We study two-digit attractors (2-attractors) in $\mathbb{R}^d$ which are self-affine compact sets defined by two contraction affine mappings with the same linear part. They widely studied literature under various names: twindragons, tiles, 2-reptiles, etc., due to many applications approximation theory, construction of multivariate Haar systems and other wavelet bases, discrete geometry, number...

Surface-enhanced Raman scattering (SERS) from a self-affine surface is shown to be very large. A theory is developed expressing this SERS in terms of the eigenmodes of a self-affine surface; the theory successfully explains the observed SERS from cold-deposited thin films that are known to have a self-affine structure. Spatial distributions of local fields at the fundamental and Stokes frequenc...

A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves seve...

Fractal image compression is based on the rather poorly motivated assumption that “natural” images exhibit significant affine self-similarity. The accuracy of this assumption is evaluated by a comparison between the statistics of natural images and those of a multiresolution stochastic model designed to generate images exhibiting affine self-similarity as assumed by fractal coding techniques. T...

A certain ‘pressure’ functional Φ(T1, . . . , TN ), defined as the limit of sums of singular value functions of products of linear mappings (T1, . . . , TN ), is central in analysing fractal dimensions of self-affine sets. We investigate the continuity of Φ with respect to the linear mappings (T1, . . . , TN ) which underlie the self-affine sets.