wildmyron wrote:I made this p39 using the p3 bumper I posted earlier...I was hoping for p36 because the reaction supports p36 streams, but that doesn't work out. I can't quite figure out the math behind what period loops can be made with this kind of interaction. If I understand correctly there's no way to enlarge the loop in order to make it work at p36 - it requires another reflector with a different delay. How do I work out what's required to make it work?
Actually period 36 is perfectly doable. Good thing, too, because we have a critical shortage of alternate color-preserving reflectors that work at p36. A CP semi-cenark can be overclocked to p36, but we'd run out of gliders in the loop after a while.
To figure this kind of thing out, first work out the total period of the loop -- 39*4 = 156 in this case. Then start adding 8N until you get a multiple of the period you want. In this case, +3fd, stretching the loop three cells diagonally to get to 180 ticks, is the minimum. You have to add one more glider to the loop to get p36:
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x = 50, y = 50, rule = B3/S23
The next loop of the right size is +12fd. So there you could make the bumper mechanisms 90-degree rotationally symmetrical, but you have to have seven gliders in the loop so the whole thing is only C4 symmetric with a time shift (or however you say that):
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x = 59, y = 59, rule = B3/S23
Every time you add 9fd -- 9*8=72 ticks -- you have to add two more gliders to the loop to fill it up at p36.
There's a weird optical illusion in both of these, where it looks like the gliders couldn't possibly be evenly spaced... but oscar reports them both as p36 oscillators.
The cases where enlarging the loop doesn't help are situations where you want some number like 8N, but what you have is 8N+k for nonzero k. No matter how many eights you add it never seems to help.