Jordan Schettler

Assistant Professor of Mathematics
San Jose State University
San Jose, CA
I am a mathematician whose research interests include number theory and connections of mathematics to art and music. Of particular interest to me is the creation of visualizations of deep mathematical concepts; the visualizations serve as educational tools creating access of topics to wider audiences.
A Resolution of Dali's Swallowtail
A Resolution of Dali's Swallowtail
00:02:52
Jordan Schettler (video and animations)
2017
https://drive.google.com/file/d/0B9S1VUmNX1xrOGt2a01lMVpLZG8/view?usp=sharing
Inspired by Salvador Dali's fondness for catastrophe theory, I created a 4D version of Dali's last painting. This was done by resolving the singularities in the swallowtail and scaling parameters very carefully in the resulting space curve so that a 90 degree rotation gives one an appropriate cubic S-curve. By layering two copies of the space curve from different angles and slanting/breaking the frame, we can get a 3D version of the painting which looks like itself or its reflection from various perspectives. Then a 4D rotation is applied and stereographically projected back to 3D which creates a version of the painting that swims around itself.