> The significance of this discovery is that it shows that, contrary to intuition, they do exist.
Do you know why wasn't it found so far? Looking at one of the stages, it consists of only two cells. That's something that should be picked up by anyone trying to run a brute-force search for gliders in well under a minute. It's a bit hard to accept for me that it's been an unknown thing for anyone who asked the question. Even the smallest glider on the standard grid is larger in all of the steps. Here you have to consider placing it in a number of places too, but... is this the first time different grid was really considered?
I suspect the main difficulty is not in finding the glider pattern, but in proving that it is in fact a glider. This is not brute-forceable with an aperiodic tiling, pretty much by the definition of an aperiodic tiling.
Let's say you have a pattern P, and you want to check if it's a glider. In Conway's Life, this is straightforward and mechanical: iterate the future states of P, and check if any of them are P but translated some distance. But on a Penrose board, this is not possible: if you translate the pattern, the board is different. You cannot assume that because P translated successfully once, it will translate again (i.e. you cannot "induct").
Furthermore, because the tiling is aperiodic, even brute-forcing the possible patterns is troublesome. Every pattern must specify its origin! On Conway's life, there is only 1 possible 1-tile starting pattern, and only 2 non-trivial 2-tile patterns, because it doesn't matter where you are. Starting your pattern at (0,0) doesn't make it any different than starting at (12,-156). That's not the case on a Penrose board: there are an infinite number of 2-tile cases, one for every possible board location, because they're all different!
If you restrict the vertices you are looking at to the ones within some fixed distance from a central vertex, there are only finitely many cases. This could make brute-forcing possible. (I do agree, though, that this is non-trivial and it looks like that was mainly what you were getting at).
It's not just a matter of the grid, it's also a matter of the rule that is carried out on that grid.
It looks like this is a 4+ state rule, meaning the rule space is massive. To brute force this you would need to not only brute force your way to that small configuration of cells, but you would need to do it for a huge number of different rules before settling on one (I can't say what percentage of this state space would support small gliders, but my intuition says it's relatively rare).
I think maybe you are looking at this from the perspective of studying the game of life, where the rule is already chosen.
Do you know why wasn't it found so far? Looking at one of the stages, it consists of only two cells. That's something that should be picked up by anyone trying to run a brute-force search for gliders in well under a minute. It's a bit hard to accept for me that it's been an unknown thing for anyone who asked the question. Even the smallest glider on the standard grid is larger in all of the steps. Here you have to consider placing it in a number of places too, but... is this the first time different grid was really considered?
I feel like I'm missing some bigger picture here.