# Leo Bleicher

My mathematical art forms several large series exploring the creation of complex forms through sequences of simple operations or representations of simple relationships. The operations include geometric transformations, neighbor finding, attraction/repulsion and others. These computational processes attempt to replicate features of both geologic and organic morphogenesis.

Sequential Coordinate Transformations deconstruct typical patterns and tilings; only one copy of the primitive object is used. Application of symmetry preserving transformations leads nowhere. However, addition of interleaved symmetry breaking operations allows each sequence to build a unique form. Sequences can thus be thought of as the genetic code for the resulting image. In exploring these forms thousands of images are generated, rated, and recombined to yield further generations of images.

This image was created by application of a sequence of 3D geometric transformations to a collection of spheres on the faces of a hollow cube. The exact sequence to produce this image was obtained through the use of a genetic algorithm using subjective aesthetic appeal as the fittness function.

This image was created by application of a sequence of 3D geometric transformations to a collection of spheres on the faces of a hollow cube. The exact sequence to produce this image was obtained through the use of a genetic algorithm using subjective aesthetic appeal as the fittness function.