Now showing items 1-6 of 6

  • A commutative noncommutative fractal geometry 

    Samuel, Anthony (University of St Andrews, 2010) - Thesis
    In this thesis examples of spectral triples, which represent fractal sets, are examined and new insights into their noncommutative geometries are obtained. Firstly, starting with Connes' spectral triple for a non-empty ...
  • Dimension and measure theory of self-similar structures with no separation condition 

    Farkas, Ábel (University of St Andrews, 2015-11-30) - Thesis
    We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any ...
  • Dimension theory and fractal constructions based on self-affine carpets 

    Fraser, Jonathan M. (University of St Andrews, 2013-11-29) - Thesis
    The aim of this thesis is to develop the dimension theory of self-affine carpets in several directions. Self-affine carpets are an important class of planar self-affine sets which have received a great deal of attention ...
  • Directed graph iterated function systems 

    Boore, Graeme C. (University of St Andrews, 2011-11-30) - Thesis
    This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed ...
  • The geometry of self-affine fractals 

    Miao, Jun Jie (University of St Andrews, 2008) - Thesis
    In this thesis we study the dimension theory of self-affine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems. We give ...
  • Sixty years of fractal projections 

    Falconer, Kenneth John; Fraser, Jonathan Macdonald; Jin, Xiong (Birkhauser, 2015-07-31) - Book item
    Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted ...