On numerical approximations of the area of the generalized Mandelbrot sets

In the present work, the area of the generalized Mandelbrot sets is defined as the double limit of the areas of the plotted generalized Mandelbrot sets in a given square lattice, using the finite escape algorithm, while the lattice resolution and the number of iteration counts, used to plot them, te...

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Bibliographic Details
Published in:Applied mathematics and computation 2013-08, Vol.219 (23), p.10974-10982
Main Authors: Andreadis, Ioannis, Karakasidis, Theodoros E.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Area
Asymptotic properties
Counting
Finite escape algorithm
Generalized Mandelbrot set
Infinity
Lattice points
Lattices
Mathematical analysis
Regression analysis
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Summary:In the present work, the area of the generalized Mandelbrot sets is defined as the double limit of the areas of the plotted generalized Mandelbrot sets in a given square lattice, using the finite escape algorithm, while the lattice resolution and the number of iteration counts, used to plot them, tends to infinity. The asymptotic behavior of the areas of the generalized Mandelbrot sets in terms of their degree growth is investigated. Finally, numerical approximations of the area of the Mandelbrot set are proposed by using tools from regression analysis.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2013.04.052