Fractal generation method based on asymptote family of generalized Mandelbrot set and its application

Volume 10, Issue 3, pp 1148--1161 http://dx.doi.org/10.22436/jnsa.010.03.24

Publication Date: March 20, 2017 Submission Date: December 16, 2016

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Authors

Shuai Liu - College of Computer Science, Inner Mongolia University, Hohhot, China. Zheng Pan - College of Computer Science, Inner Mongolia University, Hohhot, China. Weina Fu - College of Computer and Information Engineering, Inner Mongolia Agricultural University, Hohhot, China. Xiaochun Cheng - Department of Computer Science, Middlesex University, London, UK.

Abstract

Generalized Mandelbrot set (k-M set) is the basis of fractal analysis. This paper presents a novel method to generate k-M set, which generates k-M set precisely by constructing its asymptote family. Correctness of the proposed method is proved as well as computational complexity is researched. Further, application of the generation method is studied, which is used to analyze distribution of boundary points and periodic points of k-M set. Finally, experiments have been implemented to evaluate the theoretical results.

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Keywords

• Fractal generating method
• generalized Mandelbrot set
• asymptote family
• boundary point
• periodic point.

MSC

•  37F10

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