for example, search for constellations that send gliders back and forth through empty space. If you have one of period p, you can make one of period p + 8n for

for example, search for constellations that send gliders back and forth through empty space. If you have one of period p, you can make one of period p + 8n for every n in Ν by moving the guns further away from each other. Find a few guns that take longer to ‘reload’ upon getting ‘hit’. Search on, and hopefully, you can find the 7 other modulos. And it need not be glider guns. It could also be constellations that send a ‘ripple’ through occupied space back and forth. I guess such ones can be made with smaller periods, but may require larger constants than 8 because you typically can’t move them further apart by a single cell. Edit: another comment mentions https://conwaylife.com/wiki/P43_Snark_loop https://conwaylife.com/wiki/P43_Snark_loop, a single construct that can be tweaked to have any period ≥ 43.