# David M. Freeman

Growing up, I always thought that I would pursue a career in the visual arts. However, my vocational pursuits took an unexpected turn when I decided to become a double major in math and visual art as an undergraduate student. I subsequently obtained a PhD in math while putting my artistic pursuits on hold for a number of years. At present, I am exploring ways in which I can return to the creation of visual art equipped with my experience as a researcher in the field of Geometric Function Theory. My work below is an expressions of my current interest in finding aesthetically pleasing and mathematically interesting ways to visually represent a given rational number via objects such as non-periodic substitution tilings of the Euclidean plane.

This image represents a portion of the Pythia substitution tiling discovered by Dirk Frettlöh, with geometry determined by roots of the polynomial x^11-x^3-1. It is composed of 858 similar, non-overlapping right triangles of 11 different sizes arranged using 28 different orientations. Triangles with the same orientation, up to a rotation by 180 degrees, have received the same color. The image was produced using Python code and enhanced using Adobe Illustrator and Photoshop CC. The color scheme has been selected in order to convey a layered, light-hearted mood in which horizontal, vertical, and diagonal patterns interlace to form alternatingly positive and negative space for the eye to explore.

This image represents a portion of the Pythia substitution tiling discovered by Dirk Fretthlöh, with geometry determined by roots of the polynomial x^19-x^5-1. It is composed of 858 similar, non-overlapping right triangles of 11 different sizes arranged using 28 different orientations. Triangles with the same orientation have received the same color (within a bit of artistic liberty). The image was produced using Python code and enhanced using Adobe Illustrator and Photoshop CC. The color scheme has been selected in order to convey a fragmented, textured landscape in which the contrast between vertical and horizontal patterns is highlighted and energized. This image also possesses a colder, wintry atmosphere.