Jim Anthony
While teaching at Westminster, I had the opportunity to introduce how mathematics can be used to generate art to my liberal arts 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 combinations of art and mathematics.
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. Originally, I was not going to generate this image as the images take days to generate and I did care for the small sample image that I had produced. I am thrilled that I produced the large version as it is my most popular piece.
The first fractal that I was introduced to (many years ago) was the Sierpinski Triangle. I fell in love with the beauty of the fractal. Recently I was reintroduced to fractals and started generating my own artwork. This variation of the triangle is produced by using an Iterated Function System with three functions and one non-linear variation. I love how beautiful images can be produced using even simple mathematical functions.
In my creation of mathematical fractals using an iterated function system, I was attempting to reproduce images that resembled flames. This flame fractal uses eight different functions with associated colors and eleven non-linear variations.