GENERATION AND GRAPHICAL ANALYSIS OF MANDELBROT AND JULIA SETS IN MORE THAN 4 DIMENSIONS

A method to define and generate Mandelbrot and Julia sets in more than four dimensions is presented. A doubling process is used to create fr om the set of real numbers a hypercomplex number system of arbitrary d imension. Since the new number system is closed under addition and mul tiplication, it can be used to generate Mandelbrot and Julia sets of c orresponding dimension. generation of these sets in more than four dim ensions is discussed. A graphical analysis manifests the sets are frac tal in these higher dimensions. Symmetrical properties of Mandelbrot a nd Julia sets are observed and reported. Copyright (C) 1996 Elsevier S cience Ltd