Leo Bleicher

Statement

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.

Films

Gradual variation of the rotation amount between successive polar, cylindrical or spherical transformations applied to a plane results in an animation of the transition between interesting points in the parameter space. Visualization of the resulting distorted plane and its normal vectors with a slab and spheres created this movie. Additional 'decoration' includes a marker at the coordinate origin and hierarchical clustering of the normal vector markers. Normal vector markers are colored based on their starting position adjacent to the original plane. Still frames were computed with Pipeline Pilot and rendered with POV Ray.