One of the approaches in pattern recognition is the use of fractal geometry. The property of self-similarity of fractals has been used as a feature in several pattern recognition methods. All fractal recognition methods use global analysis of the shape. In this paper we present some drawbacks of these methods and propose fractal local analysis using the partitioned iterated function systems wit...

The escape-time method was introduced to generate images of Julia and Mandelbrot sets, then applied to visualize attractors of iterated function systems. This paper extends it further to language-restricted iterated function systems (LRIFS's). They generalize the original de nition of IFS's by providing means for restricting the sequences of applicable transformations. The resulting attractors ...

Let μ be a self-similar measure on R generated by an equicontractive iterated function system. We prove that the Hausdorff dimension of μ∗n tends to 1 as n tends to infinity, where μ∗n denotes the n-fold convolution of μ. Similar results hold for the Lq dimension and the entropy dimension of μ∗n.

Wireless sensor and actor networks (WSANs) are made up of a large number of sensing devices which are resource-impoverished nodes and powerful actuation devices: both are equipped with computation and communication capabilities. These devices cooperate to manage sensing and perform acting tasks. Numerous work conducted in the field of WSANs assumes the existence of addresses and routing infrast...

We extend Falconer’s formula from [1] by identifying the Hausdorff dimension of the limit sets of almost all contracting affine iterated function systems to the case of an infinite alphabet, non-autonomous choice of iterating matrices, and time dependent random choice of translations.

In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras. Let (X, d) be a compact metric space, and let an iterated function system (IFS) be given on X, i.e., a finite set of continuous maps σi: X → X, i = 0, 1, · · · , N −1. The maps σi transform the ...