Digital Sculpture
Department of Mathematics, University of Illinois
Please read my statement on
Optimal Geometry as Art
The sculpture "Minimal Flower 3" is constructed mathematically as
a minimal surface, modeling a soap film spanning a complicated knotted
boundary wire. Surface tension pulls the film tight, to minimize
its surface area. The resulting shape has 3-fold and 2-fold
rotational symmetry but no mirror symmetry; it consists of
a central monkey-saddle surrounded by three looped and twisted
bands. Topologically it thus forms a nonorientable punctured
Dyck surface. The piece is an homage to the American sculptor
Brent Collins, whose "Atomic Flower II" inspired me to attempt
to capture the same intricate topology and symmetry as a minimal
surface. The sculpture is produced directly from the computer model
using a 3D-printer. Instead of thickening the minimal surface
by a constant amount, we make the object thinner at the edges
and thicker in the middle by doubling the soap film and blowing
(virtual) air between the two sheets; facing surfaces thus have equal
and opposite constant mean curvature.
Click on any image below to see a larger version.
At Intersculpt:Ohio in Dayton, January 2002
VRML version of the sculpture Minimal Flower 3
