To find the box dimension of the Cartesian product of the middle-middle-thirds' Cantor set with itself. Concept Introduction: Fractals are the complex geometric shapes with fine structure at arbitrarily small scales. A Cantor set consists of an infinite number of infinitesimal pieces separated by gaps of various sizes. The capacity or box dimension of S given as, d = lim ε → 0 ln ( N ( ε ) ) ln ( 1 ε ) , if limit exists.

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Chapter 11.4, Problem 4E

Interpretation Introduction

Interpretation:

To find the box dimension of the Cartesian product of the middle-middle-thirds' Cantor set with itself.

Concept Introduction:

Fractals are the complex geometric shapes with fine structure at arbitrarily small scales.

A Cantor set consists of an infinite number of infinitesimal pieces separated by gaps of various sizes.

The capacity or box dimension of S given as,

d=limε→0ln(N(ε))ln(1ε), if limit exists.

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