Totalistic spaceships

[Rich Holmes]

What's known about spaceships in totalistic 2-state Moore-neighborhood
CAs other than B3/S23 (Life), B34/S34 (3/4 Life), B36/S23 (Highlife),
B2/, etc? I'm aware of David Bell's 10/93 writeup and of the
spaceships included in the (Mac) LifeLab 3.0 distribution. I've been
doing some searches for small spaceships under various rules and so
far have come across a few; on the long shot chance these haven't been
reported before, here they are. All are orthogonal, shown here moving
to the right.

B3/S124:

o.o
..o
..o
o.o (c/2)

B34/S356:

.o..o
ooo.o
.o..o (c/4)

B35/S134:

..o. (Cute! One more cell and it'd be a Life lightweight; one less
...o and it'd be a Life glider; instead it's a c/3, and the other
oooo two generations look nothing like a lightweight or a glider.)

oo..
...o
...o
oo.. (c/6)

So far, aside from some haphazard looking, I've searched for
spaceships one of whose generations will fit in a 3x4 rectangle in the
following rules:

B2/Snnnn where nnnn is all combinations up to 0123
B3/Snnnn where nnnn is all combinations up to 0123 as well as
4, 04, 14, 014, 24, 024, 124, 0124.

Aside from the one ship in B3/S124 shown above, the only spaceships of
this size (with period up to 20) in any of these rules are the Life
glider and the three known from B2/ (each of which also is found in
some variants of the Life or B2/ rules).

--
- Rich Holmes

Of course it's daft, it's traditional.
- Terry Pratchett

[Rich Holmes]

In article <RSHOLMES.9...@gamera.syr.EDU> rsho...@gamera.syr.EDU (Rich Holmes) writes:

>So far, aside from some haphazard looking, I've searched for
>spaceships one of whose generations will fit in a 3x4 rectangle in the
>following rules:
>
> B2/Snnnn where nnnn is all combinations up to 0123
> B3/Snnnn where nnnn is all combinations up to 0123 as well as
> 4, 04, 14, 014, 24, 024, 124, 0124.

I misspoke; I hadn't yet done B3/S0124. That turns out to have one
small spaceship, moving diagonally up and left at c/14 with period 14
(glide reflection at generation 7):

.OO
...
O..
O..

This also is the only spaceship for this rule in a larger area, 4x5.

I've now done some more searching and found two more spaceships, both
in B3/S35:

.OO OOO.
.OO and ..OO
OOO OOO.
O..

Both are orthogonal to the right. The first of these has speed c/2
and period 8, with a rather interesting history: generation 2 looks
like gen. 0 with an extra, trailing bit; then gen. 4 is a glide
reflection of gen. 2, etc. Random initial fields with this rule tend
to evolve to a rather sparse state, but I've seen this spaceship
produced from a random initial state that was sufficiently large.

The second has speed c/2, period 2. This one also works in B3/S035;
the first is no longer a spaceship but a minimalist puffer train,
leaving behind a trail of isolated cells!