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American Journal of Physics -- September 1994 -- Volume 62, Issue 9, pp. 813

The ‘‘mystery’’ of the quadratic Mandelbrot set

Wolfgang Metzler

Fachbereich Mathematik/Informatik, Universität Gesamthochschule Kassel, 34109 Kassel, Germany

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Numerical simulations suggest that the Mandelbrot set for binary numbers z=x+γy with x, y∊R and γ2=α+γβ (α,β∊R given) is a simple filled‐in square in the perplex case, i.e., α=1, β=0. The paper gives a proof of this experimental result.

KEYWORDS and PACS

Keywords

FRACTALS, ITERATIVE METHODS, MAPS, CHAOTIC SYSTEMS, DYNAMICAL SYSTEMS, STRANGE ATTRACTORS

PACS

History
Received Nov 1993
Accepted Feb 1994

PUBLICATION DATA

ISSN:

0002-9505 (print)  

ARTICLE DATA

Permalink
http://dx.doi.org/10.1119/1.17465


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