Supervisor: Dr Ian Morris
Project description:
Attractors of iterated function systems are a class of fractal objects which include some of the most familiar fractal sets which are typically encountered on a first course in the subject, such as the von Koch curve and the Sierpinski triangle. When the symmetries of these sets are conformal - meaning, roughly, that the smaller copies of the fractal are not substantially distorted - the geometry of these sets is relatively well-understood. In the non-conformal case, by contrast, there are a great many open questions. I can supervise a range of topics in this area. Some possible directions of study include any of the following: investigating the Hausdorff dimension of "box-like" self-affine sets in the irreducible case; understanding the dimensions of projected images of fractal sets and measures, in either the linear or the nonlinear cases; developing the theory of non-autonomous self-affine fractals, or of self-affine fractals incorporating Markovian or other constraints.
Further information:
How to apply Entry requirements Fees and funding