Chapter 11.3, Problem 2E

Interpretation Introduction

Interpretation:

To find the similarity dimension of the limiting set. For generalised Cantor set we begin by removing an open interval of length $\text{0 < a }\text{}\text{< 1}$ from the middle of $\left[0,1\right]$. At subsequent stage, we remove an open middle interval from each of the remaining intervals, and so on.

Concept Introduction:

• The dimension is the minimum number of coordinate required to describe every point in the set.

• For instance, a smooth curve is one-dimensional because every point on it is determined by one number, the arc length from some fixed reference point on the curve.

• Power law state that the dimension of the set equals the exponent $\text{d}$ is;

  $\text{N}\left(\text{ε}\right)\propto \frac{\text{1}}{{\text{ε}}^{\text{d}}}$.