We present a method for transforming a simple plane figure or motif into another, which is related to it in a definite way, by applying a group of systematic geometric transformations. The method creates certain classes of star motifs from a basic plane figure. We demonstrate that surface design is an ‘atomic’ and a ‘self-assembly’ process, and expansion, figure and motion are the only properties in design which can be directly represented geometrically. By applying a group of fundamental point transformations of the plane, and rearranging the axis of the reflection, we transform a simple figure into a series of complex star motifs. Our ultimate aim is to develop the invariants of design and creative process, and to bring the formal side of art within the purview of mathematics.