Variations on perfection: the Sequin-Collins sculpture generator

Rarely do the pursuits of fine artists, computer scientists/engineers, and mathematicians converge. Sculpture inspired by minimal surfaces offers an exception. As the term implies, a minimal surface is concerned with economy, both in surface area and in the energy expended to bend the surface. Such surfaces can extend infinitely and do not self-intersect. For example, Scherk's second minimal surface is characterized by interlocking saddle forms set 90 degrees to each other. The number of saddle forms (orders) can vary. The paper shows a Scherk's surface of the third order (three saddles coming together). Stacking and mirroring these surfaces creates an interlocking surface comprised of saddle surfaces and holes, and extending the stack results in a form known as a Scherk's Tower. The paper shows examples of a Scherk's Tower of the second order in its generic form and with a twist, a bend, and a twist plus a bend applied.