# Mona Hazeem: Similarities and Hausdorff dimension in fractal geometry

**Time: **
Mon 2022-02-07 10.30 - 11.30

**Location: **
Zoom

**Video link: **
674 5036 1253, contact arias@math.su.se to get the password

**Respondent: **
Mona Hazeem

**Abstract:** In this paper, we discuss key characteristics of fractals, we introduce a self-similar structure with the help of iterated function systems and Hausdorff dimension. We show that the attractor of an iterated function system is unique and then present the theory of Hausdorff measure, which provides a general notion of the size of a subset of \(\mathbb{R}^n\). The main theorem provides a simple formula to compute the Hausdorff dimension of a self-similar set where the open set condition holds.