In a previous paper I discussed the topic of aperiodic tiling for the plane (Glassner, 1998). This technique helps us create patterns with lots of theme and variation, like the leaves on a tree. I continue discussing the subject. The basic approach is to take a bunch of 2D shapes and impose rules on how they can connect, like the pieces of a jigsaw puzzle.
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Andrew Glassner (1998) studied this question.