Journal
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
Volume 10, Issue 3, Pages 1148-1161Publisher
INT SCIENTIFIC RESEARCH PUBLICATIONS
DOI: 10.22436/jnsa.010.03.24
Keywords
Fractal generating method; generalized Mandelbrot set; asymptote family; boundary point; periodic point
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Funding
- National Natural Science Foundation of China [61502254]
- EUFP7 WIDTH project
- VALCRI project
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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. (C)2017 All rights reserved.
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