Laird Robert Hocking

Statement

As a kid, I grew up exploring coastal British Columbia, sometimes bringing home treasure that I found. I would sometimes feel an intense need to find out what the view is like from a mountain visible in the distance. Similarly, as an adult I find myself intensely curious about, for example, "What do 3D cross-sections of 4D Menger sponges look like?". In both cases, an answer exists - I just have to go out and find it (either by climbing the mountain, or by doing the math). In this spirit, I see mathematical art less as a creative process and more one of exploration and discovery. Just like when I was a kid, I rarely find anything interesting. However, I occasionally stumble up a treasure which I want to take home (with a 3D printer).

Artworks

This piece consists of a 3D Menger sponge (left) as well as 3D diagonal cross sections of two types of 4D Menger sponge. The cube on the left is diagonally cut into two halves held together with magnetism. When they are pulled apart, a pattern identical to that of the hexagonal face of the piece on the far right is revealed. This is because the 2D faces of 3D cross sections of 4D Menger sponges can be expressed in terms of 2D cross sections of 3D Menger sponges. In the middle, a 3D diagonal cross section of a second kind of 4D Menger sponge is etched in glass. A 2D slice of a 3D sponge yields a hexagon with interior hexagram holes. Similarly, a 3D slice of this 4D sponge yields a octahedron with stellated octahedron interior cavities.