We study supports of M -re ̄nable functions by means of attractors of iterated function systems, where M is an integer greater than (or equal to) 2. Most of the time, the re ̄nable function Á is not explicitly known. We need to study their properties from the re ̄nement mask. Under the assumption of local linear independence, we show that the support equals to the attractor of an iterated function...

A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.

In this paper, we give a theoretically founded transition from Iterated Function Systems based on aane transformations to Partitioned Iterated Function Systems. We show that there are two essential steps, namely, restricting the aane transformations, and solving the evoked problem of ink dissipation. In this paper, we give a theoretically founded transition from Iterated Function Systems based ...

We prove that the family of all invariant sets of iterated systems of contractions R → R is a nowhere dense Fσ type subset in the space of the non-empty compact subsets of R equipped with the Hausdorff metric. An iterated function system (IFS for short) is a finite collection (T1, . . . , Tn) of weak contractions of a metric space X. By a weak contraction we mean a mapping T : X → X such that d...

Boundary Controlled Iterated Function Systems is a new layer of control over traditional (linear) IFS, allowing creation of a wide variety of shapes. In this work, we demonstrate how subdivision schemes may be generated by means of Boundary Controlled Iterated Function Systems, as well as how we may go beyond the traditional subdivision schemes to create free-form fractal shapes. BC-IFS is a po...

Recurrent iterated function systems (RIFSs) are improvements of iterated function systems (IFSs) using elements of the theory of Marcovian stochastic processes which can produce more natural looking images. We construct new RIFSs consisting substantially of a vertical contraction factor function and nonlinear transformations. These RIFSs are applied to image compression.

an Iterated Function System (IFS), which leads to a solution that involves finding an Eulerian cycle in a certain graph and then to finding generators for the multiplicative group of a finite field. We start with an introduction to IFS fractals and the problem of generating an image of the attractor of an IFS. For a more complete introduction to the theory of Iterated Function Systems, we refer...

A fundamental requirement of any vision system designed to perform recognition tasks is a library of representations of objects it is likely to encounter. The classic approach to constructing such representations is to decompose the shape into simple primitive elements. However, for complex shapes it is usually necessary to use a large number of such primitives to achieve an accurate decomposit...

The principle of attractor image coding presented in this paper is based on the theory of IFS (Iterated Function Systems). The algorithm exploits piece-wise similarities between blocks of diierent sizes. To improve the algorithms based on regular and square blocks, we propose an adaptive Delaunay triangulation of the image support. The originality of the method is to map the triangles on specii...