Two iterations of the Hilbert curve with different colors. This was made by laser cutting two sheets of paper. (Photo: Edmund Harriss) Two iterations of the Hilbert curve with different colors. This was made by laser cutting two sheets of paper. (Photo: Edmund Harriss)

This is a part of my Hilbert curve explorations that took place during the Illustrating Mathematics program at the Institute for Computational and Experimental Research in Mathematics (ICERM). I believe that we can gain understanding by looking at an object – in this case the Hilbert curve – from different perspectives, so I set forth to play with the curve in many different ways:

This project has also been documented on the ICERM project pages, and it has found it’s way to the Illustrating Mathematics book, published by the American Mathematical Society (AMS).

If you want to know more about the Hilbert curve, check out one of these books:

  • Michael Bader, An Introduction with Applications in Scientific Computing, Springer-Verlag Berlin Heidelberg, 2013.
  • Doug McKenna, Hilbert Curves: Outside-In and Inside Gone, Mathemæsthetics, Inc. (2019).
The Hilbert curve. More squiggly! The Hilbert curve. More squiggly!

Hilbert Curves

November 30, 2020
The Hilbert curve. No fuss. Very Straight. The Hilbert curve. No fuss. Very Straight.