Artists
Logan Apple
Software Engineer
Seattle, Washington, USA
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 10 years, tying together themes of nature, space, and geometric patterns. I love bringing math to life in vibrant images with elements that tie into the real world! 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
"The Furtive Garden" 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. Via chaos game, we can render an image of this attractor over time.
This piece is a logarithmically tiled elliptic split with a spherically transformed camera. Each split is cropped at a certain limit and filled with a crackle transformation to create the starry inlays. A depth sine transformation and additional unlinked crackle transformations create a perception that the elements of the inlay are floating out and escaping the splits.
"Inversion" 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. Via chaos game, we can render an image of this attractor over time.
This piece has the camera transformed by a -3rd power Julia transformation, with the main body being an elliptic split composed by a 2nd power Julia transformation creating a geometric petal pattern. The central body within the flower is distorted by a loonie transformation with a radius of 1, creating a boundary to which the petals converge.