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School of Mathematical Sciences

CS - Dr Ian Morris

Non-conformal self-affine fractals 

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 
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