UM
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 PublicationApplied Mathematics and Computation
ISSN00963003
Volume220Pages:668-675
AbstractDynamic 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.
KeywordBound Fractals Generalized Mandelbrot set Mandelbrot set Rational exponent
DOI10.1016/j.amc.2013.06.096
URLView the original
Language英語
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Cited Times [WOS]:29   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.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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