Related papers: Abstract Fractals
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the…
We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in…
In many problems of classical analysis extremal configurations appear to exhibit complicated fractal structure. This makes it much harder to describe extremals and to attack such problems. Many of these problems are related to the…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…
A stochastic model relating the parameters of astrophysical structures to the parameters of their granular components is applied to the formation of hierarchical, large-scale structures from galaxies assumed as point-like objects. If the…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
We introduce the notion of (abelian) similarity scheme, as a constructive model for topological self-similar fractals, in the same way in which the notion of iterated function system furnishes a constructive notion of self-similar fractals…
The method of spectral decimation is applied to an infinite collection of self--similar fractals. The sets considered belong to the class of nested fractals, and are thus very symmetric. An explicit construction is given to obtain formulas…
A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely…
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
A fractal function is a function whose graph is the attractor of an iterated function system. This paper generalizes analytic continuation of an analytic function to continuation of a fractal function.
Self-projective sets are natural fractal sets which describe the action of a semigroup of matrices on projective space. In recent years there has been growing interest in studying the dimension theory of self-projective sets, as well as…
By slight modification of the data of the Sierpinski gasket, keeping the open set condition fulfilled, we obtain self-similar sets with very dense parts, similar to fractals in nature and in random models. This is caused by a complicated…