# Mathematical ImageryMathematicians and artists create strong, stunning, works in all media and explore the visualization of mathematics

# Mathematically-Inspired Images :: Kerry Mitchell

My work is composed primarily of computer generated, mathematically-inspired, abstract images. I draw from the areas of geometry, fractals and numerical analysis, and combine them with image processing technology. The resulting images powerfully reflect the beauty of mathematics that is often obscured by dry formulae and analyses. An overriding theme that encompasses all of my work is the wondrous beauty and complexity that flows from a few, relatively simple, rules. Inherent in this process are feedback and connectivity; these are the elements that generate the patterns. They also demonstrate to me that mathematics is, in many cases, a metaphor for the beauty and complexity in life. This is what I try to capture.

— *Kerry Mitchell *

"Golden Cat" is a manipulated photograph. The photo has been manipulated through the use of a three-dimensional version of Pickover's "Popcorn" dynamical system. While this was chosen to add chaotic structures to the image, the serendipitous appearance of the cat became the focus.

"Pigeon" is a manipulated photograph of a pigeon. The photo has been manipulated through the use of a Fourier-series-inspired version of Pickover's "Popcorn" dynamical system. This was chosen to add chaotic structures to the image.

"Mystery 57" is a manipulated photograph of the artist as a child. The photo has been manipulated through the use of a Fourier-series-inspired version of Pickover's "Popcorn" dynamical system. This was chosen to add chaotic structures to the image.

"Seahorse Corral" is a Mandelbrot-type fractal image. Instead of iterating a single polynomial, the formula iterates a rational function composed of two polynomials. The resulting fractal is visually similar to the standard quadratic Mandelbrot set, but adds a great deal of additional structure.

"Who Was She?" is a tribute to my mother, who passed away in 2016. The fractal is a version of a fourth-power Newton's method fractal, employing a complex relaxation parameter.

The genesis of this image has nothing to do with waves; it is a representation of the complex numbers that can be expressed using the base 1 + i. Yet, the spirals inherent in the arithmetic are suggestive of Hokusai's 'The Great Wave Off Kanagawa'.

This Lincoln image was created with math. The image is made up of 500 square tiles of five different types. Typically, I use these tiles to create a sona image, which is a continuous, closed curve around an array of points, such that the curve goes around each point once. In Lincoln, the dots are removed for clarity. The width of the curve was changed on every tile to mimic the grayscale level of that part of the portrait.

This image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration.

This is a tessellation of Penrose tiles. In this set, there are two different tile shapes, a fat rhombus and a thin rhombus. Penrose tiles are remarkable because they can be arranged (as they are here) such that the tiling never repeats, no matter how many tiles are used. Also, each tile is filled with four pursuit curves, the dark curves from each corner to a point near the center of the tile. Imagine a mouse in each corner of the tile. At the same time, each mouse begins moving toward (pursuing) the next mouse. The tracks of the mice are pursuant curves.

This image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. I often find simple images to be the most compelling. I like to let the structure be the focal point, not necessarily the coloring methods of the color palette.

This work was created using a technique very similar to that used in Penrose Pursuit image, also in this album. However, instead of drawing the lines forming the pursuit curves, this image was rendered buy shading the areas inside of the tiles.

This image is in my Mandelbrot and Julia sets collection of images showing the dynamics of a formula under repeated iteration. "Curiosity" celebrates both the unsung measure of central tendency, the harmonic mean, and the Curiosity rover's landing on Mars in August 2012.