On a numerical approximation of the boundary structure and of the area of the Mandelbrot set

dc.creator	Andreadis, I.	en
dc.creator	Karakasidis, T. E.	en
dc.date.accessioned	2015-11-23T10:22:15Z
dc.date.available	2015-11-23T10:22:15Z
dc.date.issued	2015
dc.identifier	10.1007/s11071-015-1917-4
dc.identifier.issn	0924-090X
dc.identifier.uri	http://hdl.handle.net/11615/25562
dc.description.abstract	Based on the boundary scanning method, a partition of the boundary of the Mandelbrot set is defined. The various classes of points of the boundary according to their divergence from the interior and the exterior of the Mandelbrot set are discussed. Then, numerical invariants of its structure under increase in the lattice resolution and the number of maximum iteration counts used to plot it are provided. Furthermore using Pick's theorem, an alternative numerical approximation of the area of the Mandelbrot set based on the number of points of the boundary and of the interior of the plottedMandelbrot set is provided. An analytic support of the numerical results obtained in approximating the area of the Mandelbrot set is also provided.	en
dc.source	Nonlinear Dynamics	en
dc.source.uri	<Go to ISI>://WOS:000352695100070
dc.subject	Mandelbrot set	en
dc.subject	Boundary scanning method	en
dc.subject	Area	en
dc.subject	Pick theorem	en
dc.subject	Finite	en
dc.subject	escape algorithm	en
dc.subject	Counting pixel method	en
dc.subject	NOISE	en
dc.subject	Engineering, Mechanical	en
dc.subject	Mechanics	en
dc.title	On a numerical approximation of the boundary structure and of the area of the Mandelbrot set	en
dc.type	journalArticle	en

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