Plotting basins of end points of rational maps with Sage

Abstract

The aim of this work is to present a new program written in Sage which allows us to visualize the attraction basins associated to the end points of a discrete semi-flow induced by a rational function on the Riemann sphere by using its geometry and complex structure. One interesting novelty brought by the developed program is that it is able to plot fractals not only in a determined rectangular area of the complex plane, but also on the whole surface of the Riemann sphere. Another advantage of the program is that it permits us to visualize not only the attraction basins of fixed points, but also the basins of end points associated with periodic points. In addition, some applications of the described algorithms to Numerical Analysis and Fractal Geometry are suggested.