Introduction to fractal dimension

Abstract

When studying geometrical objects less regular than ordinary ones, fractal analysis becomes a valuable tool. Over the last 40 years, this small branch of mathematics has developed extensively. Fractals can be defined as those sets which have non-integer Hausdorff or Minkowski dimension. In this report, we introduce certain definitions of fractal dimensions, which can be used to measure a set’s fractal degree. We introduce Minkowski dimension and Hausdorff dimension and explore some examples where they coincide, as well as other examples where they do not.