Results 191 to 200 of about 6,088,715 (228)
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Spirals in the Mandelbrot set II
Physica A: Statistical Mechanics and its Applications, 1994Abstract The alpha function is used to quantify the (asymptotic) structure of the various branches and embedded spirals around the left-hand side of the main cardioid in the Mandelbrot set.
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2006
Notions and Notation Summary Fragments of Theory Map f(x) = X2 + c: From Standard Example to General Conclusions.
V. Dolotin, A. Morozov
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Notions and Notation Summary Fragments of Theory Map f(x) = X2 + c: From Standard Example to General Conclusions.
V. Dolotin, A. Morozov
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1994
As already pointed out in Chap. 9, discrete iterated maps appear almost routinely in studies of nonlinear dynamical systems, e.g. as Poincare maps. Because they are discrete, such maps are much simpler to study (both numerically and analytically) than continuous differential equations. In general, the maps can be written as $$ {r_{n + 1}} = F({r_n},
H. J. Korsch, H.-J. Jodl
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As already pointed out in Chap. 9, discrete iterated maps appear almost routinely in studies of nonlinear dynamical systems, e.g. as Poincare maps. Because they are discrete, such maps are much simpler to study (both numerically and analytically) than continuous differential equations. In general, the maps can be written as $$ {r_{n + 1}} = F({r_n},
H. J. Korsch, H.-J. Jodl
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Field lines in the Mandelbrot Set
Computers & Graphics, 1992Abstract A technique for displaying color images of field lines surrounding the Mandelbrot Set using angle-slicing decomposition and a “contrast color lookup table,” is described. A modification of this method, which compensates for the spatial-frequency doubling inherent in angle-slicing decomposition, can produce black and white images that even ...
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THE INDEX ON THE MANDELBROT SET
International Journal of Bifurcation and Chaos, 1993It is known that the index on the Mandelbrot set introduces a Fibonacci partition. In this paper we will give an interpretation of this property.
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Noise-perturbed quaternionic Mandelbrot sets
International Journal of Computer Mathematics, 2009Quaternionic Mandelbrot sets (abbreviated as M sets) have been a focus on the research in high-dimensional fractals. This paper explores the topological structure and the fission evolution of the quaternionic M sets under noise perturbations as well as the boundaries of their regions of stability.
Y. Y. Sun, X. Y. Wang
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2011
In this lecture, we shall discuss the geometric and topological features of the complex plane associated with dynamical systems whose evolution is governed by the iterative scheme \(z_n {\rm + 1}\,{\rm = }\,f{\rm (}zn{\rm ), }\,z_{0\,} {\rm = }\,p{\rm }\,{\rm where}\,{\rm }f{\rm (}z{\rm )}\) is a complex valued function and \(p\, \in \,C.\) Such ...
Ravi P. Agarwal +2 more
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In this lecture, we shall discuss the geometric and topological features of the complex plane associated with dynamical systems whose evolution is governed by the iterative scheme \(z_n {\rm + 1}\,{\rm = }\,f{\rm (}zn{\rm ), }\,z_{0\,} {\rm = }\,p{\rm }\,{\rm where}\,{\rm }f{\rm (}z{\rm )}\) is a complex valued function and \(p\, \in \,C.\) Such ...
Ravi P. Agarwal +2 more
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Midgets of superior Mandelbrot set
Chaos, Solitons & Fractals, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Negi, Ashish, Rani, Mamta
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Fractal diffusion patterns of periodic points in the Mandelbrot set
Chaos, Solitons & Fractals, 2021Dakuan. Yu, Wurui Ta, Youhe Zhou
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The Mandelbrot Set: Ordering the Julia Sets
1992The Mandelbrot set is certainly the most popular fractal, probably the most popular object of contemporary mathematics at all. Some people claim that it is not only the most beautiful but also the most complex object which has been seen, i.e., made visible.
Heinz-Otto Peitgen +2 more
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