James Anthony

Statement

A few years ago, I had the opportunity to introduce how mathematics can be used to generate art to my liberal arts mathematics students. Some of my students were interested in the connection between mathematics and art and I realized that I was not alone in my appreciation of that connection. Since then, I have had the opportunity to see how the mathematics of fractals is represented in art and nature. From the connections between mathematics and nature or creating artwork based on music, to analyzing whether cells are cancerous by determining their fractal dimension, I find all parts fascinating! At one point, I found only the mathematics beautiful. Now, I have an appreciation for the wondrous combination of art and mathematics.

Artworks

In my creation of mathematical fractals using an iterated function system, I was attempting to reproduce images that resembled flowers. This flame fractal uses multiple functions with associated colors and rotational symmetry.

Flame Fractals are generated using a set of functions and variations. The functions are assigned colors and then repeatedly selected at random to map the current point in the plane to a new point. The color of the visited point is then altered based on the selected function. Nonlinear variations can be applied to generate stunning works of art. The uniqueness of the artwork comes from the various functions and colors used. Minute changes to the functions can produce vastly different images. This is part of a collection of images where I was attempting to generate flowers.