Logan Apple

Statement

I'm Logan Apple, a Caltech graduate who loves creating fractal art. My artwork focuses on composing mathematical transformations in iterated function systems, painting them with colorful gradients, and rendering infinitely scalable designs. I've been exploring the intersection of math and art for over 8 years, tying together themes of nature, space, and geometric patterns. ‍ I love being able to take math—which people frequently see as cold and calculating—and bring it to life in vibrant images. I often address pressing environmental issues and make them the foci of my pieces. I've also previously hosted presentations on dynamical systems and created tutorials to teach others how to make their own fractal art.

Artworks

"Amber Memories" is an iterated function system (IFS) fractal. Iterated function systems are finite sets of contraction mappings on a complete metric space. Thanks to Banach's Contraction Mapping Theorem, there exists a fixed attractor which we'll converge to in any such set of functions. By playing the chaos game, we can render an image of this attractor over time. ‍ The main body is constructed from a 3rd power Julia transformation and a foci transformation adjusted by pre and post curl transformations. The camera itself is transformed using a hypertiling, which splits the singular plant into four. Additional detailing is provided by spiral, depolar, and crackle transformations.