Fractal Measures for Parabolic IFS

Fractal Measures for Parabolic Ifs

Lq DENSITIES FOR MEASURES ASSOCIATED WITH PARABOLIC IFS WITH OVERLAPS

We study parabolic iterated function systems (IFS) with overlaps on the real line and measures associated with them. A Borel probability measure μ on the coding space projects into a measure ν on the limit set of the IFS. We consider families of IFS satisfying a transversality condition. In [SSU2] sufficient conditions were found for the measure ν to be absolutely continuous for Lebesgue-a.e. p...

Fractal Compression of Images with Projected Ifs

Standard fractal image compression, proposed by Jacquin[1], is based on IFS (Iterated Function Systems) defined in R. This modelization implies restrictions in the set of images being able to be compressed. These images have to be self similar in R. We propose a new model, the projected IFS, to approximate and code grey level images. This model has the ability to define affine IFS in a high dim...

IFS on the Multi-Fuzzy Fractal Space

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...

Fractal Compression Using Ifs Operators on Transforms

Standard fractal image compression techniques rely on using an IFS operator directly on the image function. However, sometimes it is more convenient to work on some transformed version of the image. For example, an MRI image is scanned in as frequency data. Thus, it is more natural to work on the Fourier Transform of the image rather than on the image itself. Furthermore, if your image quality ...