COURSES Alejandro B. Engel Department of Mathematics and Statistics Rochester Institute of Technology email: abesma@rit.edu Phone: (716) 475 2123 NICE MATH. RESEARCH OTHER

 Non Classic Sets Ever wondered what lies hidden within these black regions of Mandelbrot and Julia Sets? Well, if you did, you came to the right place.The Classic Mandelbrot and Julia Sets "color" the rate at which the iterations of a seed point leave a disk of a large given radius. Inside these sets, the iterations are bounded, and usually converge towards an attracting orbit. What your are going to see is the colored interior of these sets, using two types of "coloring". Type one measures how many iterations it takes to get within a disk of a given small radius of a point in the attracting orbit. Type two measures how many iterations it takes for the real or imaginary part to come closer than a given small distance from the real or imaginary part of a point in the attracting orbit. The images you are going to see are not for the meek! They contain total nudity of the interior of Mandelbrot and Julia Sets. All right, then: get the show started...! INTERIORS The "interior" of both Mandelbrot and Julia sets are largely unexplored. Thus, most of the properties you may discover will be new.Embark in this fascinating enterprise of exploring and discovering the "interior" of these Sets. May be someday there will be a property that will bear your name.