After retiring from teaching in 2014, I migrated into interactive book production, using Apple’s iBooks Author. Making the graphics and movies for the book, I started concentrating on producing nice-looking images, pushing the limits of my computer saving or crashing. The Joint Mathematics Meetings in Atlanta was my first show as an artist. I actually had two pieces accepted but I didn’t scroll enough on the gallery site and only brought one canvas. I’ve included the other work here because I can.
“A Fine Mesh We’re In” by Dan Bach, 2016
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.
“Growing Parallel Normal Curves” by Dan Bach, 2016
The starting red curve has a center of curvature at each of its points. The colored parallel curves go toward that center in increasing amounts. Some groups of curves are rotated, some are reduced in number, but all originate from the same ball-shaped bundle at the top, appropriately used as the dansmath.com logo.