Algorithm for external argument calculation of the nodes of a shrub in the Mandelbrot set

Abstract

Misiurewicz points are essential points of the Mandelbrot set. External arguments are the most useful tool in order to analyze these points; therefore, it is important to go deeper in the study of the external arguments' calculation of these points. In this paper we introduce an algorithm to calculate the external arguments of the branch points, or nodes, of a shrub, since such nodes are the most outstanding Misiurewicz points of the chaotic region of the Mandelbrot set. Devaney and Moreno-Rocha had already presented a paper where they calculated the external arguments of one of these Misiurewicz points, the main node of a shrub. Our algorithm widens the study of Devaney and Moreno-Rocha because it allows one to calculate the external arguments of any node of the shrub.