Associate Professor of Mathematics
Humans have long used pattern as a means to understand and discern the behavior of the world around us. This exploration often leaves us debating whether patterns of design or behavior are inherent in a system under investigation or if we devise them as a means to understand the system’s behavior. Perhaps pattern’s origin is less important than the artistic and scientific beauty often uncovered in its pursuit. Sixfold Symmetry stages scientific and mathematical thought alongside artistic rendition, showcasing inherent, intrinsic patterns as well as premeditated, deliberate ones. Two of the disciplinary tools or perspectives I often use when investigating patterns as a scientist and mathematician, or that I harness to construct patterns, are algorithms and dynamic processes. The exhibition, through its interdisciplinary breadth, explores both of these ideas.
One pattern investigated in the show is the six-sided symmetry of the snowflake. The German mathematician and astronomer Johannes Kepler presented the essay, Strena seu de nive sexangula (On the Six-Cornered Snowflake) to his patron and benefactor, Johannes Matthaeus Wacker von Wackenfels, as a New Year’s gift for 1611. Kepler considers the origin of the snowflake’s intricate hexagonal structure: “There must be some definite cause why, whenever snow begins to fall, its initial formations invariably display the shape of a six-cornered starlet.”(1) Within his essay, Kepler looks for the agent of form, questioning whether the snowflake’s pattern is imposed by God or if the hexagonal form is inherent in the purpose it serves. Kepler seeks analogies in the construction of other natural forms, such as seed packing in a pomegranate or the hexagonal cells in a honeybee hive. These problems all apply to three-dimensional close packing, a concept still relevant in current explorations of molecular structures and orientation. His description of this phenomenon ultimately came to be known as Kepler’s conjecture. While close-packing theories continued to evolve in many contexts, Kepler’s conjecture was finally proven in 1998 by mathematician Thomas Hale using computational methods.
Kepler’s investigation of the origin and function of sixfold symmetry in the snowflake weaves science and art together in a way captured in the microphotographs of snowflakes by Wilson Bentley and the digitally derived Snowfakes by the contemporary mathematicians David Griffeath and Janko Gravner. Through these images we explore the intersection of science, including underlying design and composition, and artistic interpretation.