Physics, Mathematics & Computer Science
Event Title
Generalized Mandelbrot Sets
Document Type
Oral Presentation
Location
Indianapolis, IN
Subject Area
Physics, Mathematics & Computer Science
Start Date
11-4-2014 9:30 AM
End Date
11-4-2014 10:30 AM
Sponsor
Bill Johnston (Butler University)
Description
A complex point z0 is in the famous Mandelbrot Set fractal when an iterative process applied to z0 and using the function z2 stays bounded. We investigate what happens if we change the function so that z2 is now composed with a Mobius transformation, indexed on a parameter a. The Mandelbrot set corresponds to a = 0. What happens when we change a = 0 to other values, repeating the same iterative process and then drawing the sets? Do these Generalized Mandelbrot Sets have similar properties as the original? This presentation describes some surprising results, illustrates the sets in computer-generated movies, and uses transcendental functions to produce further set generalizations.
Generalized Mandelbrot Sets
Indianapolis, IN
A complex point z0 is in the famous Mandelbrot Set fractal when an iterative process applied to z0 and using the function z2 stays bounded. We investigate what happens if we change the function so that z2 is now composed with a Mobius transformation, indexed on a parameter a. The Mandelbrot set corresponds to a = 0. What happens when we change a = 0 to other values, repeating the same iterative process and then drawing the sets? Do these Generalized Mandelbrot Sets have similar properties as the original? This presentation describes some surprising results, illustrates the sets in computer-generated movies, and uses transcendental functions to produce further set generalizations.