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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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The Box‐Counting Dimension

The Box‐Counting Dimension

Chapter:
(p.187) 18 The Box‐Counting Dimension
Source:
Chaos and Fractals
Author(s):

David P. Feldman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199566433.003.0019

There are several examples of fractals that are not exactly self-similar, as is the case with small parts of the random Koch curve which exhibit statistical self-similarity but not identicality. The dimension of a handful of fractal objects, including the Cantor set, the Sierpiński triangle and carpet, and the Koch curve, can be determined. This chapter considers the box-counting dimension, which extends the concept of dimension to objects that are not exactly self-similar. Instead of focusing on how many small copies of an object are contained in a large copy, it explains how the volume or size of the overall shape changes as measurement scales change.

Keywords:   fractals, self-similarity, box-counting dimension, Sierpiński triangle, Koch curve, Cantor set

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