# Carlo Sequin

Prof.

University of California, Berkeley

Berkeley, CA

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.

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.

Lawson's Minum-Energy Klein Bottle

9" x 6" x 4.5"

FDM model

2011

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.

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

Symmetrical Half-way Point for Torus Eversion

6" x 5.5" x 4"

3D-print by Shapeways

2011

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.

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.