Plotting basins of end points of rational maps with SageLuis Javier Hernandez Paricio, Miguel Maraņon Grandes, Maria Teresa Rivas Rodriguez
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.
Tbilisi Mathematical Journal, Vol. 5(2) (2012), pp. 71-99. |