Central Path Art

Abstract

The central path revolutionized the study of optimization in the 1980s and 1990s due to its favorable convergence properties, and as such, it has been investigated analytically, algorithmically, and computationally. Past pursuits have primarily focused on linking iterative approximation algorithms to the central path in the design of efficient algorithms to solve large, and sometimes novel, optimization problems. This algorithmic intent has meant that the central path has rarely been celebrated as an aesthetic entity in low dimensions, with the only meager exceptions being illustrative examples in textbooks. We undertake this low dimensional investigation and illustrate the artistic use of the central path to create aesthetic tilings and flower-like constructs in two and three dimensions, an endeavor that combines mathematical rigor and artistic sensibilities. The result is a fanciful and enticing collection of patterns that, beyond computer generated images, supports math-aesthetic designs for novelties and museum-quality pieces of art.