Results 131 to 140 of about 1,561 (174)

Warped midgets in the Mandelbrot set

Computers & Graphics, 1994
Abstract Warped midgets in the Mandelbrot set have been measured, using an algorithm that allows the positions of the head, and cardioid atoms (north and south) of any midget to be found, once one has placed the cursor on the computer terminal somewhere inside any midget.
A. G. Davis Philip, Michael Frame, Adam Robucci   +2 more
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Chaotic bands in the Mandelbrot set

Computers & Graphics, 2004
Peer ...
G. Pastor, M. Romera, Gonzalo Álvarez, Fausto Montoya Vitini   +3 more
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The Mandelbrot Set

1986
For polynomials of second order, p(x) = a2x2 + a1x + ao, an almost complete classification of the corresponding Julia sets can be given in terms of the Mandelbrot set. First note that p(x is conjugate to p c (z)=z2 + c by means of the coordinate transformation \( x \mapsto z = a_2 x + a_1 /2,with{\text{ }}c = a_0 a_2 + \frac{{a_1 }} {2}\left( {1 ...
Heinz-Otto Peitgen, Peter H. Richter
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The Mandelbrot Set

2018
The Mandelbrot set is a simple application of complex numbers that reveals an amazing degree of complexity that would have remained hidden without the digital computer. I remember discovering the set in the mid-1980s, and tried running the program on my BBC micro. It took forever, and was not worth the wait.
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3D representation of the Mandelbrot set

The Visual Computer, 1994
A new 3D representation of the Mandelbrot set is presented. Although the method employing the Douady Hubbard's potential function has been useful for the 3D representation of the Mandelbrot set, in our new method 3D pictures are generated by setting height components normal to the plane of the original Mandelbrot set.
Kenji Nagashima, Hiroyuki Morimatsu
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The Universal Mandelbrot Set

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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A note on inverted mandelbrot sets

The Visual Computer, 1990
A simple technique is described for demonstrating artistically interesting behavior in chaotic systems defined by complex dynamics. In particular, the Mandelbrot set for the iterative process\(\zeta \to \zeta ^p + (1/u)^p \) is explored.
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Evolutionary Exploration of the Mandelbrot Set

2006 IEEE International Conference on Evolutionary Computation, 2006
The Mandelbrot set is an infinitely complex fractal defined by a simple iterative algorithm operating on the complex numbers. Views of the Mandelbrot set are a common form of fractal art. Presented here is a collection of fitness functions that permit three-parameter evolutionary search of the Mandelbrot set to locate interesting views.
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JULIA AND MANDELBROT SETS OF CHEBYSHEV FAMILIES

International Journal of Bifurcation and Chaos, 2001
We present one-parameter families of rational functions of arbitrary degree d which are globally generalized polynomial-like of degree d and roughly speaking locally quadratic-like everywhere, where the parameter appears not only as a purely multiplicative factor but also in a more complicated nonlinear way.
Franz Peherstorfer, Christoph Stroh
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Julia and Mandelbrot Sets

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, Kanishka Perera, Sandra Pinelas   +2 more
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