Mitchell was born in Iowa, United States, in 1961. His parents were LeRoy and Shirley Mitchell. His father was an art teacher and mother was a stay-at-home mother until Mitchell started seventh grade. Mitchell was a Presidential Scholar in 1979 and went on to pursue engineering at and graduated from Purdue University in aerospace engineering, did a master's degree at Stanford University, and then a PhD work at Purdue. He worked at NASA doing aerospace research. He then worked as a scientist at Arizona Science Center. He served as a mathematics and science professor at the University of Advancing Technology in Tempe, Arizona. As of 2015, he works as a manager at Maricopa County Community College District in Tempe, Arizona.
Like many others, I was amazed at the beauty that arose from iterating such a simple formula. Unlike most, I had the means and inclination to investigate the process further, which fed both sides of me.
In 1999, Mitchell published his Fractal Art Manifesto. The artist Janet Parke notes that in the manifesto, Mitchell suggests that fractal art cannot be made by a computer alone, and that not everyone who has a computer can necessarily make good fractal art. Instead, she explains, Mitchell is arguing that the artist's creative process is needed to inject elements such as the considered selection of colours and gradients, the merging of multiple layers, and decisions on composition such as by zooming in to a fractal.
Mitchell also prepared tutorials on how to create fractal art with tools including Ultra Fractal. In 2011 he served on the panel of the "Fractal Art Contest".