1Department of Mathematics, Temple University, 1805 North Broad Street, Philadelphia, PA-19122
2G. Millán Institute of Fluid Dynamics, Nanoscience and Industrial Mathematics, University Carlos III de Madrid, Av. Universidad 30, 28911, Leganés, Spain
* E-mail address: seibold@temple.edu URL: http://www.math.temple.edu/∼seibold
** E-mail address: yfarjoun@ing.uc3m.es
Commissioned by MIT's in-house artist Jane Philbrick, we evolve an abstract 2D surface (resembling Marta Pan's 1961 “Sculpture Flottante”) under mean curvature, all the while calculating the eigenmodes and eigenvalues of the Laplace-Beltrami operator on the resulting shapes. These are then synthesized into a sound-wave embodying the “swan song” of the surfaces as the evolve to points and vanish. The surface is approximated by a triangulation, and we present a robust approach to approximate the normal directions and the mean curvature. The resulting video and sound-track were parts in the Jane Philbrick's exhibition “Everything Trembles” in Lund, Sweden, 2009.
53C44, 58C40, 68U05, sculpture, mean curvature, Laplace-Beltrami, eigenmodes, art, sound
