Regular Patterns

We turn to patterns that extend through out the entire plane in some regular fashion. Below, a pattern from fourteenth century Egypt, and a design by the Dutch artist M. C. Escher .

Examine the GSP sketches *333 and 632 for interactive examples (We'll figure out these names later).





Q3: Find at least three more examples of planar patterns in the world around you... In each of these, identify all centers of rotation and mirror lines.

What is a regular pattern?

Q4: In what sense are each of the following "regular patterns"?
(Be generous-- the concept is really rather loose!)
In what ways are they not "regular patterns"?

From Ernst Haeckel's 1904 classic Art Forms in Nature (Dover)

From Jean Andrews' Peppers: the domesticated capsicum (UTexas Press)

(by C.Goodman-Strauss (6)

from The Divine Proportion by Huntley (Dover)


In general such things are hard to truly pin down. But you should at least be thinking about a motif, repeated in some regular fashion. We next turn to

The Rules of the Game
to outline



(5) The Escher print is from Doris Schattschneider's Vision's of Symmetry: the Notebooks of M.C. Escher.

  Chaim Goodman-Strauss
  Dept. Mathematics
  Univ. Arkansas
  Fayetteville, AR 72701