6 papers
The fractal structure of elliptical polynomial spirals
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
We investigate fractal aspects of elliptical polynomial spirals; that is, planar spirals with differing polynomial rates of decay in the two axis directions. We give a full dimensi…
Dimensions of fractional Brownian images
Stuart A. Burrell
This paper concerns the intermediate dimensions, a spectrum of dimensions that interpolate between the Hausdorff and box dimensions. Potential theoretic methods are used to produce…
Projection theorems for intermediate dimensions
Stuart A. Burrell, Kenneth J. Falconer, Jonathan M. Fraser
Intermediate dimensions were recently introduced to interpolate between the Hausdorff and box-counting dimensions of fractals. Firstly, we show that these intermediate dimensions m…
Digit expansions of numbers in different bases
Stuart A. Burrell, Han Yu
A folklore conjecture in number theory states that the only integers whose expansions in base and contain solely binary digits are and . In this paper, we p…
The dimensions of inhomogeneous self-affine sets
Stuart A. Burrell, Jonathan M. Fraser
We prove that the upper box dimension of an inhomogeneous self-affine set is bounded above by the maximum of the affinity dimension and the dimension of the condensation set. In ad…
On the dimension and measure of inhomogeneous attractors
Stuart A. Burrell
A central question in the field of inhomogeneous attractors has been to relate the dimension of an inhomogeneous attractor to the condensation set and associated homogeneous attrac…