Bridges 2024 Exhibition of Mathematical Art, Craft, and Design

Andrew Malek

Artists

Andrew Malek

Art and Mathematical Sciences Student

Clemson University

Clemson, South Carolina, USA

amalek124@yahoo.com

Statement

Through my four years of university, I have studied mathematics and art separately. This piece has allowed me to combine my disciplines to visualize the interesting mathematical and geometric concept of complex numbers. Artistically, I have always had an interest in strong uses of color, line, and space; and mathematically I have always liked geometry and number theory. For these reasons, I was immediately drawn to the spirals and infinite repetition that form naturally in the powers of complex numbers. This work is a piece emphasizing the natural curvature and repetition of the lines that are created through multiples of these numbers.

Artworks

Image for entry 'Fractal Flower from Loxodromes'

Fractal Flower from Loxodromes

17.0 x 61.0 x 61.0 cm

Styrofoam, acrylic paint, inkjet printer, digital.

2024

Additional info

The power of a complex number, when the power varies, can be visualized as a never-ending spiral which is self-similar across different scales in the complex plane. It spirals out from the origin (source) toward infinity (sink). Inspired by fractals found in nature, I created this piece which is composed of images of these spirals under Mobius transformations. All curves are colored based on the magnitude of the complex number. The design is presented on the complex plane together with the Riemann Sphere. Loxodromes, which correspond to the spirals under the stereographic projection, are carefully located and painted on the sphere. An animation which zooms in and out from the source and sink is also made to highlight the fractal patterns.