Logan Apple

Statement

My art focuses on composing mathematical functions in iterated function systems, painting them with colorful gradients, and rendering infinitely scalable designs. I've been creating fractal art for over 7 years, tying together themes of nature, space, and geometric patterns. I will often address pressing environmental issues, such as the Australian wildfires of 2019-2020, and make them the foci of my pieces. I love being able to take math—which people frequently see as cold and calculating—and bring it to life in vibrant images. I've previously hosted presentations on dynamical systems and chaos theory, the basis of iterated function systems, and created tutorials on how people can make their own fractal art.

Artworks

"The Wandergreen" is an iterated function system (IFS) composed of spherical transforms, eyefish lensing, Gaussian blurred circlecrops, and hexagonal tilings. Iterated function systems are finite sets of contraction mappings on a complete metric space. Thanks to Banach's Contraction Mapping Theorem, we know there exists a fixed attractor which we will converge to in any such set of functions. By playing the chaos game (start with a fixed point $x_0$ and generate successive iterations as $x_{k+1} = f(x_k)$ where $f$ is a random iterator), we converge to an image of this attractor over time.