For fixed k ≥ 2 and fixed data alphabet of cardinality m, the hierarchical type class of a data string of length n = k for some j ≥ 1 is formed by permuting the string in all possible ways under permutations arising from the isomorphisms of the unique finite rooted tree of depth j which has n leaves and k children for each non-leaf vertex. Suppose the data strings in a hierarchical type class a...

Given any compact connected manifold M , we describe Copen sets of iterated functions systems (IFS’s) admitting fully-supported ergodic measures whose Lyapunov exponents alongM are all zero. Moreover, these measures are approximated by measures supported on periodic orbits. We also describe C-open sets of IFS’s admitting ergodic measures of positive entropy whose Lyapunov exponents along M are ...

Recursive image subsampling which yields support areas approaching fractals is described and analyzed using iterated function systems. The subsampling scheme is suitable in, e.g., hierarchical image processing and image coding schemes. For hexagonally sampled images a hierarchical subsampling structure is given which yields hexagon-like regions with fractal borders.

In this small note an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Applications of this method to approximation of distribution functions and estimation are presented. Résumé. Dans cette petite note un système de fonction itéré sur l’espace de fonctions de repartition est construit. Le pr...

We characterize the coordinate functions of Hilbert's space-lling curve using a directed-graph iterated function system and use this to analyze their fractal properties. In particular, we show that both coordinate functions have graphs of Hausdorr dimension 3 2 and level sets of dimension 1 2 .

The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the...

The sequence {Fn} is called the iterated function system corresponding to {fn}. For readability, we denote by F(Ω, X) the set of all iterated function systems made from functions in Hol(Ω, X). By Montel’s theorem (see for example [2]), the sequence Fn is a normal family, and every convergent subsequence converges uniformly on compact subsets of Ω to a holomorphic function F ∈ Hol(Ω, X). The acc...

In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of the...

Iterated function systems have been powerful tools to generate fractals. However, the requirement of using the same maps at every iteration results in a fractal that may be too self-similar for certain applications. We present a construction in which the maps are allowed to be updated at each iteration in order to generate more general fractals without changing the computational complexity. We ...

Craig M. Wittenbrink Baskin Center for Computer Engineering & Information Sciences University of California, Santa Cruz Santa Cruz, CA 95064 USA Abstract Reconstruction is used frequently in visualization of one, two, and three{dimensional data. Data uncertainty is typically ignored, and a de ciency of many interpolation schemes is smoothing which may indicate features or characteristics of the...