“The Beauty and Complexity of the Mandelbrot Set”

In this richly illustrated video-lecture John H. Hubbard of Cornell University discusses computer graphics which are the subjects of much current research in pure mathematics. The talk combines real time computer experiments, slides and video to explain the origin and meaning of these remarkable pictures. Prof. Hubbard begins by describing the process of iteration and its place in the history of mathematics. He then shows how it is used to create pictures of Julia sets. Part II of the lecture is devoted to the Mandelbrot set and the computer program used to draw it. Hubbard uses his computer to demonstrate the relationship between the Mandelbrot set and Julia sets. He then shows a supercomputer animated zoom into a portion of the Mandelbrot set’s boundary which reveals an extraordinary richness of detail. Part III discusses the character of the electric fields which would surround electrically charged objects shaped like Julia sets and the Mandelbrot set. In conlusion, Prof. Hubbard makes a few remarks about the philosophical significance of these pictures and programs especially with regard to the field of genetics.