Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 11.4, Problem 3E
Interpretation Introduction

Interpretation:

To find the box dimension of the Menger sponge.

Concept Introduction:

  • If S is a subset of the D-dimensional Euclidean space and N(ε) is the minimum number of D-dimensional cubes of side ε, then by the power law:

    N(ε)1εd

  • The box dimension d is given as:-

    d = limε0ln N(ε)ln(1ε)

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