## Doug Dunham |

Color print,11” by 11”, 2007.

This pattern contains lizards, fish, and bats representing the three
classical elements, earth, water, and air. The pattern is inspired by
M.C. Escher's Notebook Drawing Number 85. In this hyperbolic pattern,
four
blue lizards meet head-to-head, five red fish meet head-to-head, and
three
yellow bats meet head-to-head, unlike Escher's pattern in which three of
each animal meet head-to-head. The symmetry group of this pattern is
generated by reflections across the lines of bilateral symmetry of each
of the animals; its symmetry group is the hyperbolic kaleidoscope group
*543, in orbifold notation.

Doug Dunham, Professor of Computer Science, Department of Computer Science,
University of
Minnesota Duluth

Duluth, Minnesota, USA

"The goal of my art is to create repeating patterns in the hyperbolic
plane.
These patterns are drawn in the Poincare circle model of hyperbolic
geometry,
which has two useful properties: (1) it shows the entire hyperbolic
plane in
a finite area, and (2) it is conformal, i.e. angles have their Euclidean
measure, so that copies of a motif retain their same approximate shape
as
they get smaller toward the bounding circle. Most of the patterns I
create
exhibit characteristics of Escher's patterns: they tile the plane
without
gaps or overlaps, and if colored, they are colored symmetrically and
adhere
to the map-coloring principle that adjacent copies of the motif are
different
colors. My patterns are rendered by a color printer. Two challenges
are
to design appealing motifs and to write programs that facilitate such
design
and replicate the complete pattern."