Fractal property of generalized M-set with rational number exponent | |
Liu S.1; Cheng X.3; Lan C.1; Fu W.1; Zhou J.1; Li Q.1; Gao G.1 | |
2013-08-14 | |
Source Publication | Applied Mathematics and Computation |
ISSN | 00963003 |
Volume | 220Pages:668-675 |
Abstract | Dynamic systems described by f(z) = z + c is called Mandelbrot set (M-set), which is important for fractal and chaos theories due to its simple expression and complex structure. f(z) = z + c is called generalized M set (k-M set). This paper proposes a new theory to compute the higher and lower bounds of generalized M set while exponent k is rational, and proves relevant properties, such as that generalized M set could cover whole complex number plane when k < 1, and that boundary of generalized M set ranges from complex number plane to circle with radius 1 when k ranges from 1 to infinite large. This paper explores fractal characteristics of generalized M set, such as that the boundary of k-M set is determined by k, when k = p/q, where p and q are irreducible integers, (GCD(p, q) = 1, k > 1), and that k-M set can be divided into |p-q| isomorphic parts. © 2013 The Authors. Published by Elsevier Inc. All rights reserved. |
Keyword | Bound Fractals Generalized Mandelbrot set Mandelbrot set Rational exponent |
DOI | 10.1016/j.amc.2013.06.096 |
URL | View the original |
Language | 英語 |
Fulltext Access | |
Citation statistics | |
Document Type | Journal article |
Collection | University of Macau |
Affiliation | 1.Inner Mongolia University China 2.Hohhot University for Nationalities 3.Middlesex University |
Recommended Citation GB/T 7714 | Liu S.,Cheng X.,Lan C.,et al. Fractal property of generalized M-set with rational number exponent[J]. Applied Mathematics and Computation,2013,220:668-675. |
APA | Liu S..,Cheng X..,Lan C..,Fu W..,Zhou J..,...&Gao G..(2013).Fractal property of generalized M-set with rational number exponent.Applied Mathematics and Computation,220,668-675. |
MLA | Liu S.,et al."Fractal property of generalized M-set with rational number exponent".Applied Mathematics and Computation 220(2013):668-675. |
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