Dan Bach

3D math artist / interactive book author
dansmathshop
Northern California, USA
Hi, Dan Bach here. I was a college mathematics teacher in California for three decades, and employed Mathematica in the classroom, for teacher workshops, and at conference talks. My students, over the years, used it to create math movies, graphics, and sounds; these were done as class assignments or purely for pleasure. They convinced me that my calculus graphs looked like art. These days I'm a 3D math artist and interactive book author.
Vine Superloop
50 x 40 cm
Inkjet Print on Canvas
2020
Using Mathematica to create 3D parametric curves, I made a loopy tube surrounded by a thin green one, which to me looked like a vine, so then it needed some leaves. The tube is a trigonometric lissajous curve, and the vine winds around it based on a local frame spinning along the tube's length. The leaves are thin, flat cylinders whose axes align along three things: the tangent vectors of the vine, and the normal and binormal vectors at points along the "inner tube." The shadow was made from a partial z-squashing, a forward rotation, and an image blur of the original model. Follow the link for an interactive 3D version!