Authors
Orly Shenker
Hebrew University of Jerusalem
Abstract
In recent years the magnificent world of fractals has been revealed. Some of the fractal images resemble natural forms so closely that Benoit Mandelbrot's hypothesis, that the fractal geometry is the geometry of natural objects, has been accepted by scientists and non-scientists alike. The present paper critically examines Mandelbrot's hypothesis. It first analyzes the concept of a fractal. The analysis reveals that fractals are endless geometrical processes, and not geometrical forms. A comparison between fractals and irrational numbers shows that the former are ontologically and epistemologically even more problematic than the latter. Therefore, it is argued, a proper understanding of the concept of fractal is inconsistent with ascribing a fractal structure to natural objects. Moreover, it is shown that, empirically, the so-called fractal images disconfirm Mandelbrot's hypothesis. It is conceded that the fractal geometry can be used as a useful rough approximation, but this fact has no bearing on the physical theory of natural forms
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DOI 10.1016/0039-3681(94)90072-8
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References found in this work BETA

The Emperor’s New Mind.Roger Penrose - 1989 - Oxford University Press.
The Aesthetic Value of Fractal Images.Larry Short - 1991 - British Journal of Aesthetics 31 (4):342-355.

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Chaos.Robert Bishop - 2015 - Stanford Encyclopedia of Philosophy.
Self-Organised Criticality—What It is and What It Isn’T.Roman Frigg - 2003 - Studies in History and Philosophy of Science Part A 34 (3):613-632.

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