Ok here is a post mainly about some of the process I have been working on to make repeatable pattern tiles. I started thinking about this stuff years ago based on some of M.C.Eschers early experiments with stamps.
The first thing you do is work out how many times you want the edge of each side to touch.
Here is a tile that is 11 units square. The pattern hits the edge of each side 5 times (the red/even numbers).
This next tile is a little more complicated and more geometric, it is 17 units across and the pattern hits the edge 8 times.
Then you just rotate the square -90 degrees to get 4 variations...
From this one tile and its variations you can make endless patterns.
Here things get more complicated with two tiles...
And then we really get moving with a bunch of tiles and the variations.
The next thing I am starting to work on is using different tones in the patterns and using these tones to replicate photographic images like this one of Groucho Marx using 6 tones. It isn't quite working yet but it is getting there.