Results 171 to 180 of about 2,419 (215)

THE INDEX ON THE MANDELBROT SET

International Journal of Bifurcation and Chaos, 1993
It 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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π IN THE MANDELBROT SET

Fractals, 2001
The Mandelbrot set is arguably one of the most beautiful sets in mathematics. In 1991, Dave Boll discovered a surprising occurrence of the number π while exploring a seemingly unrelated property of the Mandelbrot set.1 Boll's finding is easy to describe and understand, and yet it is not widely known — possibly because the result has not been ...
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Field lines in the Mandelbrot Set

Computers & Graphics, 1992
Abstract 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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Spirals in the Mandelbrot set II

Physica A: Statistical Mechanics and its Applications, 1994
Abstract 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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GEOMETRY OF THE ANTENNAS IN THE MANDELBROT SET

Fractals, 2002
In the Mandelbrot set, the bulbs attached directly to the main cardioid are called the p/q-bulbs. The reason for this is that the largest component of the interior of these bulbs consists of c-values for which the quadratic function Qc(z) = z2 + c admits an attracting cycle with rotation number p/q.
Devaney, R. L., Moreno Rocha, M.
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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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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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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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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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