A special type of graphs of fractal curves with mathematica 11.0

Authors

DOI:

https://doi.org/10.17268/sel.mat.2019.01.15

Keywords:

Fractal function, iterative, iterated functions system

Abstract

In this article we generate graphs of fractal curves, which are determined as fixed points of a contractive operator. To do this, we consider five points P1; P2; P3; P4 y P5 in the plane and two affine transformations w1;w2, the same ones that will constitute a system of iterated functions (IFS) with only two contractive transformations. for the visualization of the graphs a program in mathematica 11.0 called fractalfunction has been created and we choose as the starting point of the iterative process the set [P1; P5]

References

Tarrés, J. Sobre la historia del concepto topológico de curva, Historia de la Gaceta (Departamento de geometría y topología de la Universidad Complutense de Madrid), (2010), pp. 66–67.

Mandelbrot, B. The Fractal Geometry of Nature, International Business Machines Thomas J. Watson Research Center, (1983), pp.1.

Falconer, K. Fractal geometry, Mathematical foundations And Applications, Cambridge University Press (1989), pp. 123–128, pp.130–135, pp. 160–166.

Plaza, S. Fractales y generación computacional de imágenes, Monografías del IMCA (Instituto de Matemática y ciencias afines), (1990), pp. 22–24, pp. 24–26, pp.29.

Rodriguez, R. La teoría de fractales: Aplicación experimental e implicaciones en la metodología de la ciencia, tesis magistal Facultad de filosofía y letras, Universidad Autónoma de Nuevo León, (1995), pp. 15–26.

Cid, M. C., Conjuntos fractales autosimilares y el operador de Hutchinson, tesis Facultad de ciencias físicas y matemáticas, Benemérita Universidad Autónoma de Puebla, (2012), pp. 14–21.

Hutchinson, J. E. Fractals and self similarity, Department of Pure Mathematics, Faculty of Science, Australian National University.(1981), pp. 10–15.

Aguirre, J. Curvas fractales, Sigma: Revista de matemáticas Vol. 20, Vitoria - España (2002), pp. 82–83.

Massopust, P. R. Fractal Functions, Fractal Surfaces and Wavelets, Academic Press (1994), pp. 135–145.

Gray, J. Mastering Mathematica Programming Methods and Applications, University de Illinois, Academic Press (1994), pp. 15–17, pp. 154–159, pp. 469–482.

Rincón, L. Curso intermedio de probabilidad, Departamento de Matemáticas. Facultad de Ciencias UNAM. México DF (2007), pp.17–18.

Hansen, R. La dimensión de Mendés France. Relación entre su espectro multifractal y el formalismo termodinámico. Aplicación a sistemas tipo Henon., Tesis doctoral. Área de Ciencias Matemática UBA. (2009), pp. 18–19.

Published

2019-07-21

How to Cite

Correa Erazo, S. B., & Sandoval Cornejo, A. (2019). A special type of graphs of fractal curves with mathematica 11.0. Selecciones Matemáticas, 6(01), 128-139. https://doi.org/10.17268/sel.mat.2019.01.15

Issue

Section

Communications