Let (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) be a contractive iterated function system (IFS), where X is a compact subset of R. It is well known that there exists a unique nonempty compact set K such that K = ⋃m j=1 wj(K). Moreover, the Ruelle operator on C(K) determined by the IFS (X, {wj} m j=1, {pj} m j=1) (2 ≤ m < ∞) has been introduced in [FL]. In the present paper, the Ruelle operators det...

The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some...

Let 91 be a ~-complete ultrafilter on the measurable cardinal ~. Scott [ 1 3 ] proved V ¢ L by using 91 to take the ultrapower of V. Gaifman [ 2] considered iterated ultrapowers of V by cg to conclude even stronger results; for example, that L n ~(6o) is count-able. In this paper we discuss some new applications of iterated ultra-powers. In § § 1-4, we develop a straightforward generalization o...

We are concerned with function approximation and image representation using Iterated Function Systems (IFS) over L p (X;): An N-map IFS with grey level maps (IFSM), to be denoted as (w;), is a set w of N contraction maps w i : X ! X over a compact metric space (X; d) (the \base space") with an associated set of maps i : R ! R. Associated with each IFSM is a contractive operator T with xed point...

We establish domain-theoretic models of nite-state discrete stochastic processes, Markov processes and vector recurrent iterated function systems. In each case, we show that the distribution of the stochastic process is canonically obtained as the least upper bound of an increasing chain of simple valuations in a prob-abilistic power domain associated to the process. This leads to various formu...

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...

A recurrent iterated function system (RIFS) is a genaralization of an IFS and provides nonself-affine fractal sets which are closer to natural objects. In general, it’s attractor is not a continuous surface in R. A recurrent fractal interpolation surface (RFIS) is an attractor of RIFS which is a graph of bivariate continuous interpolation function. We introduce a general method of generating re...

Conventional scene graphs use directed acyclic graphs; conventional iterated function systems use infinitely recursive definitions. We investigate scene graphs with recursive cycles for defining graphical scenes. This permits both conventional scene graphs and iterated function systems within the same framework and opens the way for other definitions not possible with either. We explore several...

We characterize the coordinate functions of Hilbert's spacelling curve using a directed-graph iterated function system and use this to analyze their fractal properties. In particular, we show that both coordinate functions have graphs of Hausdor dimension 3 2 and level sets of dimension 1 2 .

The attractor is a central object of an iterated function system (IFS), and fractal transformations are the natural maps from the attractor of one IFS to the attractor of another. This paper presents a global point of view, showing how to extend the domain of a fractal transformation from an attractor with non-empty interior to the ambient space. Intimitely related is the extension of addressin...