Tbilisi Mathematical Journal

Plotting basins of end points of rational maps with Sage

Luis Javier Hernández Paricio, Miguel Marañón Grandes, and María Teresa Rivas Rodríguez

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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.

Note

The authors acknowledge the financial help given by project API12/10.

Article information

Source
Tbilisi Math. J., Volume 5, Issue 2 (2012), 71-99.

Dates
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768904

Zentralblatt MATH identifier
1280.37001

Subjects
Primary: 37-04: Explicit machine computation and programs (not the theory of computation or programming)
Secondary: 14E05: Rational and birational maps 00A66: Mathematics and visual arts, visualization

Keywords
Discrete semi-flow Sage rational map complex dynamical system

Citation

Paricio, Luis Javier Hernández; Grandes, Miguel Marañón; Rodríguez, María Teresa Rivas. Plotting basins of end points of rational maps with Sage. Tbilisi Math. J. 5 (2012), no. 2, 71--99. https://projecteuclid.org/euclid.tbilisi/1528768904


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