The box-dimension (or 'capacity') of a class of self-affine sets in the plane in calculated. The formula for box dimension given here has a similar form to Bowen's formula for the Hausdorff dimension of self-similar sets, involving the topological pressure of certain functions. The sets studied here appear in two contexts; as graphs of generalized Weierstrass functions and as repellors in some maps of the cylinder. The authors use the techniques of the 'Singularity Spectrum' in order to carry out the calculations. (Copyright (c) 1988 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)
展开▼
