Kenneth Falconer

Fractals and intermediate dimensions

We will give a short overview of aspects of fractals such as iterated function systems and self-similar and self-affine sets and introduce Hausdorff and box-counting dimensions. In particular we will look at sets where these dimensions differ. We will then show how Hausdorff and box-counting dimensions can be regarded as particular cases of a spectrum of `intermediate’ dimensions’ and discuss the intermediate dimensions of various sets and examine their geometrical properties.