I spent a little time looking around the Wikipedia and Wolfram articles on Penrose Tiling, the Domino Problem, Wang Tiles, etc., but I'm having a little trouble getting into them. A lot of these resources are fairly non-linear in that they often have circular dependencies of concepts that you need to know.
For example, I can tell that aperiodicity is important somehow, but I don't know why and I'm not quite sure about the actual definition.
I keep seeing tiling linked in unexpectedly (e.g. L-systems, the Entscheidungsproblem) or in non-mathematical places (games, geometric art... even Neal Stephenson's Anathem) that it seems important and I'd really like to know more.
So, with that said: does anyone have any resources they'd recommend? I'm looking for something fairly complete or at least introductory, not just an article about a certain facet. Books are fine, visual or interactive resources are great. Would love descriptions of practical implications and relationships with other fields.