Introduction to Hausdorff Measures and Fractals

The attached link is Senior Integrative Project in Carleton College that my group and I did over last term: COMPSFINAL. The project was underwent over Fall 2014 and Winter 2015 under supervision of Allison Tanguay.

The main purpose of the paper is to introduce the idea of Lebesgue measure and \alpha-dimensional Hausdorff measure, fractals and their behaviors, non-fractal sets and related conjecture.

Lee’s Challenge #1:

Consider an arbitrary non-negative real number, namely \beta. Can we always construct a set of which strict Hausdorff dimension is \beta?

Introduction to Hausdorff Measures and Fractals