fn = (k −mod(n, k))fbn/kc +mod(n, k)fdn/ke + an, n ≥ k, there is a unique continuous periodic function f∗ : R→ R with period 1 such that fn = nf(logk n)+o(n). If (an) is periodic with period k, ak = 0, and the initial conditions (fi : 1 ≤ i ≤ k − 1) are all zero, we obtain a specific iterated function system S, consisting of k continuous functions from [0, 1] × R into itself, such that the attr...

We investigate when the Hutchinson operator associated with an iterated function system is continuous. The continuity with respect to both the Hausdorff metric and Vietoris topology is carefully considered. An example showing that the Hutchinson operator on the hyperspace of nonempty closed bounded sets need not be Hausdorff continuous is given. Infinite systems are also discussed. The work cla...

In this paper, two new paradigms are proposed with fractal collage and reconstruction residuals to enhance FIC. In the first new paradigm, FIC is optimized using the reconstruction residuals. In the second paradigm, the selected collage residuals are used to correct the iterated function system (IFS) of FIC, and an effective technique for coding the selected collage residuals is applied based o...

LRIFS's (Language-Restricted Iterated Function Systems) generalize the original de nition of IFS's (Iterated Function Systems) by providing tools for restricting the sequences of applicable transformations.In this paper, we study an approach of LRIFS's based on matrices and graph theory. This enables us to generate a matrix which elements are attractors.

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...