A visual analysis of calculation-paths of the mandelbrot set

In this paper we present a new method for analyzing some properties of the Mandelbrot Set. The algorithm used for our visual analysis is closely connected to Pickover Stalks and Buddhabrot method. Pickover Stalks method created biomorphs, diverse and complicated forms greatly resembling invertebrate organisms. Our method extends these previously developed methods that introduce the concept of preserving information about calculation steps when calculating the Mandelbrot Set. We create images that visualize statistical information for the calculation-paths of points tested for belonging to the Mandelbrot Set. Two variations of this method are presented: one that only takes into account the paths taken and one that also uses information about their lengths. We have developed software that enables us to analyze new properties of the Mandelbrot Set that can be seen when these new display methods are used. In this paper we also present in detail important features of our software.