Dan Bach

3d math artist / interactive book author
northern california, usa

Is it math or is it art?

Multivariable Calculus can provide us with plenty of nice-looking graphs, patterns, and intricate pictures. I have been using Mathematica for over 25 years in the classroom, in teacher workshops and conference talks, and now outside of academics as a 3D math artist and interactive book author. My students and I have inspired each other to create math-based graphics, movies, and sounds; either as class assignments or purely for pleasure.

Whether it's free-form drawing or graphing formulas, if you think it looks nice, and it makes you look twice, then we can call it art!

A Fine Mesh We're In
40 x 40 cm
Inkjet Print on Canvas

A central curve (not shown) has tangent, normal, and binormal directions at each point, making a local {T, N, B} frame. Using a trigonometric combination of the N and B vectors, we describe a toroidal mesh of curves with hues of green, yellow, and orange. Spheres of varying colors and sizes are placed along an equatorial helix and some try to escape their bonds.

Square Gets Loopy
40 x 40 cm
Inkjet Print on Canvas

What if a square wanted to explore its curvy side? Or what if a loopy lissajous figure craved some right angles? You can watch either curve morph into the other, known in math 'circles' as a homotopy. How do you think this 3D model would look, viewed from other angles?