On numerical approximations of the area of the generalized Mandelbrot sets

Abstract

In the present work, the area of the generalized Mandelbrot sets is defined as the double limit of the areas of the plotted generalized Mandelbrot sets in a given square lattice, using the finite escape algorithm, while the lattice resolution and the number of iteration counts, used to plot them, tends to infinity. The asymptotic behavior of the areas of the generalized Mandelbrot sets in terms of their degree growth is investigated. Finally, numerical approximations of the area of the Mandelbrot set are proposed by using tools from regression analysis. (C) 2013 Elsevier Inc. All rights reserved.