We next introduce a visual notation for the analysis of planar patterns-- a motif, repeated in a regular fashion.
We need some visual notation for
Patterns propogate simply by repeating the motif and the generators as pictured below. This always works-- if you get a conflict, the motif and generators were "illegal".
If our motif is repeated by congruences, we are applying a series of rotations, reflections and translations. We will examine a few more examples and then explore the general case. In time we must find out which combinations do not lead to trouble. Next, though, we'll apply our new notation and analyze some pix!
Chaim Goodman-Strauss Dept. Mathematics Univ. Arkansas Fayetteville, AR 72701 email@example.com 501-575-6332