# Carlo Sequin

My professional work in computer graphics and geometric design has
also provided a bridge to the world of art. In 1994 I started to
collaborate with Brent Collins, a wood sculptor, who has been creating
abstract geometrical art since the early 1980s. Our teamwork has
resulted in a program called “Sculpture Generator 1” which allows me
to explore many more complex ideas inspired by Collins’ work, and to
design and execute such geometries with higher precision.

More recently I have become interested in mathematical and topological
concepts such as the regular homotopies that permit immersions of a
torus or a Klein bottle to be smoothly transformed into other shapes
in the same class. I then try to turn the mathematical models that
illustrate these concepts into aesthetically pleasing sculptural
maquettes.

A torus can be turned inside out with a regular homotopy.

This is a symmetrical half-way point of such a torus eversion. It
shows the same amount of both surface sides. How to actually carry
out the transformation from this point into an either all-red or
all-green torus in the energetically least costly way is still an
open problem.

A gridded model of a Klein bottle (Euler characteristic 0, genus
2) with the minimal possible total surface bending energy.

This energy is calculated as the surface integral over mean
curvature squared.