Shape grammars are being used with increasing success and appeal in th
e design studio. In order to further this work, relationships between
the rules of grammars and the kinds of designs they produce must be be
tter understood. In this paper, correlations are established between t
he symmetry properties of rules and the symmetry properties of designs
generated by rules. This work not only sheds light on the behaviors a
nd outcomes of grammars, it also leads to interesting results new to t
he field of symmetry.