The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e., contraction receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief ...

Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will conc...

We provide necessary and sufficient conditions for a graph-directed iterated function system to be strictly contracting.

Language theoretic aspects and algorithmic properties of particular classes of context-free collage languages and of patterns generated by iterated function systems are studied. These classes are defined by restricting the allowed transformations to a sort of similarity transformations called grid transformations. It turns out that, thanks to this restriction, the language classes have nice clo...

Let M be a compact connected m-dimensional manifold. We denote by Diff(M) the space of all C1-diffeomorphisms from M to itself endowed with C1-topology. For a collection of diffeomorphisms L = {f1, . . . , fn} ⊂ Diff(M), the iterated function system (abbrivately IFS) G(M ; f1, . . . , fn) on M generated by L is given by iterates fi1o · · · ofik with ij ∈ {1, . . . , n}. Recall that an IFS G(M ;...

In this article we study the common dynamics of two different Pisot substitutions σ1 and σ2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions σ1 and σ2. Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function systems, we actually study topological and ...

Fractal shaped antennas and fractal miniaturized elements are becoming a promising new family of devices with a wealth of potentially useful applications [1]. Owing to the facility of manufacturing fractal devices (the metallisation process of fractal antennas up to a few iterations of the recursive process that generates the fractal structure is a relatively simple task), several different pro...

We consider infinite conformal iterated function systems in the phase space Rd with d ≥ 3. Let J be the limit set of such a system. Under a mild technical assumption, which is always satisfied if the system is finite, we prove that either the Hausdorff dimension of J exceeds the topological dimension k of the closure of J or else the closure of J is a proper compact subset of either a geometric...

Iterated Function Systems (IFSs) are among the best-known methods for constructing fractals. The sequence of pictures E0; E1; E2; : : : generated by an IFS fX; f1; f2; : : : ; ftg converges to a unique limit E , which is independent of the choice of starting set E0, but completely determined by the choice of the maps fi. Random context picture grammars (rcpgs) are a method of syntactic picture ...

Before rendering 2D or 3D fractals with iterated function systems, it is necessary to calculate the bounding extent of fractals. We develop a new algorithm to compute the bounding box which closely contains the entire attractor of an iterated function system. r 2003 Elsevier Science Ltd. All rights reserved.