  A two-dimensional configuration is a coloring of the infinite grid Z^2 with
finitely many colors. For a finite subset D of Z^2, the D-patterns of a
configuration are the colored patterns of shape D that appear in the
configuration. The number of distinct D-patterns of a configuration is a
natural measure of its complexity. A configuration is considered having low
complexity with respect to shape D if the number of distinct D-patterns is at
most |D|, the size of the shape. This extended abstract is a short review of an
algebraic method to study periodicity of such low complexity configurations.
