Dan Bach
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!
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?
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.