I'm planing to write a game based on octagon tiles. Currently I'm wondering how many images I really need. That is something about graph theory, I know that, but not only.
I want to connect each side of the eight sides, but in some cases I also want to connect all eight sides or just two so the complexity grows immense. If I'm not totally confused that ends in 88 which is 2048. Well of cause there are already many dublicated e.g. left to right is equal with right to left. When I'm very tricky I can rotate the image of left to right which I rotate by 90° to get top to buttom. I'm sure there are quiet more things like like mirroring.
My question is now how many images do I really need?
Here is my basic idea as image, of cause it still has some problems, as you can see on my image too but I think it should not be too hard to find a simple solution for such cases.