Fractal geometry is not the geometry of nature

Orly R. Shenker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

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.

Original languageAmerican English
Pages (from-to)967-981
Number of pages15
JournalStudies in History and Philosophy of Science
Volume25
Issue number6
DOIs
StatePublished - Dec 1994

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