I've been looking at more hybrids, including through my partials collection. I've looked at honey farm, pi, R, and LOM so far. I have not looked at B or century yet, nor have I looked at traffic lights with 2D displacement (i.e. movement on both axes), although I'm aware an 8+10 century shuttle already exists.
I got the idea from this p150 (hybrid of 64 and 236), which was found by multiple people back in 2024.
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x = 73, y = 43, rule = B3/S23
45bo$43b3o$42bo$42b2o2$39bo$39bo3$37b2o3b2o19bo$38b5o19b2o$39b3o8bo10b
2o3b2o$32bo7bo8bobo8b3o$10b2o18b3o16bob2o8b2o$10bo18bo22bo9b2o5b2o$8bo
bo18b2o21b2o9bo5bobo$4b2o2b2o61bo$4b2o6bo58b2o$12b3o$15bo27bo5b3o$4b2o
8b2o25b3o5b2o$40b2o5b2obo$2o2bo2bo31bo7b3o$2o6bo3b2o26b2o5bo$5b5o$5bo
2b2o22b2o$5bo2bo23bobo$6bobo25bo$32bobo$9b2o21b2o$9bobo$10b2o2$7b2o28b
2ob2o$8bo29bob2o$5b3o28bobo$5bo28b3obo$33bo3bo$30bo2b4o$30b3o$33b2o$
32bo2bo$33b2o!
This is an example of what I was looking for, although after I created it, I saw that it was already known. It's p21, as a hybrid of p20 and p22 lumps of muck shuttles.
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x = 40, y = 32, rule = B3/S23
9b2o$9b2o2$7b4o11b2o$6bo3bo11bo3b2o$6b2o16bo2bo$23b2obo8b2o$6b2o8b3o7b
4o6bo$2b2obobo6b2o2bob2o2b2o4bo5bob2o$o2bob2o7bo2b2o7b2o4bo2b2o2bo$2ob
o10b3o6b2o3bo4bo3b2o$3bo20bobo2bo3bob2o$3b2o3b2o7bo6bo3bo4bo2bo$9bo7bo
7b2ob4obobo$6b3o12b2o4bo4b2ob2o$6bo8bo3bo2bo4bob2o$13b3obob2o5b2obo$
12bo4bo11bo$9bo2bobobob2obo7b2o$9b3o4bobob2o$12b2obo2bo$7b4obobo3bo$7b
o2bobo4bo$12bo$11bo4bo$11b5o2$11b2obobo2bo$11bob2ob4o$15bo$15bobo$16b
2o!
Back to the partials:
Here are two complete pi-heptomino hasslers that rotate 90° per quarter cycle; the full periods are p152 and p160. By hybridizing it and replacing the sparkers with compatible periods, we could create a p154 or p156 (or theoretically p158 but 2×79 feels a lot trickier for valid sparkers).
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x = 122, y = 57, rule = B3/S23
19b2o$19b2o2$17b4o$13b2o2bo2bo2b2o$13bobobo2bobobo87bo$15bobob2obo88bo
bo$14b2obo2bob2o87bobo$16b3o59b2o11b2o17b2obob2obo$18bo60bo11bo16bo4bo
bob2o$17b3o58bo13bo2b2o14b3o$18bo2bo4bo51b2o5bo5b2o2bo11bo3bo2bo$19bo
6b3o52b2obobob2o6b3o14b2o$14bob2o4b2o5bo11b2o8b2o23b5obobobobob6o3bo8b
o$13bo3bobo4bo3b2o11b2o5b2o2bo22bo4bo3bobo3bo4bo2b2o10b5o$13bo6bobobo
16bobo3bo2b2o24b3ob2o2bobo2b2ob3o20bo$14bobo4b3o18bo2b4o29bo5bobo5bo
17b5o$41bo3b2ob2ob3o54bo$42bobobo3bo2bo25bo3bo3bo3bo21b2o$45bob2obo2bo
b2o24bo7bo17bo3bo2bo$30b2o9bo7b5ob2o43b2o9b3o$30bobo6bo2b2o56bobo5bo4b
obob2o$32bo6bo2bo6b3o50bo7b2obob2obo$30bobo6bo3bo5bo2bo47bobo8bobo$30b
2o9b2o8b2o47b2o9bobo$112b2ob2o$44b2o68bobo$13b2o29bo38b2o15bo13bo$12bo
bo27bobo37bobo27bobo$12bo29b2o38bo15b3o11b2o$11b2o67bobo$80b2ob2o$4b2o
8b2o67bobo$4bo2b2o5b2o67bobo$5b2o2bo3bobo62bob2obob2o$8b4o2bo63b2obobo
4bo$2ob3ob2ob2o3bo67b3o$2obo2bo3bobobo67bo2bo3bo17bo7bo$3bo2bob2obo70b
2o21bo3bo3bo3bo$3b5o7bo72bo$13b2o2bo15bobo4b3o39b5o17bo5bobo5bo$5b3o6b
o2bo14bo6bobobo37bo20b3ob2o2bobo2b2ob3o$4bo2bo5bo3bo9b2o3bo3bobo4bo38b
5o10b2o2bo4bo3bobo3bo4bo$4b2o8b2o11bo5bob2o4b2o45bo8bo3b6obobobobob5o$
28b3o7bo43b2o14b3o6b2obobob2o$30bo6bo2bo41bo2bo3bo11bo2b2o5bo5b2o$36b
3o44b3o14b2o2bo13bo$37bo40b2obobo4bo16bo11bo$35b3o40bob2obob2o17b2o11b
2o$33b2obo2bob2o40bobo$34bobob2obo41bobo$32bobobo2bobobo40bo$32b2o2bo
2bo2b2o$36b4o2$36b2o$36b2o!
p54 (hybrid of 48 and 60); 60 is known but 48 is also incomplete. Honey farm, offset (4,0) from the obvious center. The domino spark must be just a domino and nothing else; anything "behind" the domino will cause it to fail.
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x = 19, y = 24, rule = B3/S23
2b2o$2b2o$2b2o$2bo$bobo$2bobob3o$3bob4o5b2o$4bo8bo2bo$13b2obo$16b2o$
13b2o3bo$12bo2b3o$11bob2o$12bo2bo$6bo7b2o$5b3o$4b5o$3b2o3b2o$ob3o3b3o$
o2b2o3b3o$4b5ob3o$5b3o3bobo$6bo6bo$13b2o!
p91 (hybrid of 56 and 126); 126 is complete but 56 is not. It feels hard to get the spark in.
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x = 29, y = 29, rule = B3/S23
21b2o$17b2o3bo$18bo3bobo$18bob2obobob2o$7bo11bobobob2obo$7b3o12b2o$10b
o10bo2b4o$9b2o6b2o2b2obo2bo$17b2o2b2obobo$25bo4$3b2o$3b2o4$3bob2o9b2o
2b2o$b3ob2o7b2obo6b2o$o13bo9b2o$b3ob2o7b3o4bo$3bobo6bo7bo$3bobo6bo8bo$
4bo$16b2o$17bo$14b3o$14bo!
This one is pretty much impossible, but it shows more of what I was doing. p209 partial, hybrid of 146 and 272, 146 is complete but 272 is not. 209 is 11×19.
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x = 39, y = 33, rule = B3/S23
17b2o5b2o$12b2o3b2o5b2o3b2o$4b2o6b2o15b2o6b2o$5bo31bo$5bobo27bobo$6b2o
27b2o5$36b2o$24b2o3b2o4bobo$23bo2bob3o5bo$24b2o2b2o$28b3o$29b2o2$25bo$
25bo$2b2o20bobo$bobo21bo$bo7bo15bo$2o6bobo$9b2o6$12b2o$13bo$10b3o$10bo!
In the images below, here are the reference cells. For the R-pentomino, it matches the official conduit orientation, rotated 90° so forward is up. LOM doesn't have an official conduit orientation, but since it looks identical after a 180° flip, only an orientation needs to be defined, not a center cell. "18, 40" in the R-pentomino section is completely incompatible.
The wiki page on honey farm shuttles lists offsets already, so I used that rather than creating a table.
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x = 13, y = 5, rule = LifeHistory
10.3A$.A8.A.A$ACA6.A2.A$2.A6.A.A$9.3A!
User:HotdogPi/My discoveries
Periods discovered:
All evens ≤128 except 52,58,78,82,92,94,98,104,118,122
5-15,㉕-㉛,㉟㊺,51,63,65,73,75
1㊳㊵㊹㊼㊽,54,56,72,74,80,90,92
217,240,300,486,576
Guns: 20,21,32,54,55,57,114,117,124,126
SKOPs: 32,74,76,102,196
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