The dimension spectrum of a conformal iterated function system (CIFS) is the set all Hausdorff dimensions its various subsystem limit sets. This brief note provides two constructions – (i) compact perfect that cannot be realized as CIFS; and (ii) similarity IFS whose has zero dimension, thus not uniformly which resolve questions posed by Chousionis, Leykekhman Urbański, goes on to provoke fresh...

In this paper, the new concept of non-autonomous iterated function system is introduced and also shown that non-autonomous iterated function system IFS(f_(1,∞)^0,f_(1,∞)^1) is topologically transitive for the metric space of X whenever the system has average shadowing property and its minimal points on X are dense. Moreover, such a system is topologically transitive, whenever, there is a point ...

We present an algorithm to construct a bounding polyhedron for an affine Iterated Function System (IFS). Our algorithm expresses the IFS-bounding problem as a set of linear constraints on a linear objective function, which can then be solved via standard techniques for linear convex optimization. As such, our algorithm is guaranteed to find the optimum recursively instantiable bounding volume, ...

Weextend both theweak separation condition and the finite type condition to include finite iterated function systems (IFSs) of injective C1 conformal contractions on compact subsets of Rd . For conformal IFSs satisfying the bounded distortion property, we prove that the finite type condition implies the weak separation condition. By assuming the weak separation condition, we prove that the Haus...

A simple, yet unifying method is provided for the construction of tilings by tiles obtained from the attractor of an iterated function system (IFS). Many examples appearing in the literature in ad hoc ways, as well as new examples, can be constructed by this method. These tilings can be used to extend a fractal transformation defined on the attractor of a contractive IFS to a fractal transforma...

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.

Iterated function systems have been recently applied to the field of image coding. This paper exploits the fractal properties included in the coding and decoding schemes, in order to add useful tools for image processing. The first contribution consists of an improvement of the classical fractal zoom which allows, with a unique code, to increase the image resolution without loss in sharpness. T...