AforAmpere wrote:wildmyron wrote:Nevertheless, here's the first 2c/5 orthogonal ship I have found in this rule (making good use of the above fuse):

Nice! That is smaller than I thought it would be to be honest. I can't find any frontends for C/2, but I have no proof that they are impossible yet. Is there some way to prove it?

Let's assume symmetry for simplicity.

The width of the leading edge of a c/2 engine alternates either between 1 and 3 or between 2 and 4.

Regardless of which, the only possibility that allows the center to survive and contribute to the next advancement is one bit followed by one bit:

Since the leading bit must remain alive to become the trailing bit 2 generations later, all four dots must experience birth and the trailing bit must survive to give S5.

But ensuring the front tip's survival via S1 leaves only three undeclared neighbors for the trailing which cannot be on since S234 isn't there.

We have two options for our frontend:

`...o... ..ooo..`

.o.o.o. o.ooo.o

oo...oo

...o... ..ooo..

.o.o.o. .ooooo.

??...??

(exactly one of the ?'s on each side is ON)

It looks improbable that c/2 exists.

When I started writing this post I thought maybe I'd end up with an argument that could be extended inductively into an interminable ribbon (similar to infinite lines in GoL needed for lightspeed) but I'm not sure if anything concrete is reachable from there now.