We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of th...

For a substitution satisfying the Pisot, irreducible, unimodular condition, a tiling substitution plays a key role in the construction of Rauzy fractals (see [15, 3]). To try extending techniques developed for substitutions to automorphisms, [6] gives the way to construct Rauzy fractals by using tiling substitutions for automorphisms related to hyperbolic companion matrices of quadratic polynom...

Fractals are mathematical or natural objects that are made of parts similar to the whole in certain ways. In this paper a software reliability forecasting method of software failure is proposed based on predictability of fractal time series. The empirical failure data (three data sets of Musa’s) are used to demonstrate the performance of the reliability prediction. Compared with other methods, ...

Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limit of a sequence of compact planar sets, where each set is the projection of a finite union of faces of unit cubes. We exploit this combinatorial definition to prove the connectedness of the fractal associated with any...