Logan Apple
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.
"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.