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Chaos and FractalsAn Elementary Introduction$
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David P. Feldman

Print publication date: 2012

Print ISBN-13: 9780199566433

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199566433.001.0001

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Random Fractals

Random Fractals

Chapter:
(p.173) 17 Random Fractals
Source:
Chaos and Fractals
Author(s):

David P. Feldman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199566433.003.0018

This chapter explores ways of generating fractals other than a deterministic procedure. In particular, it considers fractal-generating mechanisms that involve randomness or irregularity. The discussion begins by describing what happens when a little bit of randomness or noise is added to an otherwise deterministic process. It looks at the Koch curve, a classic fractal, and its self-similarity, as well as irregular fractals such as the Sierpiński triangle. It then explains how random and irregular fractals can be extended and refined to produce images that bear a striking resemblance to real landscapes. The chapter concludes by discussing the long-term fate of the orbit in the chaos game, an affine transformation, and the collage theorem.

Keywords:   fractals, randomness, irregularity, Koch curve, self-similarity, Sierpiński triangle, landscapes, chaos game, affine transformation, collage theorem

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