2bo3b5o$24bo5bo6b2o4b2o$25bo3b2o20bo$25bo2bo21bobo$27bo15b
2o6bo$43b2o3$23b2o$23b2o$31bobo$29b3ob2o$33b3o5$27b3o$28b2ob3o$29bobo
$38b2o$38b2o!

[WhiteHawk]

Reduction to p14 using a different supporting catalyst

Code: Select all

x = 35, y = 17, rule = B3/S23
25b2o$16bo9bo5b2o$16bo8bo5bobo$25b2o5bo2$25b2o3b5o$2o11b2ob3o5bobo2bo
4bo$bo17bo4b2o3bobo$bobo15b2o9b2o$2b2o7b2o$6b2o4bo$5bobo5b3ob2o10b2o$
5b2o22b2o3$15bo$15bo!

EDIT: Even closer to p43, only missing F=30

Code: Select all

x = 115, y = 91, rule = B3/S23
69b2o3b2o$70bo2bobo$68bo4bo$67bob4ob4o$54b2o8bo2bo4bobo2bo$52b3o8bobo
bob2obobo6bo$47b2o2bo4bo7bo2bo2bob2o7b3o$47bo3bob2ob3o8b2o15bo$48b3ob
obo4bo23b2o$50bobo3b3o$50bobobobo$45bo5b2ob2o11bo12bo14bo$45b3o18b2o11b
2o8b2o3bobo$48bo16b3o11bobo7b2o4bo$47b2o6b2o4b2o3b2o$55b2o4bo2bo2bo6b
2o$51b2o21bo2b2o4b3o$23bo27b2o22b2obo4bo$22bobo19b2o13bo4bo18bob2o$20b
3obo19b2o13bo2b2o11b3o8bo8bo$19bo4bob2o23b2o6b2o14bo2bo5b2ob3o4bobo$19b
obobobobo9b2o9b2o2bo13b2o8bobo4b3ob2o5bo2bo$20b2obobo11b2o8bo4bo13b2o
9bo8bo8b3o$24bobo32b2o25b2obo$25bo33b2o28bo4bob2o$37b2o4b2o2bo2bo4b2o
30b3o4b2o2bo$2o10bo23bo2bo2bo2bo3b2o4b2o6b2o32b2o$bo8b2ob2o4b3o10bo3b
o2bo2bo2bo17bo$bobo6b2ob2o4bo2bobo5bo3bo2b2o4b2o19b3o10bo4b2o7bobo13b
2o$2b2o8bo2bo4bo2bobo3bo26b2ob2o5bo9bobo3b2o8b2o13bo$6b3o4b2o8bobo2bo
5bo20bobobobo15bo14bo12bobo$9bo18bo3b2o9b2o8b3o3bobo43b2o$6bo3bo17bo3b
o10b2o7bo4bobob3o36bobo$5b2o3bo18bo23b3ob2obo3bo23b2o10bo2bo$4bo5bo2b
obo8b2o4b3o22bo4bo2b2o23bo11bo2bo$9bo3bobo2bo4bo2bo8b2o20b3o29b3o9b2o
$4bo3bo5bobo2bo4b2ob2o6bobo18b2o33bo5bo10bo$6bo10b3o4b2ob2o8bo57b2o9b
3o$26bo10b2o57b2o7bo$105b2o$13bo78b2o$12bobo76bobo9bo$13bobob2o72bo11b
o$11bobobobobo70b2o11bo$11b2obo4bo$14bob3o$14bobo73b2o16b2o$15bo75bo16b
2o$91bobo$92b2o3$101bo$100b3o$100bob2o$103b2o$100bob2o$100b3o8b2o$101b
o9bobo$113bo$113b2o2$88b2o$89bo$89bobo9bo$90b2o8b3o$99b2obo$98b2o$99b
2obo$100b3o$101bo3$109b2o$109bobo$93b2o16bo$93b2o16b2o3$99bo6b2o$99bo
5bobo$99bo5bo$104b2o$96b2o4bo$97bo4bob4o$94b3o10bo$94bo5b3obobo$99bo3b
2ob2o$100b2o3bo$102b2obo$102bobo!

Also some modest improvements to p48 partial, though several gaps still exist

Code: Select all

x = 74, y = 62, rule = B3/S23
58bo$56b2obo$56bo3bo$54bo5bo$54bo5bo2bo$54bo7bobo$56b4o2b2o$43bo3bo$42b
obobobo7b4o2b2o$43b2ob2o6bo7bobo$54bo5bo2bo$40bo9bo3bo5bo$39bo11bo4bo
3bo$39bo3b2ob2o3bo4b2obo$40b3obobob3o7bo$41b2obobob2o$42b2o3b2o$52b2o
$54bo$53bobo$55bo$51bo2bo8b3o3b3o$62bo3bobo3bo$51bobo8bo3bobo3bo$61bo
b4ob4obo$49b2o10b2o9b2o$44b2o2bo2bo$44b2o2bo2bo$49b2o14b2ob2o$39bo24b
obobobo$38bobo24bo3bo$38bobo8b2o$36b3ob2o6bo2bo2b2o$22b2o11bo12bo2bo2b
2o$16b2o5bo12b3ob2o7b2o$16b2o5bob2o11bob2o$24bobo19bobo$29b2obo12bo$3b
obo9b3o11bob2o9bob2o3bo$2bob2o9bobo3b3o18bo$2bo3b2o5bo7b2o19bo5bo$2ob
2o3bo4bo5bob2o20bo3bo$bobob3o5bo3bob2o18b2o3b3o$o2bobo9b5o6bob2obo7b2o
14b2o$3obo21bo4bo6bo2bo11bo2bo$10bob2obo10bob2obo7b2obo3b2o4bob2o$2b2o
6bo4bo23b2obo5bo4bo2b3o$2bo7bob2obo6b5o14bo4b2o6b2o3bo$4bo16b2obo3bo19b
o8b2o$3b2o14b2obo5bo20bo4b2obo$19b2o7bo4bo13bobo4bo2bo$18b3o3bobo5b2o
14b2o5b2o$9b2obo11b3o$9bob2o17b3o2bobo$15bobo14bob4o8bo$15b2obo5b2o10b
2o7bobo$18bo5b2o18bo3bo$18b2o23bo3bo$42bo3bo$41bo3bo$42bobo$43bo!

[KtT]

604-cell omnifrequent p50:

Code: Select all

x = 128, y = 73, rule = B3/S23
13bo$12bobo$13bo$4bo$3bobo10b2o$3bobo6b2obobo$b3ob2o8bo$o4bo6bo2bo$b6o
7bo$3bo9bobo$12bo7bo$12bo2bo4bo$11bo8bo$12b2o59b2o4b2o$72bobo4bobo$72b
o8bo$69b2obobo4bobob2o$6b2o11b2o46bo2bobobo4bobobo2bo$6b2o4bo6bo47b2o
3bobob2obobo3b2o$12bo4bobo51bo2b2o2b2o2bo$13bo3b2o52b2obo4bob2o$13bo20b
o40bo2bo$12bobo19b3o32b5o6b5o$11bobo23bo30bo16bo13b2o$11b2o23b2o15b2o
13b2o3b2o4b2o3b2o13bo$21bobo29b2o19b6o17bobo$21b2o16b2o27b2o2b2o6b2o2b
2o7b2o2b2o$14b2o5b2o9bo5bobo26bobo14bobo6b2o$14b2o8b3o3b3o5b2o28bo16b
o33bo$29bo24bo52b2o9bobo$29b2o22bobo44b2o5bo10bob3o$52bo49bo2bobo7b2o
bo4bo$37bo15b2o45b2o3b2o8bobobobobo$19b2o9bo5b3o78bobob2o$20bo8bobo3b
2o2bo54bo21bobo$17b3o8bo2bo7b2o10bo41b3o21bo$17bo11b2o3bo3bobo9b3o39b
2ob2o4b2o$30bo7b2o9bo2b2o24bo12b3ob3o6bo17bo$24b2o6bo4b2o9b2o27b3o12b
2ob2o4bobo18bo3b2o$25bo4b3o3b2o10bobo3bo21b2o15b3o6bo10bo7b3o2b2o$22b
3o7bo4b2o10b2o15bo9b2o16bo16b3o8b2o$22bo15b2o10b2o4bo7b3o10bo31b2o4bo
$34bo3bobo10b2o3b3o4bo28bo15b2obobob2o$39b2o9b2o4bo6b2o26bobo13bo2b2o
b2obo$35b2o2bo9b2o7bo15bo12b2obobo15b2o3bo$36b3o9bobo3bo3b2o14b2o10bo
bobobobo8b2o7bo$37bo10b2o7bo2bo13b2o10bo4bob2o7bobo13b2o$49bo2b2o3bob
o12b3o12b3obo10bo15b2o$50b3o5bo14bo15bobo9b2o$34b2o15bo38bo$36bo78b2o
$33bobo22b2o51b2o2b2o$34bo24bo50bobo$49b2o5b3o51bo$48bobo5bo52b2o$48b
2o$34b2o$34b2o15b2o13bo16bo$51bo13bobo14bobo$52b3o11b2o2b2o6b2o2b2o$54b
o17b6o$66b2o3b2o4b2o3b2o$66bo16bo$67b5o6b5o$73bo2bo$69b2obo4bob2o$69b
o2b2o2b2o2bo$65b2o3bobob2obobo3b2o$65bo2bobobo4bobobo2bo$67b2obobo4bo
bob2o$70bo8bo$70bobo4bobo$71b2o4b2o!

[WhiteHawk]

I return to this thread with a pass at p53

Code: Select all

x = 165, y = 64, rule = B3/S23
8b2o3b2o$8bobo2bo$4bob2o2bo3bo$4b2obobob4o5bo$9bo10b3o10b2o$10bo2b2o8b
o9bo$14bo7b2o7bobo$14bob2o13b2o$8bo2bob2obo2bo$9b2o5bob2o63bo$16bo64b
3o$15b2o55b2o6bo$bo6b3o61bobo5b2o$o7b3o43b2o18bo$bo52b2o18b2o10b2o$85b
obo$24b3o27b4o16b2o9b2o$23bo3bo26bo3bo2b2o11bobo5bo6b2o$8b2ob2o10b2ob
2o29b2o2b2o12bo5bobo5bobo6b2o3b2o$8bo3bo34bo24b3o16bo6bobo2bo$9b3o33b
3o24bo7b2o2bo6bob2ob2o2bo3bo$44bo34bo3bo8bob2obobob4o5bo$34bo9b2o16b2o
16b4o14b2obo8b3o10b2o19b2o$25b3o7bo25bo2bo2b2o11b3o6bo13b2o8bo9bo20bo
bo$25b3o6b6o21bo2bo2b2o19b2o14bo7b2o7bobo22bo4b2o$19b2o14b2o3bo7b2o12b
2o23b2o15bob2o13b2o19b4ob2o2bo2bo$19bo16b2ob2o6bobo33bobob2o10b2o2b2o
bo2bo32bo2bobobobob2o$16b2obo5b2o8bo4bo8bo32bo2bo13b2o5bob2o35bobobob
o$16bo2bob2obo2bo7b2ob2o22b2o18bo2b2o19bo39b2obobo$3b2o13b2obo13bo21b
2o2bo2bo9bo8b2o20b2o43bo$2bobo7b2o7bo14b2ob2o16b2o2bo2bo9bobo38bo$2bo
9bo8b2o2bo12b3o21b2o10b2o38b3o19b2o$b2o10b3o10bo13b2obo36b2o31b5o19bo
7b2o$15bo5b4obobob2obo7b2ob2o35bo30bo5bo18bobo5b2o$21bo3bo2b2ob2obo6b
2o10bo24b3o30b2o5b2o18b2o$22bo2bobo6bo16b3o8b2o14bo18b2o3b2o6b2o7b2o$
21b2o3b2o6bobo13bo8bo2bo2bob2o27bobo3bobo6bobo3bobo32bo$35b2o7b2o3bob
o6bobobob2obobo25b2o7b2o6b2o3b2o18bo15b2o$39b2o3b2o4b2o7bo2bo4bobo2bo
23b2o5b2o30b3o14b2o$38bobo21bob4ob4o24bo5bo30bo$38b2o10b2o11bo4bo29b5o
31b2o$51bo13bo2bobo28b3o38b2o6b2o13b2o$44b2o5bobo10b2o3b2o29bo38bobo6b
o9b2obo2bo$45bo6b2o55b2o20b2o8bo7b3o5bobob3o$42b3o64bo19b2o2bo17bo5bo
bo$42bo63b2obo5b2o13bo2bo21b3ob5o$106bo2bob2o2b2o10b2obobo21bo3bo4bo$
93b2o13b2obo15b2o25b2o2bobo$92bobo7b2o7bo14b2o31b2o$92bo9bo8b2o13bo6b
3o$91b2o10b3o8bob2o14b4o$105bo5b4obobob2obo8bo3bo$111bo3bo2b2ob2obo6b
o2b2o7bo$112bo2bobo6bo16b3o$111b2o3b2o6bobo5bobo5bo$125b2o6bo5bobo$129b
2o9b2o$128bobo$128b2o10b2o$141bo$134b2o5bobo$135bo6b2o$132b3o$132bo!

[KtT]

1600-cell omnifrequent p44:

Code: Select all

x = 155, y = 158, rule = B3/S23
12b2o40bo$13bo38b2o$3bo9bob2o37b2o$b3o8b2o2bo36bo$o3b2o5bo2b2o66b2o$b
3o2bo3bobobo18b2o47bo$3bobobo2bo5bo16b2o16bo27b2obo9bo$3bo2bobob3obo35b
obo26bo2b2o8b3o$4bo3bo2b2obo35bobo27b2o2bo5b2o3bo$9bo3b2o3bo6bo6b2o17b
o9b2o18bobobo3bo2b3o$4b2o2bo5bo9bo7bob2o20b2o3b2o16bo5bo2bobobo$3b2o8b
2o6bob2obo7b2o22bo22bob3obobo2bo$2bobo8bo2bo4bo3bo6bob2o6b3o36bob2o2b
o3bo$2b2o5bo3b2o6bo10b2o7bo20b2o6bo6bo3b2o3bo$8bobo2b3o24bo5bo4b2o7b2o
bo7bo9bo5bo2b2o$2b2o5bo3b2o6bo10b2o6b2obo2bo3bobo7b2o7bob2obo6b2o8b2o
$2bobo8bo2bo4bo3bo6bob2o4b2obo2bo2bo2bob2o4b2obo6bo3bo4bo2bo8bobo$3b2o
8b2o6bob2obo7b2o7bobo3bo2bob2o6b2o10bo6b2o3bo5b2o$4b2o2bo5bo9bo7bob2o
7b2o4bo5bo24b3o2bobo$9bo3b2o3bo6bo6b2o20bo7b2o10bo6b2o3bo5b2o$4bo3bo2b
2obo36b3o6b2obo6bo3bo4bo2bo8bobo$3bo2bobob3obo22bo22b2o7bob2obo6b2o8b
2o$3bobobo2bo5bo16b2o3b2o20b2obo7bo9bo5bo2b2o$b3o2bo3bobobo18b2o9bo17b
2o6bo6bo3b2o3bo$o3b2o5bo2b2o27bobo35bob2o2bo3bo$b3o8b2o2bo26bobo6bo28b
ob3obobo2bo$3bo9bob2o27bo5b3o8b2o16bo5bo2bobobo$13bo35bo11b2o18bobobo
3bo2b3o10bo19bo$12b2o35b2o29b2o2bo5b2o3bo8bobo17bobo$57b2o20bo2b2o8b3o
9bobo6b2ob2o6bobo$41b2o14bo21b2obo9bo10b2ob2o2b2o2bobo2b2o2b2ob2o$41b
2o12bobo24bo22bo19bo$55b2o25b2o21bob2ob3o5b3ob2obo$106bo3bo9bo3bo$107b
o2bo9bo2bo$108bobo4bo4bobo$110bo3bobo3bo$49bo56b2o7bo7b2o$48b3o54bo3b
o11bo3bo$47b2obo50bo2bob2o5b5o5b2obo2bo$46b2o53b4obobobobob3obobobobo
b4o$37b2o8b2obo5b3o26b2o$36bobo9b3o34bobo15bobob2o3b2o3b2o3b2obobo$36b
o12bo38bo14b2o3b5o5b5o3b2o$35b2o49b2obo$85bobobo$89bob2o$81b2obobob2o
2bo$81bo4bobo2bo19bo7bo$56b2o24b2o5b2o20b2o5b2o$43bo12bo28bo27bo3bo$42b
3o9bobo23b3o2bo3b2o21b2o3b2o$34b3o5bob2o8b2o21bobo3b2o3bobo$45b2o30b2o
b4o3bo$42bob2o34bo2bo3bob4o16bo11bo15bo$42b3o16bo18bobo3b2obo2bo17b2o
b2ob2ob2o15bobo$43bo15b3o19bobobo25b3o3b3o16bobo7b2o$58bo26bob2o23bo5b
o14b2obo2b2o2b2o2bo2b2o$58b2o73b2o2bobo3bo3bobo2bo$83b2o3bo47b2o2bo3b
3obobo2bo$53bo30b3o2bo49b2o5bobob2obo$36b2o14bobo29bo4bo25bo15bo14bob
o4b2o$35bobo13bo4b2o26bo30bo15bo15bo2b3o$35bo16bo5bo28b2o26bo14b3o15b
2o2bo$34b2o18b2o2bo26b2o64bo$42b2o11bob2o26bo42bo5bo17b3o$43bo57b2o23b
o9bo17bo$40b3o55bo4bo21b2o4bo4b2o$40bo47b2o2bo4bo3bobo20b2o4b3o4b2o$87b
obo3bo4bo2b2o22bo2b3ob3o2bo$87bo4bo27b2o4b2obo3bob2o$55b2obo29b2o29bo
bo6b2o3b2o10bo$55bo2b2o45bo13bo8b2o3b2o9bobo$55bo5bo42b2o12b2o6b2obo3b
ob2o8bo$56b2o4bo12bo26b2o21bo2b3ob3o2bo$59bobo13bo30bo17b2o4b3o4b2o$60b
o14bo25bo4bo18b2o4bo4b2o$101bo2b3o11bob2o4bo9bo4b2obo$51bo50bo3b2o10b
2obo6bo5bo6bob2o$50bobo69b2obo11bob2o$49bo4b2o16bo5bo23b2obo18b2o4b3o
4b2o$50bo5bo14b3o3b3o25bobobo10b3o8bo8b3o$52b2o2bo13b2ob2ob2ob2o17bo2b
ob2o3bobo7bo2bo9bo9bo2bo$53bob2o12bo11bo16b4obo3bo2bo7b2o3bo15bo3b2o$
103bo3b4ob2o8b2o3bo7bo3b2o$100bobo3b2o3bobo13bo7bo$72b2o3b2o21b2o3bo2b
3o16bo7bo$73bo3bo27bo$71b2o5b2o20b2o5b2o20b2ob2o$53b2obo14bo7bo19bo2b
obo4bo19bo3bo$53bo2b2o41bob2obobob2o20b3o$53bo5bo38b2obo26bobo$54b2o4b
o40bobobo22b2o$57bobo41bob2o$58bo4b2o3b5o5b5o3b2o14bo$63bobob2o3b2o3b
2o3b2obobo15bobo$49bo54b2o$48bobo10b4obobobobob3obobobobob4o$47bo4b2o
7bo2bob2o5b5o5b2obo2bo$48bo5bo10bo3bo11bo3bo$50b2o2bo11b2o7bo7b2o$51b
ob2o15bo3bobo3bo$68bobo4bo4bobo$67bo2bo9bo2bo$66bo3bo9bo3bo$65bob2ob3o
5b3ob2obo$65bo19bo$51b2obo8b2ob2o2b2o2bobo2b2o2b2ob2o$51bo2b2o8bobo6b
2ob2o6bobo$51bo5bo6bobo17bobo$52b2o4bo6bo19bo$55bobo$56bo2$47bo$46bob
o$45bo4b2o10bob2o4b2obo$46bo5bo9b2o2bo2bo2b2o2bo$48b2o2bo7b2o3bo4bo3b
3o$49bob2o6bo3b2ob4ob2o$60b3obobo2bobob2o$62bo3bo2bo3bobo6b2o$64b2ob2o
b2o4bo5bo$67b2o8bob2obo$76b2obobob2o$49b2obo24bobobobo$49bo2b2o23bob3o
bo$49bo5bo22b5o$50b2o4bo13b3o$53bobo$54bo7bo5bo5bo$61bobo4bo5bo4b3o$48b
2o10bo3bo3bo5bo5bo$49bo11bobo16bo$46b3o13bo7b3o$46bo$76b3o$74bob3o$53b
o19bobobo$52bobo3b3o12bo2bo$52bob4o3b3o10b2o$49b2obo9bob2o$49b2ob2o2b
2o2bobo4bo$52bo8b3o3bo$52bobo4bo5b3o$53b2o3bobobo2b3ob2o$57bobo2bob4o
3bo$57bobob2o4bobobo$55b2o2b4obobo4b2o$54bo2b2o9b3o2bo$55b2o2b9o4bo$58b
o6b2o2b3o$55b3ob2obo5b2o$54bo2bo4bob2o$55bobo2b2ob2o$52b3o3bo3bo2bo$52b
o2b3o4b3o$55bo7b2o!

[WhiteHawk]

1600-cell omnifrequent p44:

Code: Select all

Reduction to 1327 cells

Code: Select all

x = 166, y = 129, rule = B3/S23
12b2o39bo$13bo39bobo$3bo9bob2o35bobo$b3o8b2o2bo37bo$o3b2o5bo2b2o66b2o
$b3o2bo3bo2b2o18b2o47bo$3bobobo2bobo2bo17b2o16bo27b2obo9bo$3bob2obobo
bo2bo34bobo26bo2b2o8b3o$7b2o5b2o34bobo27b2o2bo5b2o3bo$4b2o2b2o2bob2o16b
3o16bo9b2o18b2o2bo3bo2b3o$3b3o9bo7b2o7bo2bo21bo3b2o17bo2bobo2bobobo$13b
3o6b3o11bo6bo13bo22bo2bobobob2obo$2bobo7bo2bo4b2o2b2o6bo2bo6b2o36b2o5b
2o$2b2o5bo2bo19b3o6b3o17b3o16b2obo2b2o2b2o$8bobobo2bo24bobo8b2o7bo2bo
7b2o7bo9b3o$2b2o5bo2bo19b3o4bo5b3o2bobo6bo11b3o6b3o$2bobo7bo2bo4b2o2b
2o6bo2bo4b2obob2o2b2obob2o4bo2bo6b2o2b2o4bo2bo7bobo$13b3o6b3o11bo6bob
o2b3o5bo4b3o19bo2bo5b2o$3b3o9bo7b2o7bo2bo7b2o8bobo24bo2bobobo$4b2o2b2o
2bob2o16b3o17b3o6b3o19bo2bo5b2o$7b2o5b2o36b2o6bo2bo6b2o2b2o4bo2bo7bob
o$3bob2obobobo2bo22bo13bo6bo11b3o6b3o$3bobobo2bobo2bo17b2o3bo21bo2bo7b
2o7bo9b3o$b3o2bo3bo2b2o18b2o9bo16b3o16b2obo2b2o2b2o$o3b2o5bo2b2o27bob
o34b2o5b2o$b3o8b2o2bo26bobo6bo27bo2bobobob2obo$3bo9bob2o27bo5b3o8b2o17b
o2bobo2bobobo$13bo35bo11b2o18b2o2bo3bo2b3o$12b2o35b2o29b2o2bo5b2o3bo$
57b2o20bo2b2o8b3o$41b2o14bo21b2obo9bo$41b2o12bobo24bo$55b2o25b2o5$48b
3o$47bo2bo$46bo3bo$46bo10bo$37b2o7bo3bo6bo$36bobo8bo2bo6bo52b2o$36bo11b
3o$35b2o$116bo19bo$115bobo17bobo$115bobo6b2ob2o6bobo$114b2ob2o2b2o2bo
bo2b2o2b2ob2o$56b2o58bo19bo$42b3o11bo59bob2ob3o5b3ob2obo$35bo6bo2bo8b
obo60bo3bo9bo3bo$35bo6bo3bo7b2o62bo2bo9bo2bo$35bo10bo72bobo4bo4bobo$42b
o3bo74bo3bobo3bo$42bo2bo15bo55b2o7bo7b2o$42b3o14b3o54bo3bo11bo3bo$58b
o53bo2bob2o5b5o5b2obo2bo$58b2o52b4obobobobob3obobobobob4o$96b2o$53bo42b
obo15bobob2o3b2o3b2o3b2obobo$36b2o14b2o45bo14b2o3b5o5b5o3b2o$35bobo13b
3o3bo39b2obo$35bo19b2obo37bobobo$34b2o18b3ob2o40bob2o$42b2o10b5o33b2o
bobob2o2bo$43bo48bo4bobo2bo19bo7bo$40b3o50b2o5b2o20b2o5b2o$40bo55bo27b
o3bo$91b3o2bo3b2o21b2o3b2o$88bobo3b2o3bobo$55b5o28b2ob4o3bo$54b2ob3o31b
o2bo3bob4o16bo11bo15bo$55bob2o13bo18bobo3b2obo2bo17b2ob2ob2ob2o15bobo
$56bo3b3o7b3o19bobobo25b3o3b3o16bobo7b2o$60b2o7bo26bob2o23bo5bo14b2ob
o2b2o2b2o2bo2b2o$60bo8b2o73b2o2bobo3bo3bobo2bo$94b2o3bo47b2o2bo3b3obo
bo2bo$54b2o8bo30b3o2bo49b2o5bobob2obo$55bo7bobo29bo4bo25bo15bo14bobo4b
2o$52b3o3bo3bo4b2o26bo30bo15bo15bo2b3o$52bo4bo5bo5bo28b2o26bo14b3o15b
2o2bo$57b3o5b2o2bo26b2o64bo$48b2o16bob2o26bo42bo5bo17b3o$48bobo61b2o23b
o9bo17bo$50bo58bo4bo21b2o4bo4b2o$50b3o46b2o2bo4bo3bobo20b2o4b3o4b2o$48b
2o3bo44bobo3bo4bo2b2o22bo2b3ob3o2bo$47bo2b3obo43bo4bo27b2o4b2obo3bob2o
$47b2obobobo11b2obo29b2o29bobo6b2o3b2o10bo$50bobo13bo2b2o45bo13bo8b2o
3b2o9bobo$50bobo13bo5bo42b2o12b2o6b2obo3bob2o8bo$49b2obobo12b2o4bo12b
o26b2o21bo2b3ob3o2bo$53b2o15bobo13bo30bo17b2o4b3o4b2o$71bo14bo25bo4bo
18b2o4bo4b2o$112bo2b3o11bob2o4bo9bo4b2obo$65b2o46bo3b2o10b2obo6bo5bo6b
ob2o$66bo66b2obo11bob2o$63b3o17bo5bo23b2obo18b2o4b3o4b2o$63bo18b3o3b3o
25bobobo10b3o8bo8b3o$81b2ob2ob2ob2o17bo2bob2o3bobo7bo2bo9bo9bo2bo$80b
o11bo16b4obo3bo2bo7b2o3bo15bo3b2o$114bo3b4ob2o8b2o3bo7bo3b2o$111bobo3b
2o3bobo13bo7bo$83b2o3b2o21b2o3bo2b3o16bo7bo$84bo3bo27bo$82b2o5b2o20b2o
5b2o20b2ob2o$82bo7bo19bo2bobo4bo19bo3bo$110bob2obobob2o20b3o$109b2obo
26bobo$112bobobo22b2o$112bob2o$74b2o3b5o5b5o3b2o14bo$74bobob2o3b2o3b2o
3b2obobo15bobo$115b2o$72b4obobobobob3obobobobob4o$72bo2bob2o5b5o5b2ob
o2bo$76bo3bo11bo3bo$77b2o7bo7b2o$81bo3bobo3bo$79bobo4bo4bobo$78bo2bo9b
o2bo$77bo3bo9bo3bo$76bob2ob3o5b3ob2obo$76bo19bo$74b2ob2o2b2o2bobo2b2o
2b2ob2o$75bobo6b2ob2o6bobo$75bobo17bobo$76bo19bo!

EDIT: here is the p43 partial above with an uncapped barrel if anyone wants to try and complete it

Code: Select all

x = 119, y = 87, rule = B3/S23
69b2o3b2o$70bo2bobo$68bo4bo$67bob4ob4o$54b2o8bo2bo4bobo2bo$52b3o8bobo
bob2obobo6bo$47b2o2bo4bo7bo2bo2bob2o7b3o$47bo3bob2ob3o8b2o15bo$48b3ob
obo4bo23b2o$50bobo3b3o$50bobobobo$45bo5b2ob2o11bo12bo14bo$45b3o18b2o11b
2o8b2o3bobo$48bo16b3o11bobo7b2o4bo$47b2o6b2o4b2o3b2o$55b2o4bo2bo2bo6b
2o$51b2o21bo2b2o4b3o$23bo27b2o22b2obo4bo$22bobo19b2o13bo4bo18bob2o$20b
3obo19b2o13bo2b2o11b3o8bo8bo$19bo4bob2o23b2o6b2o14bo2bo5b2ob3o4bobo$19b
obobobobo9b2o9b2o2bo13b2o8bobo4b3ob2o5bo2bo$20b2obobo11b2o8bo4bo13b2o
9bo8bo8b3o$24bobo32b2o25b2obo$25bo33b2o28bo4bob2o$37b2o4b2o2bo2bo4b2o
30b3o4b2o2bo$2o10bo23bo2bo2bo2bo3b2o4b2o6b2o32b2o$bo8b2ob2o4b3o10bo3b
o2bo2bo2bo17bo$bobo6b2ob2o4bo2bobo5bo3bo2b2o4b2o19b3o10bo4b2o7bobo13b
2o$2b2o8bo2bo4bo2bobo3bo26b2ob2o5bo9bobo3b2o8b2o13bo$6b3o4b2o8bobo2bo
5bo20bobobobo15bo14bo12bobo$9bo18bo3b2o9b2o8b3o3bobo43b2o$6bo3bo17bo3b
o10b2o7bo4bobob3o36bobo$5b2o3bo18bo23b3ob2obo3bo23b2o10bo2bo$4bo5bo2b
obo8b2o4b3o22bo4bo2b2o23bo11bo2bo$9bo3bobo2bo4bo2bo8b2o20b3o29b3o9b2o
$4bo3bo5bobo2bo4b2ob2o6bobo18b2o33bo5bo10bo$6bo10b3o4b2ob2o8bo57b2o9b
3o$26bo10b2o57b2o7bo$105b2o$13bo$12bobo88bo$13bobob2o84bo$11bobobobob
o83bo$11b2obo4bo$14bob3o$14bobo80b2o16b2o$15bo81b2o16bo$113bobo$113b2o
3$105bo$104b3o$103b2obo$102b2o$103b2obo$94b2o8b3o$93bobo9bo$93bo$92b2o
2$117b2o$117bo$105bo9bobo$104b3o8b2o$104bob2o$107b2o$104bob2o$104b3o$
105bo3$96b2o$95bobo$95bo16b2o$94b2o16b2o3$107bo$107bo$107bo2$109b2o$109b
o$110b3o$112bo!

[WhiteHawk]

Omniperiodic p43 (595 cells, definitely reducible)

Code: Select all

x = 119, y = 87, rule = B3/S23
69b2o3b2o$70bo2bobo$68bo4bo$67bob4ob4o$54b2o8bo2bo4bobo2bo$52b3o8bobo
bob2obobo6bo$47b2o2bo4bo7bo2bo2bob2o7b3o$47bo3bob2ob3o8b2o6b2o7bo$48b
3obobo4bo15bobo5b2o$50bobo3b3o16bo$50bobobobo$45bo21b2o26bo$45b3o3bo15b
2o16bo2bo5bobo$48bo6bo28bo3bo6bo$47b2o3bo2bo5b2o4b2o15b2o2bo$51bo3bo5b
2o4b2o5b2o$52bo2bo18bo2b2o$23bo28b3o20b2obo$22bobo19b2o$20b3obo19b2o29b
3o17bo$19bo4bob2o47bo2bo15bobo$19bobobobobo9b2o27b2o8bobo15bo2bo$20b2o
bobo12bo27b2o9bo17b3o$24bobo30b3o$13bo11bo30bo2bo34bob2o$14bo23b2o9b2o
5bo3bo33b2o2bo$2o10bobo22b3o3bo5b2o5bo2bo3b2o32b2o$bo36bo3b3o11bo6bo20b
o2b2o$bobo8bo11bo2bo14b2o16bo3b3o10bo6bo3bo18b2o$2b2o19bo3bo38bo9bobo
5bo2bo19bo$22bo4bo27bobobobo15bo27bobo$22bo2b2o16bo9b3o3bobo43b2o$14b
3o5b3o18b2o7bo4bobob3o33bo$12b2o2bo36b3ob2obo3bo23b2o5bobo$11bo4bo38b
o4bo2b2o23bo7b2o3b2o$11bo3bo19b2o20b3o29b3o8bo2bo$11bo2bo11bo8bobo18b
2o33bo8bobo5bo$37bo63bo4b3o$24bobo10b2o66bo$24bo80b2o$13bo11bo66bo$12b
obo76bo$13bobob2o72b3o8b3o$11bobobobobo$11b2obo4bo$14bob3o$14bobo80b2o
16b2o$15bo81b2o3b3o10bo$102bo2bo7bobo$105bo7b2o$82bo18bo$81bobo17bo3b
5o$81bo2bo16bo2b2ob3o$82b2o17b2o6bo$98bo2b2o4bo$98b2obo3b2o$98bo2bo3b
o$67b2o6bo18b2o5bo2bo$63b2obobo6b2o16bobo5b2o$54bo7bobobo7bobo16bo7b2o
$53bobo5bo2bo2bo24b2o8bobo$54bo7b2o2b2o35bo3bo$106bobo8b2o$108b2o7bo$
77b2o29b2o5bobo$77bo28bo2bo5b2o$55bo19bobo27bo3bo2bo$55bo13b2o4b2o27b
2o3bob2o$55bo13bo33bo4b2o2bo$101bo6b2o$56bo13bo30b3ob2o2bo$49b2o4b2o13b
o30b5o3bo$48bobo19bo38bo$48bo47b2o7bo$47b2o46bobo7bo2bo$95bo10b3o3b2o
$94b2o16b2o$58b2o2b2o7bo$51b2o5bo2bo2bo5bobo$52bo6bobobo7bo$49b3o5bob
ob2o43b3o$49bo7b2o2$109b2o$109bo$110b3o$112bo!

The loaf flip has fewer options for frequencies than SL construction/deconstruction has, but it's smaller and only requires 2 streams and not 3

EDIT:

Edit: Unrelated P28 long boat spin:

Code: Select all

Reduces the omnifrequent p28 to 151 cells

Code: Select all

x = 38, y = 51, rule = B3/S23
31b2o$23bo6bobo3b2o$23b2o4bo2bo3b2o$27bo3bo$27bobo2$27bobo$27bo3bo$23b
2o4bo2bo3b2o$23bo6bobo3b2o$31b2o3$26b2o$26b3o$21b2o2bo2bo$21b2o2bo2bo
$26b2o3$26b2o$25bo2bo2b2o$15bo9bo2bo2b2o$9bo5b3o7b3o$9b3o6bo7b2o$12bo
4b2o$11b2o$2bobo15bo4b2o$5bo13bobo3b2o$bo2bo14bo$obobo8b3o4bobo$o2bo10b
o6b2o$b2o4b3o$8bo3$3bo$2bobo15bo$2bo2bo9b2o3b2o$9bo5b2o3b2o$9bo10bo$3b
o2bo2bo8bo2bo$4b2o12bob3o$17b2o3bo$16bo3b2o$16b3obo$17bo2bo$18bo$17b2o
3b2o$17b2o3b2o$18bo!

p20 got reduced by 10 cells with a monomerization of the LOM hassler

[ElijahKen]

Does this imply the existence of an omnifrequent p55?

Code: Select all

x = 60, y = 34, rule = B3/S23
14bo2bo2b2o16b2o2bo2bo$14b4o3bo16bo3b4o$12b2o4b3o18b3o4b2o$11bo2bobo
26bobo2bo$12bobo4b4o14b4o4bobo$2b2o7b2obobo2bo2bo14bo2bo2bobob2o7b2o$
3bo10bo2b2o22b2o2bo10bo$3bob2o7b2o28b2o7b2obo$4bo3b2o40b2o3bo$9bo40bo$
20b2o16b2o$6bo2bo9bo2bo14bo2bo9bo2bo$7bobo10b2o16b2o10bobo$2b2o2bo46bo
2b2o$2bo2bo5bobo32bobo5bo2bo$3b2ob2obo2b3o30b3o2bob2ob2o$7bo4b2obo28bo
b2o4bo$3b2obobo5b2o9b2o6b2o9b2o5bobob2o$3b2ob2o17bobo4bobo17b2ob2o$27b
o4bo$27b2o2b2o$8bo2b2o8bo16bo8b2o2bo$2bobo3bo5bo7b2o12b2o7bo5bo3bobo$
4b2o2bo12b2o14b2o12bo2b2o$bo4b3o6bo2bo22bo2bo6b3o4bo$o2b2obobob4ob4o
22b4ob4obobob2o2bo$2obo2bo4bobo32bobo4bo2bob2o$3bo2bob2obob4o26b4obob
2obo2bo$3bob2o2bobo4bo26bo4bobo2b2obo$4bo2bo3bob2o30b2obo3bo2bo$5b2o4b
2ob2o28b2ob2o4b2o$21bo16bo$20bo8b2o8bo$20b3o6b2o6b3o!

[WhiteHawk]

Does this imply the existence of an omnifrequent p55?

Code: Select all

I think so. Great job!

Only p38, p31, and p19 remain without proof of omnifrequency, though several examples below p61 haven't been constructed yet.

EDIT: I guess there was a p55 emu which could have been adjusted to have multiple barrels. This gun implies a much smaller solution exists

EDIT 2: Collection of all p38 oscillators on the four EV2 stamp collections. They do technically cover all frequencies, but f=28 is only covered by Goban's period-doubled form.

Code: Select all

x = 375, y = 493, rule = B3/S23
277b3o2$281bo47b2o16b2o$281bo47b2o16b2o$105bo175bo$103b3o166b2o4bo$67b
o34bo168bobo4b2o39b2o36b2o$6b3o30b3o25bo34b2o44bo22bo99bo48bo36bo$67b
o78b3o22b3o96b2o48bobo15b2o15bobo$4bo5bo2b2o18b2o2bo5bo25b2o3bo70bo28b
o78bo25bo41b2o15b2o15b2o$4bo4b2o4bo16bo4b2o4bo19b3o3b2o3b2o15b2o52b2o
26b2o76b3o25bo$4bo11bo14bo11bo32bo14bo116b2o30b2o8bo25bobo35bo14b3o14b
3o14bo$15b2o14b2o42b2o15b2o3b2o3b3o103b2o30b2o8b2o24b2o36b3o12bobo14b
obo12b3o$93bo3b2o52b2o14b2o39b3o28b3o75bo10bo2bo14bo2bo10bo$100bo39bo
11bo14bo11bo25bo9b2o16b2o9bo3bo67b2o11b2o16b2o11b2o$9b2o26b2o25b2o34b
o39bo4b2o4bo16bo4b2o4bo25bo8bo2bo14bo2bo8bo2bobo$9bo28bo26bo34bo39bo5b
o2b2o18b2o2bo5bo25bo9bob2o12b2obo9bo3b2o2b2o$10b3o22b3o24b3o121b3o27b
2o14b2o18b2o78b2o10b2o$12bo22bo26bo79b3o30b3o154bo12bo$162b2o20bo64b2o
82b3o6b3o$162b3o19bo25b2o26b2o8b2o71bo13bo6bo13bo$162b2o20bo25bo28bo10b
o59b2o7b2obo32bob2o7b2o$164bo22bo4b2o17b3o22b3o71b2o7bo2bo32bo2bo7b2o
$137b3o46b2o4bobo18bo22bo82b3o34b3o$194bo130b2o24b2o$141bo52b2o129bob
o22bobo$141bo44bo53bo86bo22bo$141bo44bo52bo36b2o49b2o20b2o$132b2o4bo15b
o32bobo49b3o17bo16bobo$75bo42bo12bobo4b2o12b2o19bo14b2o68b2o19bo$75b3o
38b3o12bo21b2o17b2o84bobo18bo36b2o42b2o$78bo36bo14b2o40bobo45b2o48b2o
44b2o42b2o$77b2o36b2o22bo81bo49bo$139bo81bobo47bobo4b2o$5b3o30b3o95bo
bo83b2o48b2o4bo48b2o20b2o$88b2o14b2o30b2o143bo45bo22bo$3bo5bo2b2o18b2o
2bo5bo44bobo14bobo122b2o50bo43bobo22bobo$3bo4b2o4bo16bo4b2o4bo33b3o2b
obo2bo2bo14bo2bo2bobo2b3o108b2o4bo48bo43b2o24b2o$3bo11bo14bo11bo38bob
o3b2o16b2o3bobo30bobo79bo5bo36b2o49b3o34b3o$14b2o14b2o110b3o36b3o42bo
b2o37b2o8b3o30b2o7bo2bo32bo2bo7b2o$80b2o30b2o28b3o36b3o43bo41bo40b2o7b
2obo32bob2o7b2o$43b2o35bo17bo14bo66bobo138bo13bo6bo13bo$8b2o26b2o5b2o
52bobo233b3o6b3o$8bo28bo197bo41bo54bo12bo$9b3o22b3o6b2o50bo2bobo87b2o
35b3o8b2o37b2obo53b2o10b2o$11bo22bo8b2o43b2o5b2o90bobo45b2o36bo5bo$88b
2o96bo36bo48bo4b2o$186bo36bo50b2o40b2o11b2o16b2o11b2o$38bo16bo37b3o55b
obo40b2o27bo93bo10bo2bo14bo2bo10bo$38b2o3bo6bo3b2o44b2o50b2o17b2o21bo
31bo4b2o48b2o31b3o12bobo14bobo12b3o$29b3o7bob4o4b4obo7b3o29b2o40b2o14b
o19b2o12b2o4bobo30b2o4bobo47bobo30bo14b3o14b3o14bo$41bo3bo2bo3bo47b3o
33bobo32bo15bo4b2o39bo49bo$29bobo11bob4obo11bobo74bo44bo48b2o48b2o36b
2o15b2o15b2o$30bo12b3o2b3o12bo42b2o31bo44bo40bo18bobo73bobo15b2o15bob
o$38bo16bo43b2o5b2o22b2o52bo40bo19b2o73bo36bo$39bobo10bobo40bobo2bo30b
o94bobo16bo17b3o53b2o36b2o$32b2o26b2o69bobo4b2o46b3o38b2o36bo$32bo28b
o34bobo33b2o4bo22bo102bo$33b3o22b3o21bo14bo17bo25bo20b2o165b2o16b2o$35b
o22bo23b2o30b2o25bo19b3o165b2o16b2o$141bo20b2o104bo22bo$83bobo3b2o16b
2o3bobo33b3o30b3o82b3o22b3o$78b3o2bobo2bo2bo14bo2bo2bobo2b3o17b3o114b
o10bo28bo$89bobo14bobo37bo5bo2b2o18b2o2bo5bo69b2o8b2o26b2o$90b2o14b2o
38bo4b2o4bo16bo4b2o4bo68b2o$146bo11bo14bo11bo$157b2o14b2o76b2o18b2o14b
2o$79b2o36b2o132b2o2b2o3bo9bob2o12b2obo9bo$80bo36bo137bobo2bo8bo2bo14b
o2bo8bo$77b3o38b3o30b2o26b2o75bo3bo9b2o16b2o9bo$77bo42bo30bo28bo82b3o
28b3o$152b3o22b3o47b2o24b2o8b2o30b2o$154bo22bo48bobo25bo8b2o30b2o$225b
o25b3o$225bo25bo$233b2o$233bo$53b2o170b2o4bobo$54bo171bo4b2o$54bob2ob
o163bo$53b2obob2o163bo$119bo103bo$53b3o63bo$53bo2bo62bo105b3o$48bo6b2o
$48b2o71b3o$49bo$48bo8bo32bo22b2o4b2o$6b3o30b3o6b3o6b3o30b3o19bobo4b2o
$60bo32bo18bo72bo32bo$4bo5bo2b2o18b2o2bo5bo4bo2bo7b2o31b2o17b2o31bo2b
o12bo2bo21bo32bo$4bo4b2o4bo16bo4b2o4bo4bobo93bobo14bobo21bo32bo$4bo11b
o14bo11bo5bo69b2o26bo2b2o4b2o2bo26b2o3bo18bo3b2o$15b2o14b2o37b2o14b2o
29bobo6b2o8b3o10b2obo2bob2o10b3o9b3o3b2o3b2o16b2o3b2o3b3o$53bo5bo11bo
14bo11bo18b2o7b2o9bo6bo5bob4obo5bo6bo23bo14bo44b2o$52bobo4bo4b2o4bo16b
o4b2o4bo45bo3b2o2bo2bo2b2o3bo29b2o14b2o44bo2bo$9b2o31b2o7bo2bo4bo5bo2b
2o18b2o2bo5bo46b3o12b3o89b3o3b3o$9bo32bo83b2o4b3o105b2o9bo3b3o3bo$10b
3o30b3o6b3o6b3o30b3o27b2o2bo2bo2b2o3b2o6b2o10b2o6b2o18b2o26b2o24bo2bo
6b2obo3b3o$12bo32bo8bo69b2o2bo2bo2b2o3bo28bo18bo28bo21b3o3b3o8b2obo$53b
o71b3o4b2o6b3o22b3o20b3o22b3o21bo3b3o3bo2bob2obobo$53b2o87bo22bo24bo22b
o23b2obo3b3o3b2ob2o$46b2o6bo142bo43b2obo22bo$46bo2bo82b2o64b2o36bob2o
bobo22bobo$47b3o82b2o62b2o6b2o30b2ob2o26bo$198bo3bo4bo48bo$43b2obob2o
152bo4bo37b2o$43bob2obo153bo4bo10b2o13bo10bo22b2o$48bo149b2o18bo14b3o
8b2o13bo7bo$48b2o67b2o78bobo16bobo17bo7bo13b2o8b3o$117bobo77bo18b2o17b
2o22bo10bo$119b2o75b2o10bo4bo43b2o$208bo4bo33bo$111b2o95bo4bo3bo18bo26b
2ob2o$112bo97b2o6b2o15bobo22bobob2obo$112bobo4b2o95b2o18bo22bob2o$113b
2o4b2o97bo30b2ob2o3b3o3bob2o$190bo32bo22bobob2obo2bo3b3o3bo$121b3o64b
3o30b3o21bob2o8b3o3b3o$187bo32bo22b3o3bob2o6bo2bo$119bo67b2o31b2o20bo
3b3o3bo9b2o$119bo123b3o3b3o$119bo125bo2bo$193b2o14b2o37b2o$194bo14bo$
181b3o3b2o3b2o16b2o3b2o3b3o$187b2o3bo18bo3b2o$185bo32bo$185bo32bo$185b
o32bo5$83b2o83b2o$80bo2bo85bo$78b3o3b3o2b2o78bob2obo77b2o28b2o$77bo3b
3o3bo2bo77b2obob2o77bo5b2o16b2o5bo$78b3o3bob2obo163b3obobo16bobob3o$25b
o54bob2o4bo6b3o70b3o84bobo5b2o6b2o5bobo5bo$24bo2bo53bobob3o6b3o71bo2b
o84b2o5bobo4bobo5b2o4b3o$24bo2bo2bo40b2o11b2o4b3o70bo6b2o94bo2bo13bo$
26bo3bo40bobo89b2o83bo14bo8bo10b2o$30bo41bo91bo82bo2bo12bo3b2o3bo$58b
3o19bo82bo18bo22bo41bo2bo12bo8bo$57b3o19b3o27bo11b3o30b3o6b3o14b3o22b
3o41bo6bobo7bo2bo7bobo19bo$12bo40b3o22bo2bo15bo9b3o69bo28bo48bo4b2obo
4bob2o4bo19bobo$12b3o64b2o13b2o2bo7bo12bo5bo2b2o18b2o2bo5bo4bo2bo12b2o
26b2o40bo7bo5b2o6b2o5bo19bob3o$15bo14bo61b2obo3bo6b2o11bo4b2o4bo16bo4b
2o4bo4bobo81bo2bo35b2o7b2obo4bo$14b2o14b2o60bo6bo19bo11bo14bo11bo5bo82b
o2bo35bobo6bobobobobo$29b2o41bo20bo5bo30b2o14b2o37b2o14b2o45bo14b2o6b
2o15bo8bobob2o$60bo9b3o20bo6bo67bo5bo11bo14bo11bo49b2o6b2o15b2o6bobo$
20b2o35b2o2bo7bo15b2o6bo3bob2o66bobo4bo4b2o4bo16bo4b2o4bo83bo$19b2o14b
2o18b2obo3bo6b2o15bo7bo2b2o25b2o26b2o12bo2bo4bo5bo2b2o18b2o2bo5bo$20b
o14bo19bo6bo20b3o9bo28bo28bo$36b3o17bo5bo20bo41b3o22b3o14b3o6b3o11b2o
17b3o94b2o$38bo17bo6bo63bo22bo18bo124b2o10b2o$48b2o6bo3bob2o104bo13bo
6bo2bo100bob2o$49bo7bo2b2o13b2o91b2o10b3o8b2o87bo2bo9bo2bo$20bo25b3o9b
o15bo2bo22b3o58b2o6bo9bo100b2obo$20bo3bo21bo27b3o19b3o62bo2bo14b2o88b
2o10b2o$20bo2bo2bo48bo19b3o64b3o104b2o$23bo2bo56bo88bobo$25bo56bobo73b
2obob2o6b2o3b3o$63b3o4b2o11b2o73bob2obo12bo2b2obo96bo$59b3o6b3obobo88b
o7bo2bo4b5o94bobo6b2o15b2o6b2o$58b3o6bo4b2obo87b2o6bo2bo2b4ob2o90b2ob
obo8bo15b2o6b2o14bo$66bob2obo3b3o95b2o5b2o91bobobobobo6bobo35bo2bo$65b
o2bo3b3o3bo96b2ob2o93bo4bob2o7b2o35bo2bo$65b2o2b3o3b3o88b2o7bobobo94b
3obo19bo5b2o6b2o5bo7bo$72bo2bo91bo108bobo19bo4b2obo4bob2o4bo$71b2o91b
3o9b3o98bo19bobo7bo2bo7bobo6bo$164bo139bo8bo12bo2bo$304bo3b2o3bo12bo2b
o$194bo97b2o10bo8bo14bo$16b2o28b2o132b3o9b3o98bo13bo2bo$16bo5b2o16b2o
5bo143bo98b3o4b2o5bobo4bobo5b2o$17b3obobo5b2o2b2o5bobob3o132bobobo7b2o
97bo5bobo5b2o6b2o5bobo$19bobo6bobo2bobo6bobo5bo128b2ob2o110b3obobo16b
obob3o$20b2o6b2o4b2o6b2o4b3o126b2o5b2o107bo5b2o16b2o5bo$27bobo4bobo10b
o127b2ob4o2bo2bo6b2o97b2o28b2o$26b2o8b2o9b2o126b5o4bo2bo7bo$11b3o12bo
2bo4bo2bo138bob2o2bo12bob2obo$12b3o12bob2o2b2obo18bo124b3o3b2o6b2obob
2o$18bo10bo4bo10bo7b3o128bobo$16b2ob2o22b2ob2o4bo141b3o$18bo26bo6b2o124b
2o14bo2bo113b2o$12b3o164bo9bo6b2o114bo$11b3o152b2o8b3o10b2o121bobo22b
o$27b2o6b2o129bo2bo6bo13bo64b2o28b2o26b2o2b2o16b3o$27b2o6b2o12b2o138b
o18bo22bo23bo5b2o16b2o5bo30b2o15bo3b2o$48bob2o95b3o17b2o11b3o6b3o14b3o
22b3o22b3obobo16bobob3o22b2o20b2obob2o3bo$48bo3bo6b2o144bo28bo23bobo20b
obo25bo18bo2bobobob3o$49b3o7b2o84bo5bo2b2o18b2o2bo5bo4bo2bo12b2o26b2o
24b2o20b2o24bo20b2o3bobobo$50bo94bo4b2o4bo16bo4b2o4bo4bobo74b3o4b3o31b
2o23b2ob2o$39b2o104bo11bo14bo11bo5bo60bo13bo3bo2bo3bo13bo$39b2o115b2o
14b2o37b2o14b2o21bo2bo10bo5b2o5bo10bo2bo15b2o$194bo5bo11bo14bo11bo10b
o2bo11bo3bo2bo3bo11bo2bo14bo2bo9bo12b2o10b2o$63b2o6b2o120bobo4bo4b2o4b
o16bo4b2o4bo12bo13b3o4b3o13bo12b2obob2o9b3o10bobo11bo$63b2o6b2o14bo62b
2o26b2o12bo2bo4bo5bo2b2o18b2o2bo5bo19b3o18b3o19b2obo39bob2o$85bo2bo61b
o28bo72bo36bo15bo11bobo10b3o9b2obob2o$85bo2bo62b3o22b3o14b3o6b3o30b3o
12bo2bo34bo2bo13b2o10b2o12bo9bo2bo$46b2o15bo8bo13bo66bo22bo18bo54bo2b
o34bo2bo50b2o$47bo8b2obo3bo8bo3bob2o114bo56bo14b2o6b2o14bo$44b3o10bob
2o2bo8bo2b2obo7bo107b2o70b2o6b2o38b2ob2o23b2o$44bo12bo5bo8bo5bo6bo2bo
98b2o6bo117bobobo3b2o20bo$58bo5bo6bo5bo7bo2bo98bo2bo120b3obobobo2bo18b
o$51b2o5bo4bo8bo4bo9bo100b3o119bo3b2obob2o20b2o$52bo10bo8bo238b2o3bo15b
2o$49b3o4b2o5bo8bo5b2o104b2obob2o122b3o16b2o2b2o$49bo5bobo5bo8bo5bobo
103bob2obo123bo22bobo$53b3obobo16bobob3o106bo148bo$52bo5b2o16b2o5bo105b
2o147b2o$52b2o28b2o20$38b2o3b2o$37bo7bo$40bobo148b2o3b2o$38b2o3b2o145b
o7bo49b2o28b2o$193bobo52bo5b2o16b2o5bo$31b2o158b2o3b2o51b3obobo16bobo
b3o$31bobo217bobo5bo8bo5bobo5bo62b2o13b2o$33bo169b2o47b2o5bo8bo5b2o4b
3o4b2o55bobo10bo2bobo$33b2o167bobo54bo8bo10bo7b2o55b2o9b3o5bo2b2o$35b
o5bo160bo41bo9bo4bo8bo4bo5b2o61b2o10bo6b2obo2bo$33b3o5bo159b2o40bo2bo
7bo5bo6bo5bo67bobo10b2o4bobob2o$32bo8bo152bo5bo42bo2bo6bo5bo8bo5bo66b
2o4bo13bo$32b2o160bo5b3o42bo7bob2o2bo8bo2b2obo71bob2o21b2o$194bo8bo48b
2obo3bo8bo3bob2o71bo23bo$38bo163b2o41bo13bo8bo26b3o49bo21bobo$37bobo203b
o2bo47b3o68bo3b2o$36bo3bo4b2o150bo45bo2bo41bo63bo10bo$36bo3bo4b2o149b
obo45bo14b2o6b2o18b3o14b2o6b2o36b2ob2o6b2ob2o$36bo3bo148b2o4bo3bo59b2o
6b2o18bo2bo13b2o6b2o38bo10bo$37bobo149b2o4bo3bo77bo10b2o37b3o15b2o3bo
$38bo156bo3bo75bo2bo47b3o15bobo21bo$38bo157bobo76bo2bo16bo26bo21bo23b
o$37bobo157bo78bo8bo7b2ob2o22b2ob2o18b2o21b2obo$36bo3bo156bo87bo9bo10b
o4bo10bo31bo13bo4b2o$36bo3bo4b2o149bobo105bob2o2b2obo12b3o21b2obobo4b
2o10bobo$36bo3bo4b2o148bo3bo103bo2bo4bo2bo12b3o18bo2bob2o6bo10b2o$37b
obo149b2o4bo3bo92b2o9b2o8b2o33b2o2bo5b3o9b2o$38bo22b2o28b2o96b2o4bo3b
o84b2o7bo10bobo4bobo39bobo2bo10bobo$61bo5b2o16b2o5bo103bobo85b2o4b3o4b
2o6b2o4b2o6b2o33b2o13b2o$32b2o28b3obobo16bobob3o51b2o28b2o22bo92bo5bo
bo6bobo2bobo6bobo$32bo8bo10bo11bobo20bobo53bo5b2o16b2o5bo119b3obobo5b
2o2b2o5bobob3o$33b3o5bo8b3o12b2o20b2o55b3obobo16bobob3o28b2o89bo5b2o16b
2o5bo$35bo5bo7bo22b3o4b3o64bobo20bobo11bo10bo8bo89b2o28b2o$33b2o14b2o
20bo3bo2bo3bo13bo50b2o20b2o12b3o8bo5b3o$33bo36bo5b2o5bo10bo2bo56b3o4b
3o22bo7bo5bo$31bobo37bo3bo2bo3bo11bo2bo41bo13bo3bo2bo3bo20b2o14b2o$31b
2o39b3o4b3o13bo42bo2bo10bo5b2o5bo36bo$65b3o18b3o49bo2bo11bo3bo2bo3bo37b
obo$45b4o46bo44bo13b3o4b3o39b2o$45bo48bo2bo49b3o18b3o$44bo5bo4bobo36b
o2bo42bo46b4o$45bo8b3ob2o12b2o6b2o14bo41bo2bo48bo$44b2ob2o5bo4bo12b2o
6b2o56bo2bo36bobo4bo5bo$45b2o8bo3bo79bo14b2o6b2o12b2ob3o8bo$55bo3bo94b
2o6b2o12bo4bo5b2ob2o$34b2o28b2o110bo3bo8b2o$35bo21bo6bobo109bo3bo$35b
obo6bo21bo103b2o28b2o50bo70bo$36b2o28b2o101bobo6bo21bo49b3o70b3o$42bo
3bo122bo21bo6bobo48bo76bo$42bo3bo8b2o111b2o28b2o49b2o74b2o$20b2o6b2o12b
o4bo5b2ob2o131bo3bo$5bo14b2o6b2o12b2ob3o8bo122b2o8bo3bo62bo14bo32bo14b
o$4bo2bo36bobo4bo5bo120b2ob2o5bo4bo12b2o6b2o39b3o12b3o30b3o12b3o$4bo2b
o48bo122bo8b3ob2o12b2o6b2o14bo13bo9bo3bo10bo3bo28bo3bo10bo3bo9bo$6bo46b
4o121bo5bo4bobo36bo2bo12bo8bo2b2o12b2o2bo3b3o14b3o3bo2b2o12b2o2bo8bo$
13b3o18b3o29bo112bo48bo2bo12bo3bo5b3o14b3o3bo2b2o12b2o2bo3b3o14b3o5bo
3bo$6bo13b3o4b3o34bobo25b2o28b2o55b4o46bo17b2o29bo3bo10bo3bo29b2o$4bo
2bo11bo3bo2bo3bo34b2o25bo5b2o16b2o5bo75b3o18b3o23bo32b3o12b3o32bo$4bo
2bo10bo5b2o5bo61b3obobo16bobob3o42b2o39b3o4b3o13bo17bo32bo14bo32bo$5b
o13bo3bo2bo3bo20b2o30bo11bobo20bobo44bobo37bo3bo2bo3bo11bo2bo$20b3o4b
3o22bo28b3o12b2o20b2o47bo36bo5b2o5bo10bo2bo$13b2o20b2o12b3o28bo22b3o4b
3o54b2o14b2o20bo3bo2bo3bo13bo82bo22bo$12bobo20bobo11bo30b2o20bo3bo2bo
3bo13bo41bo5bo7bo22b3o4b3o38bo32bo23b3o22b3o$10b3obobo16bobob3o61bo5b
2o5bo10bo2bo38b3o5bo8b3o12b2o20b2o31b2o30b2o22bo7b2o10b2o7bo$9bo5b2o16b
2o5bo25b2o34bo3bo2bo3bo11bo2bo37bo8bo10bo11bobo20bobo86b2o26b2o$9b2o28b
2o25bobo34b3o4b3o13bo39b2o28b3obobo16bobob3o29bobo3b2o16b2o3bobo31bo12b
o$66bo29b3o18b3o75bo5b2o16b2o5bo23b3o2bobo2bo2bo14bo2bo2bobo2b3o30bo4b
o$76b4o46bo45bo22b2o28b2o34bobo14bobo14b2o18b3obo3bo2bo3bob3o$76bo48b
o2bo42bobo88b2o14b2o15bobo17b5obobo2bobob5o$75bo5bo4bobo36bo2bo41bo3b
o4b2o114bo11b3o7b2ob2obo2bob2ob2o7b3o$76bo8b3ob2o12b2o6b2o14bo42bo3bo
4b2o118bo8bo13bo4bo13bo$75b2ob2o5bo4bo12b2o6b2o57bo3bo81b2o26b2o10bo11b
o6b3o14b3o6bo$76b2o8bo3bo80bobo82bo28bo11b2o16b2o2bo10bo2b2o$86bo3bo81b
o84b3o22b3o33bo12bo$65b2o28b2o75bo86bo22bo$66bo21bo6bobo73bobo$66bobo
6bo21bo72bo3bo125bobo10bobo$67b2o28b2o71bo3bo4b2o118bo16bo$73bo3bo92b
o3bo4b2o94bo16bo11b3o2b3o11bo16bo$73bo3bo8b2o83bobo101b2o3bo6bo3b2o11b
ob4obo11b2o3bo6bo3b2o$51b2o6b2o12bo4bo5b2ob2o83bo93b3o7bob4o4b4obo10b
o3bo2bo3bo10bob4o4b4obo7b3o$36bo14b2o6b2o12b2ob3o8bo190bo3bo2bo3bo10b
ob4o4b4obo10bo3bo2bo3bo$35bo2bo36bobo4bo5bo77b2o98bobo11bob4obo11b2o3b
o6bo3b2o11bob4obo11bobo$35bo2bo48bo78bo8bo91bo12b3o2b3o11bo16bo11b3o2b
3o12bo$37bo46b4o79b3o5bo99bo16bo30bo16bo$44b3o18b3o101bo5bo100bobo10b
obo32bobo10bobo$37bo13b3o4b3o39b2o65b2o100b2o74b2o$35bo2bo11bo3bo2bo3b
o37bobo65bo101bo76bo$35bo2bo10bo5b2o5bo36bo65bobo102b3o70b3o$36bo13bo
3bo2bo3bo20b2o14b2o65b2o105bo70bo$51b3o4b3o22bo7bo5bo$44b2o20b2o12b3o
8bo5b3o72b2o3b2o$43bobo20bobo11bo10bo8bo73bobo$41b3obobo16bobob3o28b2o
70bo7bo$40bo5b2o16b2o5bo100b2o3b2o$40b2o28b2o22bo$93bobo$86b2o4bo3bo$
86b2o4bo3bo152b2o28b2o$92bo3bo152bo5b2o16b2o5bo$93bobo154b3obobo3b4o2b
4o3bobob3o$94bo157bobo6bo6bo6bobo9b2o$94bo158b2o5b2o6b2o5b2o12bo$93bo
bo167b4o19bo14b2o6b2o$92bo3bo163b3o4b3o17b2o12b2o6b2o14bo$86b2o4bo3bo
147b3o15bo4bo55bo2bo$86b2o4bo3bo148b3o13b2o4b2o54bo2bo$93bobo156bo9bo
4bo9bo6b2o15b2o6b2o13bo$94bo77b2o76b2o26b2o3bo2bo7b3o3bo2bo4bo2bo3b3o
$173bo78bo24bo6bobo12bo2bo6bo2bo11bo$99b2o72bobo69b3o37bo12bo14bo9bo2b
o$91bo8bo73b2o68b3o51bo2bo8bo2bo9bo2bo$91bo5b3o160b2o6b2o13bo14bo14bo
11bo$91bo5bo162b2o6b2o12b2o15bo2bo6bo2bo$98b2o182b2o10b2o4bo2bo4bo2bo
4b2o$99bo79bo102bo10bobo5b2o6b2o5bobo$99bobo76b3o4b3o103b3obobo16bobo
b3o$100b2o76bo111bo5b2o16b2o5bo$290b2o28b2o$88b2o3b2o92b2o$90bobo73b2o
18bo$87bo7bo69bo23bo$88b2o3b2o73bo18b2o$150bo15b2o$148bo2bo$145bo2bo2b
o24bo$145bo3bo17b3o4b3o$145bo17b2o10bo$163b2o2$145b2o16b4o$146b2o13b3o
3bo11b2o$15b2o130b2o11bo5b2o11bobo9b3o65bo$12bo2bo131bo12b2o19bo8b3o65b
o2bo$10b3o3b3o127bo23b2o9b2o3b3o69bo2bo2bo$9bo3b3o3bo9b2o134b2o3b2o88b
o3bo$10b3o3bob2o6bo2bo124bo12bo96bo$12bob2o8b3o3b3o106b2o12bo6b3o2b3o
$13bobob2obo2bo3b3o3bo106bo11b2o6b2ob4o38bo$16b2ob2o3b3o3bob2o76bo26b
3o13b2o6b5o5bo31b3o25bo14bo$3bo22bob2o80b3o24bo16b2o7b3o4bobo13b2o14b
o27bo2bo12b3o$2bobo6bo15bobob2obo78bo53bo2bobo13bo15b2o26bo2bo2bo12bo
14b2o$3bo6bobo17b2ob2o77b2o53b2o2b2o13b3o43bo3bo11b2o12b2o2bo$10bobo142b
o11bo2bo65bo25b2ob2o$11b2o77b2o23b2o34bo3bo4b2o6b3o25b3o54b3o7b3o$2b2o
16bo70bo6b2o14bobo32bo2bo2bo5bo6bo12b2o15bo53b2ob2o$3bo14b2obo68bo7bo
15b2o33bo2bo8bobo11b2o5bo14b2o19bo26bo6bo2b2o12b2o$3o13bob2o25b2o42bo
b3ob2obo10b2o11b2o26bo11b2o4bo6bo3b3o36b3o24bo7b2o14bo$o16bo24bo2bo43b
o3bobobo11b2o11bo53b4o41bo14bo8bo24b3o$25b2o13b3o3b3o38bobo6bo23bobo97b
2o14b2o34bo$25bobo11bo3b3o3bo9b2o24b3ob2o29b2o56b2o55b2o$3b2ob2o17bob
o12b3o3bob2o6bo2bo24bo86bo2bo3b2o$3bob2obobo15bo15bob2o8b3o3b3o22b3ob
2o75bo3bo3bo21b3o27b2o26bo$8b2obo31bobob2obo2bo3b3o3bo23bob2o75bo2bo4b
o17b3o30b2o14b2o11bo3bo$4b2obo3b3o3b2ob2o24b2ob2o3b3o3bob2o31bobo69b3o
21b3o32bo14bo12bo2bo2bo$4bo3b3o3bo2bob2obobo31bob2o35b3o15bo61bo66b3o
12bo2bo$5b3o3b3o8b2obo6b2o2bo20bobob2obo31bo15b3o39bo20b2o67bo14bo$8b
o2bo6b2obo3b3o4bo2b2o23b2ob2o47bobo39b2o19b2o$7b2o9bo3b3o3bo4bo10bo74b
2obo31b2o20bo$19b3o3b3o26b2o63b2ob3o30bo70bo$22bo2bo30bo10bo57bo35b3o
62bo3bo$21b2o18bo13b2o8b3o20b2o29b2ob3o31bo4bo2bo61bo2bo2bo$41b2o13bo
7bo22bobo23bo6bobo33bo3bo3bo64bo2bo$41bo22b2o21bo11b2o11bobobo3bo35bo
2bo71bo$42b2o42b2o11b2o10bob2ob3obo$53bo40b2o15bo7bo$33b2ob2o26bo28bo
bo14b2o6bo$33bob2obobo22bobo27b2o23b2o42bo4b2o$38b2obo22bo102bobo$34b
2obo3b3o3b2ob2o44b2o71bo$34bo3b3o3bo2bob2obobo41bo72b2o$35b3o3b3o8b2o
bo41b3o$38bo2bo6b2obo3b3o41bo$37b2o9bo3b3o3bo$49b3o3b3o$52bo2bo$51b2o
18$187b2o$71bo115bo$70bo2bo32b2o28b2o47bobo$70bo2bo2bo29bo5b2o16b2o5b
o47b2o$72bo3bo30b3obobo16bobob3o45bo$76bo32bobo20bobo5bo40b3o$110b2o20b
2o4b3o39b2obo$118bo6bo11bo42bo$58bo58bobo4bobo10b2o34b3o2b3o$58b3o46b
2o7bo2bo4bo2bo$61bo14bo40bobo4bobo$60b2o14b2o33bo6bo6bo6bo5bo33b2o$75b
2o22b2o10bo20bo5bo35bo18b2o$55b2o38b2obo2bo9bo20bo6bo31bo23bo$54bobo9b
2o27bo3b2o2b2o34b2o31b2o18bo$54bo10b2o14b2o13b3o2b2obo29b2o4bo52b2o$53b
2o3bo7bo14bo16bobo16b2o6b2o9b2o2bo$57bobo22b3o15bob2o13b2o6b2o10b3o$46b
2o2b2o6bo25bo10b2o2bo3bo82b3o2b3o$46bo2bo2bo42bo2bob3o5b2o76bo$43b2ob
ob2obobo38b2obob2obo7bobo72bob2o$43bo2bo6bo2bo2b2o5bo25b2obobo2bo9bo72b
3o$45b2ob4ob4o2b2o5bo3bo24bo2bob2o8b2o72bo12b2o28b2o$47bo4bo13bo2bo2b
o22b2obo6bo74b2o15bo5b2o16b2o5bo$47bob2o2b2ob5o8bo2bo25bo5bobo6b2o64b
obo16b3obobo16bobob3o$46b2obo4b2o4bo10bo26bob2o3bo7bo65bo20bobo5b2o6b
2o5bobo$49bo2bo4bo39b2ob2o9bobo64b2o10bo10b2o4bo2bo4bo2bo4b2o$49bobob
2ob2o53b2o51b2o6b2o15b2o15bo2bo6bo2bo$50b2obo95bo14b2o6b2o14bo2bo13bo
14bo11bo$53bo94bo2bo37b2o14bo2bo8bo2bo9bo2bo$53b2o52b2o39bo2bo53bo14b
o9bo2bo$100bo5bobo41bo13b2o6b2o32bo2bo6bo2bo11bo$100bo5bo2bo47b3o3bo2b
o4bo2bo3b3o20b3o3bo2bo4bo2bo3b3o$100bo6b2o41bo11bo2bo6bo2bo32b2o6b2o13b
o$108bo39bo2bo9bo14bo53bo2bo$99bo48bo2bo9bo2bo8bo2bo14b2o37bo2bo$60b2o
2b2o3b2o27b2o20bo28bo11bo14bo13bo2bo14b2o6b2o14bo$60bo3bobo2bo28b2o19b
2o41bo2bo6bo2bo15b2o15b2o6b2o$55bo5b3o2bo3bo27bo20b2o36b2o4bo2bo4bo2b
o4b2o10bo10b2o$55b3o5bobob4o48bo36bobo5b2o6b2o5bobo20bo$49b2o7bo6bobo
42bo43b3obobo16bobob3o16bobo$50bo6b2o5b2obob2o39b2o6bo34bo5b2o16b2o5b
o15b2o$45bo2bo19bobo3b2o33bo2bo5bo34b2o28b2o12bo$45b5o24bo35bobo5bo77b
3o$76bo33b2o83b2obo$47bo24b4obob2o114bo$46bobo2b2o19bo2bob2obo107b3o2b
3o$46b2o3b2o53b2o$63b3o39bobo$63bo2bo5b2o3b2o26bo81b2o$44bob2obo2bo14b
o4b2o2bobo25b2o83bo18b2o$44b2obob4o10bo2bo10bo108bo23bo$48bo14b3o121b
2o18bo$50bo24b5o128b2o$49b2o3bobo19bo2bo$54b2obob2o5b2o6bo$57bobo6bo7b
2o125b3o2b3o$54b4obobo5b3o131bo$54bo3bo2b3o5bo128bob2o$55bo2bobo3bo133b
3o$54b2o3b2o2b2o134bo$195b2o$194bobo$194bo$193b2o!

First pass at a p38 attempt - missing only F=28

Code: Select all

x = 79, y = 70, rule = B3/S23
52bobo10bobo$51bo2bo10bo2bo$50b2obo12bob2o$42b3o11b2o4b2o11b3o$32b2o24b
o2bo$32b2o7bo3bo3bob4obobo2bobob4obo3bo3bo$24b2o15bo3bo4bo3bob2o4b2ob
o3bo4bo3bo$25bo29b3o4b3o$23bo8b2o4b2o2bo3bo7b2o8b2o7bo3bo$20bo2b5o3bo
2bo2bo2bo5bo6b2o10b2o6bo$20b3o5bo2bo2bo2bo2bo4bo7b2o10b2o7bo$23b2obo2b
o2b2o4b2o6b3o22b3o$18b4obobo22bo22bo$17bo3bobobobo$17b2o4bobobo10b2o$
19bo2bo3bo11b2o$15b4o2bob3o3bob2o$15bo2bob2obo5b2obo$20bo2bo$18bo2bob
2o$18b2obo6bo$21bo5bobo6b2o$21bob2o3bo7bo$20b2ob2o9bobo$34b2o2$30b3o$
30bo2bo$23bo4bo$23bo4bo5bo$23bo4bo4bo$31bo$22bo$21b2o20bo$21b2o19b2o$
21bo20b2o$42bo$33bo$31bo4bo4bo$30bo5bo4bo$36bo4bo$31bo2bo$32b3o2$29b2o
$28bobo9b2ob2o$28bo7bo3b2obo$27b2o6bobo5bo$36bo6bob2o$30b2o8b2obo2bo$
31bo9bo2bobob2o$31bobo7bob2obob2o$32b2o5b3obo2bo$2b2o34bo3bo2b2o$3b2o
10b2o6b2o13b4o$o14b2o6b2o16bobo$2o35bob2o2b3o$bo35b2o2b2o3bo$9bo20bo9b
o2bob2o$9bo6bo6bo6bo10b2o$9bo5b3o4b3o5bo$14b12o$13b2o3b4o3b2o$3b2o9b12o
$4bo10b3o4b3o$b3o4b2o6bo6bo6b2o$bo5bobo20bobob2o$5b3obobo16bobob2obo$
4bo5b2o16b2o$4b2o!

[WhiteHawk]

Omnifrequent p38! 457 cells

Code: Select all

x = 93, y = 70, rule = B3/S23
55b2o30b2o$54bo34bo$55bobo28bobo$56bo5b2o16b2o5bo$44b2o5b3o7bo2b2o12b
2o2bo7b3o$44b2o16bo2bo12bo2bo$36b2o25b3o12b3o$37bo$35bo8b2o4b2o$32bo2b
5o3bo2bo2bo2bo4b2o26b2o$32b3o4bo3bo2bo2bo2bo4bo28bo$35bobo6b2o4b2o6b3o
22b3o$30b4obob2o21bo22bo$29bo3bobo$29b2o4b4o11b2o$31bo2bo15b2o$27b4o2b
ob3o3bob2o$27bo2bob2obo5b2obo$32bo2bobo$3b2o8b2o15bo2bob2o$4bo8bobo14b
2obo6bo$4bobo7b2o17bo5bobo6b2o$2o3b2o26bob2o3bo7bo$obo29b2ob2o9bobo$2b
o43b2o$2b2o$4bo5bo$2b3o3b3o$bo4b2o27bo$b2o6b2o24bo$9bo25bo6b2o$42bob3o
$34bo6bo5bo$3b4ob4o2b2o17b2o6b2o5bo6bo$7bo6b2o17b2o19b2o$33bo6bo5b2o6b
2o$41bo5bo6bo$42b3obo$45b2o6bo$53bo$53bo$7bo6b2o$3b4ob4o2b2o2$41b2o$9b
o30bobo9b2ob2o$b2o6b2o29bo7bo3b2obo$bo4b2o31b2o6bobo5bo$2b3o3b3o37bo6b
ob2o$4bo5bo31b2o8b2obo2bo$2b2o39bo7bobo2bobob2o$2bo40bobo3bo3bob2obob
2o$obo41b2o3bob3obo2bo$2o3b2o42bo4bo2b2o$4bobo7b2o11b2o6b2o13b4o$4bo8b
obo11b2o6b2o16bobo$3b2o8b2o34bob2o2b3o$49b2o2b2o3bo$19bo24bo7bo2bob2o
$17b2o26b2o6b2o$19bo9bo4bo9bo$28b2o4b2o$29bo4bo$15b2o10b3o4b3o$16bo13b
4o$13b3o4b2o5b2o6b2o5b2o$13bo5bobo6bo6bo6bobob2o$17b3obobo3b4o2b4o3bo
bob2obo$16bo5b2o16b2o$16b2o!

Only p19 and p31 remain

EDIT: (3/18)
Reduction to p23 (170 cells)

Code: Select all

x = 42, y = 26, rule = B3/S23
17b2o14b2o$12bo4bobob2o10bo$4b2o6b3o4bobo2bo10bo$3bobo2b2o5bo3b2o2b2o
6b5o$2bo2bobobo4b2o15bo$2b2obobo26b2o$5bob2o25bobo$2b2obo30bo$o2bobo10b
o2bo15b2ob2obo$2o2bo4b2o5b2o6b2o12bob2o$8bo2bo11bo2bo11bo$2o2bo4b2o6b
2o5b2o11b2o$o2bobo9bo2bo14bo$2b2obo25b4o$5bob2o21bo3bo$2b2obobo18b2o2b
o2bo$2bo2bobobo9b2o5b2o3b3o$3bobo2b2o4b2o3bo$4b2o4b2obobo4b3o$10bob2o
bobo4bo11bo2bo$16b2o16b4o$31bo$31b5o$35bo$33bo$33b2o!

[WhiteHawk]

Resurrecting this thread with a potential idea for a p19 (only a trivial weld of Cribbage & Goban covers all frequencies) - cribbage annoyingly covers all frequencies aside from F=9.

This p57 LCM shows that it is possible to slightly perturb the large cribbage stator.

Code: Select all

x = 39, y = 21, rule = B3/S23
28bo$27bobo$16bo10bob3o$14b3o9b2o4bo$13bo11bo2bob2o$13b2o9bob3obo6b2o
$24bo5bobo5bo$10bo15b4o2bo2bobo$b2o7b2o8bo5bo6bo$bobo16bo6b2o2b4obo$3b
o7bo8bo7bo5bo$3b2o6bo16bob4o2bo$b2o2bo5bo8b2o7bo3bob2o$o2b3o15bo8bo2b
o$obo4bo23bobo$bob3obo9b2o13bo$3bo2bo11bo$bo2b2o9b3o$b2obo10bo$4bo$4b
2o!

To prove p19 omnifrequency, it might be possible to potentially hook up a rephased reaction or partial wire to the large cribbage stator that would suffice providing an F=9 cell.

Edit (9/3): Reduction to Omnifrequent p15 (76 cells, down from 79)

Code: Select all

x = 25, y = 20, rule = B3/S23
6b2o$3b2o2bo$b3ob2o$o$b3ob2o$3bob2o2$7b3o$6bo3bo6b2o$5bo5bo4bobo$6bo3b
o5bo$7b3o5b2obo$15bo2bo2bo$15bobob2obo$8bo6bo2bo2b2o$4bo2bobobo9bo$4b
4ob2obo3bobo3b3o$8bo3bo4bo6bo$6bobo3b2o$6b2o!