Non-Cubic Space Division
"Non-Cubic Space Division" by Tor Olav Kristensen (2003)

M.C. Escher's "Cubic space division" ("Kubische ruimteverdeling") lithograph from 1952 inspired me to make this image. The shape of the cross sections of the "bars" in this image is formed by the function for a superellipse. And the cube-like shapes at the intersections of the girders are formed with the function for a superellipsoid. I "disturbed" the 3-dimensional grid by using a function that rotates the shape according to 3 noise functions; one for each of the x-, y-, and z-axes. I wanted all the shapes to be joined smoothly, so I added the functions for the "bars" and the "cubes" with the help of a "blobbing" function; the Sigmoid function. The Sigmoid function has a S-shape that is similar to the shape of the tanh() function. Here are two relevant links: [1] [2].

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