"Peer Below the Surface - No. 65.270"

Digital print of 3D model on photographic paper, 23” x 19”, 2009.

Serial coordinate transformations interleaving symmetry preserving and symmetry breaking operations yield a stunning variety of forms. A sequence of fourteen such operations in 3D create this shape from the unit square. Small spheres are initially an array of 40000 normals to the surface at a distance of 0.05. Larger spheres represent hierarchical clustering centroids of the normals in their final positions. Sequences are selected with a genetic recombination function using esthetic appeal as the fitness function. This transformation sequence begins with a cylindrical transform around the z-axis, and finishes with a spherical coordinate transform and rotation around the y-axis.

Leo S. Bleicher Owner, Cepheus Information Systems
San Diego, CA

"These images are from 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."