Chapter VIII - Parameter Spaces and Mandelbrot Sets

Abstract

This chapter discusses parameter spaces and Mandelbrot sets. Fractal geometers pretend that the surface of the earth is an abstract place and help recreate maps based on parameter spaces. Color expanses on a given cartographical image may be used to identify and demarcate different elements of the map. Inclusion of more colors on a geographical map, for example, provides more information about properties of the earth's surface, thus producing more boundaries on the map. These boundaries can give information about local geometry. The collection of possible parameter values defines a parameter space associated with the family under review. It sometimes may occur that the local shapes of the boundaries in the map reflect the shapes of the corresponding fractals. One good method for map making is based on the use of escape times and employing Mandelbrot sets.