FRACTALS from NONLINEAR IFSs of the COMPLEX MAPPING FAMILY ƒ(z) = zn + c

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Article number1850044
Journal / PublicationFractals
Volume26
Issue number4
Online published26 Jul 2018
Publication statusPublished - Aug 2018

Abstract

To generate exotic fractals, we investigate the construction of nonlinear iterated function system (IFS) using the complex mapping family f(z)= zn+(|n| ≥ 2, 3,...). A set of c-values is chosen from the period-1 bulb of the Mandelbrot set, so that each mapping has an attracting fixed point in the dynamic plane. Computer experiments show that a set of arbitrarily chosen c-values may not be able to generate a fractal. We prove a sufficient condition that if the c-values are chosen from a specific region related to a circle in the period-1 bulb, the nonlinear IFS with such complex mappings is able to generate exotic fractal. Furthermore, if the set of c-values possesses a specific symmetry in the Mandelbrot set, then the fractal also exhibits the same symmetry. We present a method of generating aesthetic fractals with Zn-1 or Dn-1 symmetry for n ≥ 2 and with Z|n|+1 or D|n|+1 symmetry for n ≤-2.

Research Area(s)

  • Filled-In Julia Set, Fractal, Iterated Function System, Mandelbrot Set, Strange Attractor

Citation Format(s)

FRACTALS from NONLINEAR IFSs of the COMPLEX MAPPING FAMILY ƒ(z) = zn + c. / CHEN, Ning; CHEN, Yinuo; CHUNG, K. W.

In: Fractals, Vol. 26, No. 4, 1850044, 08.2018.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review