Thank you for perfect answers! Seems like a binary symmetry plays some role in this game because both configs are so. And I am amazed that Period-156 has a quadro symmetry!!! (at least if I refuse to consider it as a static image).

Are there any configs (I mean, those having any interesting behaviour) with intention having more than 4 symmetry parts? Or at least just more quadro symmetry configs? I am absolutely sure (since today) there are some for any 2^n, just all unfound.

Any attemts to create Conway's life on hexagon map with apropriate rules?

upd: for a single stream of gliders, what config gives as many gliders per 100 generations as possible? No matter what else it does, I just want a line of gliders with as little space as possible.

-- It's interesting to look at the different symmetries on Catagolue, where the idea is to generate a lot of random soups with different symmetry types, and then just run those patterns and see what comes out. The D8_1 and D8_4 symmetries are 8-way symmetric, which is as high as you're going to be able to get on a square grid.

  https://catagolue.hatsya.com/census/b3s23/D8_1
  https://catagolue.hatsya.com/census/b3s23/D8_4

Scroll down to the bottom of those pages and click on, especially, some of the higher-period "xq{N}" categories. These are objects that showed up "naturally", evolving from random soups.

-- There have definitely been a number of people over the years exploring various outer-totalistic rules on a hex grid, and (to a lesser extent) isotropic non-totalistic rules: see

  https://conwaylife.com/wiki/Hexagonal_neighbourhood

-- The smallest period at which gliders can follow one another is period 14. We don't have a true period-14 gun yet, though. The closest we have is a "pseudo-period" gun -- actually period 28, but it generates two gliders per period, so you end up with a period-14 stream:

  https://catagolue.hatsya.com/object/gun_14/b3s23