Chapter 11.3, Problem 1E

Interpretation Introduction

Interpretation:

Construct the new kind of Cantor set by removing the middle half of each sub-interval instead of removing middle third

1. Find similarity dimension of the set.

2. Find the measure of the set.

Concept Introduction:

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

• Cantor set consist an infinite number of infinitesimal pieces separated by gaps of various sizes.

• The dimension of the Cantor set is not an integer it is a fraction.

• The similarity dimension d is defined as

  $\text{d =}\frac{\text{ln m}}{\text{ln r}}$ the values of m and r are determined by inspection.