Although my personal blogwall paper is not tessellating because i'm lazaaay, good old m.c. escher knew first what the masterminds will find out soon. When i was a kiddo, i would stare at the wallpaper in my bedroom as i would fall asleep. The overall pattern would emerge but finding where it started and finished was impossible. That game, that game.
Start with an image.
if you like, create a pattern using the image as a stamp. The final image should not touch the edges in any way.
Divide the image in quadrants, and switch them kitty corner: lower left and upper right, lower right and upper left. Then the space around the corners is now in the center! Fill that in with more shapes.
Sooo Simple! Now you can repeat this image forever and ever and ever and ever and ever and....
of course the other way is to take an image and kalideoscope it...it works best here with an image that does touch the edges, like how you spliced the first one, so that they can merge to create a new shape!
But the trick is, for the first block, each new quadrant you must either flip one horizontally, one vertically and one both horizontally and vertically.
Then the new block will touch forever and ever and ever and ever....
For more inspiration check out Julia Rothman's Flickr!