Dan Bach
I'm Dan Bach (@dansmath on twitter), a former college mathematics
teacher from California. I used Mathematica for over 20 years in the
classroom, teacher workshops, and conference talks. Students convinced
me long ago that my nice-looking calculus graphs could qualify on
their own as art, so I decided that makes me an artist!
Math has long been perceived by many as being separate from art, but
as creators and viewers of math art, we enjoy using both halves of our
brains! After a 35-year teaching career, I am now a 3D math artist and
interactive book author, trying to bring the joy of mathematics to an
unsuspecting audience.
The 3D Hilbert Curve is the limit of square-cornered paths that increasingly fill up the unit cube. I told Mathematica to replace the paths with spline curves. Here we have Hilbert splines 1, 2, and 3, joined by soap films between the 1-2 and the 2-3, which are just linear morphs between two parametric paths. The films then cast a translucent 'fake shadow' on the beach. (Click the link for an interactive 3D Hilbert Spline model!)