 
Summary: Mathscape scripts for translational symmetry
Michael P. Barnett,
Meadow Lakes, Hightstown, NJ 08520,
July 7, 2008
Abstract: I discuss the extension of the mathematica2
package mathscape [1, 2]
to produce graphics that have translational symmetry. The graphics include frieze
and tiling patterns. The software supports work on scientific and artistic topics in a
uniform manner.
Introduction
Translational symmetry in Euclidean space is of paramount importance in crys
tallography and many other branches of physics and physical chemistry. One
recent paper on manyelectron wave functions begins: "To exploit translational
symmetry is the primary prerequisite for band theory and band calculations.
Variations on that theme can be found in all textbooks on solid state theory."
[3]. A cursory Google search on "translational symmetry physics" found recent
research papers on quantum optics [4] and electrodynamics [5]. The ideas of
translational symmetry in space are carried over to periodicity in time in the
basic methods of relativity and quantum field theory. Recently, attention has
been directed to the translational symmetry of processes that are periodic in
