I'm not sure why you are calling it a "proof-of-concept" when it works as presented and explicitly constructs a splitter with a glider to block ratio greater than 2-eps for all eps>0...The (26+n):2n proof-of-concept, as knightlife says, is maybe "cheating a little and not entirely satisfying". I don't think it's cheating exactly,
Oh, I see where this is coming from, now. I was more interested in discovering what output ratios are possible with blockic splitters, while you are interested primarily in applications to a specific construction.but it's not a good solution for the original problem, which really needs as-few-as-possible blocks producing as-many-as-possible gliders.
(I should probably note that I am a mathematician, not an engineer...)
At any rate, it should be possible to construct a blockic splitter with arbitrarily high glider-to-block ratios, provided that we also have access to a blockic pattern which reflects a glider 90 degrees and is destroyed at the same time (a blockic reflector):
First, a single splitter splits the initial glider into two heading in opposite directions (and possibly extra). Glider A travels far away from the initial reaction. Glider B heads to the main reaction. Glider B is split into a bunch of gliders, which are positioned via reflectors to synthesize a Gosper glider gun (while it is unlikely that we could find blockic splitters which produce the exact quantity of gliders needed, extra blocks to eat stray gliders can be added trivially). After an arbitrary amount of time, glider B is reflected back around, and hits a bunch of blocks which release a sequence of gliders which destroy the glider gun (actually, is there a known glider-destruction for a Gosper glider gun?)
In fact, given that what adds gliders to the output is the distance between the reflectors which turn B around and the rest of the pattern, the number of gliders in the output can be increased arbitrarily high without the starting population exceeding some natural number N. Thus arbitrarily high output ratios are possible.
Now that that is settled, the only remaining interesting part of this problem is optimization. The above outline would be extremely difficult to make without using an obscenely high number of blocks and an enormous space for the construction/destruction. So the next thing in my mind concerning blockic splitters is...exactly what you have been doing ...
....
so yea.
