Why do these ideas happen to me?
I've been fiddling with mazes constructed by randomly selecting 0 or 1 represented by \ and / respectively (at 45 degrees) and now it's occurred to me to use hexadecimal numerals constructed of \ and / in four cells arranged in a square. So now we have a set of hexadecimal numerals which display their binary composition. It seems that now I can construct my mazes by randomly selecting from these numerals with a lot more potential to keep track of the walls and paths in the maze as it's being built. But maybe not. Maybe I just haven't thought enough about how to keep track of the paths using just \ and /. I'm intrigued by the quasi symmetry they display which is why I've arranged them as you see in the diagram.
My table shows five shape classes, each row, in which the members can be made congruent by rotation (well, I guess it's better called translation in the case of the bottom row since the rotation would have to be on a different axis). But I see another way the members of the rows are related. This also seems visual, but what I have in mind is what happens when all the members of each row are combined with the bitwise XOR (exclusive or). From that perspective I find the second from bottom row is most interesting. Maybe it should be split in two and we then have 6 sets of numbers which XOR to F, two groups of four and four groups of two. I don't think I'd ever have noticed that just looking at the 0s and 1s. Such nerdity!
