I recently expanded the wiki page on c/3 orthogonal spaceships to account for everything up to 50 cells. In the process of doing this, I noticed a bunch of commonalities between some of the smaller spaceships as follows:
If we look at four of the five smallest synthesizable spaceships so far, it turns out that they can be broken down into multiple constituent components, which I've color coded below. For the sake of convenience, I've decided to name these "ragged" (white), "crotchet" (red) and "saucer" (orange):
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x = 68, y = 19, rule = LifeSuper
2.M20.Q23.Q15.Q$.M.M18.Q.Q21.Q.Q13.Q.Q$2M20.Q.Q21.Q.Q13.Q.Q$2.M19.Q
23.Q15.Q$2M19.2Q22.2Q14.2Q$3M18.Q.Q21.Q.Q13.Q.Q2$.M.M16.3Q21.3Q13.3Q$
.3M16.3Q21.3Q13.3Q2$4.3O16.3O15.3M19.3Q$4.3O16.3O15.M.M19.3Q2$3.2O17.
2O16.3M21.Q.Q$3.2O17.2O16.2M22.2Q$5.O18.O17.M22.Q$40.2M23.Q.Q$41.M.M
21.Q.Q$42.M23.Q!
If we now look at the two smallest c/3 orthogonal spaceships, we can see that they also can be broken down into these components, but that there also exist an inner c/3 orthogonal wave (cyan) which can be stabilised at both sides by these accordingly:
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x = 28, y = 22, rule = LifeSuper
2.M20.Q$.M.M18.Q.Q$2M20.Q.Q$2.M19.Q$2M19.2Q$3M18.Q.Q2$.M.M16.3Q$.3M
16.3Q2$4.3S16.3S$4.3S16.3S2$3.2S17.2S$3.3S16.3S2$6.3O16.3O$6.3O16.3O
2$5.2O17.2O$5.2O17.2O$7.O18.O!
And this wave can be extended indefinitely:
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x = 47, y = 18, rule = B3/S23
3b2o$o2b2o$2ob2o4b2o$2o4bo2b2o$6b2ob2o4b2o$6b2o4bo2b2o$12b2ob2o4b2o$
12b2o4bo2b2o$18b2ob2o4b2o$18b2o4bo2b2o$24b2ob2o4b2o$24b2o4bo2b2o$30b2o
b2o4b2o$30b2o4bo2b2o$36b2ob2o4b2o$36b2o4bo2b2o$42b2ob2o$42b2o!
The following four spaceships can be derived through similar means, three of which I didn't even see in the updated jslife moving collection:
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x = 59, y = 64, rule = B3/S23
2$30bo$29bobo$28b2o$30bo$28b2o$28b3o2$4bo24bobo$3bobo23b3o$2b2o$4bo27b
3o$2b2o28b3o$2b3o$31b2o$3bobo25b3o$3b3o49bo$34b3o17bobo$6b3o25b3o17bob
o$6b3o45bo$35bobo15b2o$5b2o28b2o16bobo$5b3o28bo$36bobo13b3o$2b3o31bobo
13b3o$2bobo32bo$55b3o$b3o51b3o$b2o$3bo50b2o$b2o25bo25b3o$2bobo22bobo$
3bo23bobo21b3o$27bo23bobo$26b2o$26bobo21b3o$50b2o$25b3o24bo$25b3o22b2o
$51bobo$28b3o21bo$28b3o2$27b2o$27b3o2$30b3o$30b3o2$31bobo$31b2o$32bo$
32bobo$32bobo$33bo!
If we can find a way to insert fragments of this wave within the three fenceposts that we can already synthesize, then this should trivially allow for not only all seven of the smallest c/3 orthogonal spaceships to be synthesized, but for arbitrarily large syntheses as well.
I'm almost certain that I'm not the first one who has noticed this given the large existing collections of c/3 orthogonal technology, but I felt this fit here, could be of use for future syntheses, and didn't really know what to search for (especially since the forum forbids searching for "c/3").