Three students paint a large pipe structure in shades of green, blue, and purple, working together outdoors to add colorful designs to the metal surface.

A Pipe Dream: Making Space for a Space-Filling Curve

Heidi Opdyke

The Carnegie Mellon Math Club brought math to life by building an iteration of a 3D Hilbert curve using PVC pipes. This "space-filling curve" follows one single, continuous path that visits every part of space without self-intersection. The fractal design was constructed first in pieces, and then all together following the same pattern. This is the second year in a row Math Club has kicked off the year with a mathematical sculpture build. In 2025, they built "Knight's Move" which represented the moves a knight can make on a 3D chess board, and happens to be a rigid unit distance graph with no triangles.