The multifractal structure of measures generated by iterated function systems (IFS) with overlaps is, to a large extend, unknown. In this paper we study the local dimension of the m-time convolution of the standard Cantor measure μ. By using some combinatoric techniques, we show that the set E of attainable local dimensions of μ contains an isolated point. This is rather surprising because when...

Email alerting service here right-hand corner of the article or click Receive free email alerts when new articles cite this article-sign up in the box at the top This paper introduces a new class of models of digital communications channels. Physically, these models take account of the digital nature of the input. Mathematically , they are iterated function systems. As a consequence of making e...

Iterated Function Systems (IFS) raster compression techniques achieve their results by identifying self-similarities in the source image. However, not all source images contain exploitable self-similarity. We describe a compression technique that combines a Karhunen-Loeve basis set (for non self-similar aspects of an image) with a block based IFS.

We characterize those subsets S of the positive integers with the property that, whenever a point x in a dynamical system enters a compact set K along S, K contains a recurrent point. We do the same for uniform recurrence. Let X denote a (compact) metric space and f : X → X a continuous map. We will use the term (compact) dynamical system to refer to such a pair (X, f) . As usual, we write f fo...

Interpolation of two-dimensional shapes described by iterated function systems is explored. Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations. Polar decomposition is used to avoid singular intermediate transformations and to better simulate articulated motion. Unlike some other representations, s...