B2o3m56/S2om4oH (Hex Life)
If you use the Gwylim simulator, note that it uses a unique method of notation used by the person who made the simulator, and that it's written Survive/Birth. View it here. In short, numbers only refer to what is normally referred to "adjacent" placements, and they are SEPARATE from letters. 24a for example means cells are born when they touch 2 adjacent cells, 4 adjacent cells, OR (actually XOR if you want to be technical) two live cells 120 degrees apart from each other. The link explains it better than I can.
Anyhow, my findings. Anyone pressing "random" can find some of these, but others took a bit more fiddling.
First of all there's two natural spaceships, a 2c/3 p3 I call "Hawk" and a c/2 p4 I call "Slider" (it looks a lot like a Glider).
In orthogonal life you have diagonal ships and orthogonal ships. In hex you have ships that travel in the corner direction of a hex, and ships that travel in the side direction of a hex. I will call these corner ships and side ships. The Hawk is a corner ship and the Slider is a side ship. Because of this nature, they can never travel parallel to each other, and there's 12 non-knight directions to travel in.
You can put Hawks close to each other to combine them into one ship producing dots in between, I call this "Hawkmates".
I only found one of these and it occurred naturally!
9c/21 (?) p42 Fly Puffer (corner ship)
I haven't been able to find many of these. The rule seems to move around a lot more than it stays still.
p30 "Sprawler" - this one shows up naturally too, and more often than you might expect.
p22 "Hawkicide" - I found this when experimenting with Hawk guns (more on that later).
You can combine Flies, Gulls, and even Sprawlers together in a number of ways without changing their periods.
Hawkicide can also be extended.
Small 2-and-3-way guns are extremely common in random soups. The rest of these I manufactured. For the triangular ones, the Hawks are launched in the direction of the points of the triangle.
1-way Hawk Gun (p22) - made by combining a two way gun and a Hawkicide.
2-way Hawk Gun (p22) - natural.
2-way Hawk Gun (p9), and extension - made from combining two 3-way guns.
3-way Hawk Gun (p9) - natural.
3-way Hawk Gun (p22) - made from combining two 2-way guns at a different state. Fires 2 up and 1 down.
4-way Hawk Gun 1 (p9), and extension - made from combining two 3-way guns.
4-way Hawk Gun 2 (p9), and extension - made from combining two 3-way guns.
4-way Hawk Gun 3 (p9), and extension - made from combining two 3-way guns.
6-way Hawk Gun (p9) - made from combining six 6-way guns.
2-way Hawkmate Gun (p22), and extension - made from combining two 2-way Hawk Guns.
I have no idea what to do with any of these, so maybe you guys can help me out. There's got to be some kind of higher level design possible with this rule given all the moving parts.
Hawk + Fly = Death of Fly
Hawk + Fly = Fly Puffer (moving 60 degrees to the right of the Hawk's direction)
Hawk + Fly = Slider (moving 30 degrees to the left of the Hawk's direction)
Hawk + Hawk = Death of the back Hawk
Slider + Slider = Death of the back slider
That's all I have for now. Is this rule not interesting? I'd love for somebody to help me find more things and especially to help me figure out some kind of engineering because I'm new and terrible at it.
EDIT: Feel free to suggest a slightly different rule that preserves most of the patterns above if you think it will lead to more involved design.