Visual Notation

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

• a translation
• a rotation of order n
• a reflection
• the intersection of two mirror lines with angle pi / n
• a glide reflection
• finally, the motif itself

  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".

  

   

  Q5: For example, what patterns are generated by these motifs? Do any of these generate the same pattern? Do all of these actually generate a pattern or do some lead to a violation of the rules?
  

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  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!

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  To theGallery
  to outline
  

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  Chaim Goodman-Strauss
  Dept. Mathematics
  Univ. Arkansas
  Fayetteville, AR 72701
  strauss@comp.uark.edu
  501-575-6332