Tile patterns need not be the standard repetitions of conventional tiles. A little creativity with tile design allows an end user to create arbitrary non-repeating long-range patterns. All that is required is a tile image that inter-mates on all four (or three or six) edges and does something useful internally. Here’s a sample black and white line image:
Each edge has 15 lines intersecting the edge at 45 degrees which continue on to an edge, either directly or with internal 90 degree turns. Tiling a surface with these tiles, randomly oriented, produces a non-repeating pattern over the entire surface and disguises the tile edges:
Multiple sets of inter-mating tiles
can be used to produce dramatic non-repeating covers by randomly selecting which tile to use and its orientation at each tile site.
Any group of four distinct images or objects that could be reasonably glued together four different ways would work as well. Just be sure to use images that hide the periodic nature of the tiles.