We consider calculation of the dimensions of self-affine fractals and multifractals that are the attractors of iterated function systems specified in terms of upper triangular matrices. Using methods… (More)

Under certain conditions the ‘singular value function’ formula gives the Hausdorff dimension of self-affine fractals for almost all parameters in a family. We show that the size of the set of… (More)

multifractals. However, the approach may be found rather sophisticated by those more concerned with applications. and their singularities: the characterisation of strange sets', Phys. Rev.… (More)

We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We… (More)

We show how multifractal properties of a measure supported by a fractal F ⊆ [0, 1] may be expressed in terms of complementary intervals of F and thus in terms of spectral triples and the Dixmier… (More)

We study a particular class of moving average processes which possess a property called localisability. This means that, at any given point, they admit a “tangent process”, in a suitable sense. We… (More)

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… (More)

We investigate the box dimensions of the horizon of a fractal surface defined by a function f ∈ C[0, 1]2. In particular we show that a prevalent surface satisfies the ‘horizon property’, namely that… (More)

We find the almost sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically… (More)

Given a compact subset F of R2, the visible part VθF of F from direction θ is the set of x in F such that the half-line from x in direction θ intersects F only at x. It is suggested that if dimH F ≥… (More)