# Judy Holdener

When creating artwork I do not see myself as a mathematician who uses algorithms and formulae to create interesting visual patterns. Nor am I an artist who uses mathematics to carry out my artistic vision. Rather, I am an observer and a thinker who seeks to understand patterns in the mathematical and physical worlds in which I live. Both worlds contain realistic and abstract components, and it is the interplay between the realistic and the abstract that I find most exciting. Making use of abstraction, symbols, technology and imagery, I seek to communicate my ideas, experiences and feelings to others, and through my artwork I hope to make abstract mathematical ideas more concrete for some while making reality more abstract for others.

The human brain is remarkable in its ability to fill in missing information as it works to make sense of the data it receives from the surrounding world. In this work I illustrate this phenomenon in the context of the visual system using Hilbertâ€™s famous space-filling curve. Varying the thickness of the sixth iterate of the curve as it traverses the plane, I 3D printed a portrait of David Hilbert. The width of the rectangular piping along the curve at a point depends on the intensity of the pixel at that point. Using the well known photograph of Hilbert sporting a brimmed hat, the piping is wider when the intensity of the pixel is lower (where the image is darker) and thinner when the intensity is higher (where the image is brighter).