For many of us, the first time we appreciated the art of math was when we played with a Spirograph. However, it's a long way from addition and subtraction to epicycloids, and very few of us actually study math that far. But those who do sometimes end up creating some very beautiful artworks based on mathematics and geometry.
Sculptor Bathsheba Grossman creates metal and crystal artworks of forms found in math, physics, biology, and astronomy. Grossmen shows us Borromean rings, hypercubes, gyroids, fractals, Calabi-Yau spaces, and interlaced sculptures based on the five Platonic solids. I particularly like this Voronoi network wrapped onto a Möbius toroid, sculpted in white glass.
The Julia set is a fractal equation that produces a series of rather pleasing spirals. Designer Marc Newson took that fractal shape and designed a necklace of 2,000 diamonds and sapphires that took jewelry craftsmen 1,500 hours to put together. Note that the necklace is not symmetrical, but still has a sense of balance. See how the jeweler, Boucheron, advertises the necklace.
Probably the best known artist to use math concepts in his works is M.C. Escher. Many of his 2-dimensional drawings turned 3-dimensional geometry on its head. The lithograph titled Waterfall illustrates the concept of the Penrose triangle, also called the impossible triangle. Escher also explored tessellations in many of his drawings.
Paul Nylander was one of the developers of the Mandelbulb that we saw in a previous math post. He is a computer engineer and an artist who renders math and science concepts into colorful images including animated .gifs to help us visualize their 3- or 4-dimensional structures. Shown is a Dodeca-Spidroball, a variation on the spidron, which was invented by Daniel Erdely in 1979.
Belgian mechanical engineer Jos Leys renders and animates all kinds of math concepts into beautiful forms that boggle the mind. His artworks include fractals, Kleinian groups, inversive geometry, recursions, tessellations, knots, and tilings in both images and video renderings to show 3- and 4-dimensional effects. The image above is called Indra200, an example of "Kleinian jewelry". Other artists rendering math images worth checking out include Torolf Sauermann, Brian Johnston, Mehrdad Garousi, and the late Titia Van Beugen.
Creating visual representations of math concepts became easier with computer rendering software and digital video capabilities. That doesn't mean it is simple. Homporgo, the artist who created this video of a Mandelbox zoom said in a comment:
Believe me Bill, I wanted to go further too, but at the end part a single frame took 18 minutes to render, and the whole 1:27 minute video needed 12 days nonstop rendering. I felt thats more than enough at the time.
Twelve days! The result looks worth it to me. How about you? See more fractals on video in this post.