Random sequential adsorption of particles with size polydispersity (PRSA) is investigated. For the PRSA with a power-law small-size distribution, P ( R ) ~ R ~ l, we reveal the fractal nature of the arising patterns. The fractal dimension Df is found to decrease from 2 to DA = 1.305 .... the fractal dimension of the Apollonian packing, as ~ increases from 0 to ~ . We examine PRSA by a combinati...

The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that...

The compression performance of fractal image coding is considered using the wavelet-based fractal coder with no search or classi cation of the domain blocks. A new partitioning scheme is introduced as a variant of earlier schemes which further improves the compression performance. The Wavelet-Based Fractal Transform (WBFT) links the theory of multiresolution analysis (MRA) with iterated functio...

Let QJ be a bounded open set of RDn (n > 1) with "fractal" boundary F. We extend Hermann Weyl's classical theorem by establishing a precise remainder estimate for the asymptotics of the eigenvalues of positive elliptic operators of order 2m (m > 1) on Q. We consider both Dirichlet and Neumann boundary conditions. Our estimate-which is expressed in terms of the Minkowski rather than the Hausdorf...

We review recent findings of self-similarity in complex networks. Using the box-covering technique, it was shown that many networks present a fractal behavior, which is seemingly in contrast to their small-world property. Moreover, even non-fractal networks have been shown to present a self-similar picture under renormalization of the length scale. These results have an important effect in our ...

Diffusion limited aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding bound...

In this report, we present a simple geometric generation principle for the fractal that is obtained when applying Newton's method to nd the roots of a general complex polynomial with real coee-cients. For the case of symmetric polynomials z ? 1, the generation mechanism is derived from rst principles. We discuss the case of a general cubic and are able to give a description of the arising fract...

We study fluctuational transitions in a discrete dynamical system that has two co-existing attractors in phase space, separated by a fractal basin boundary which may be either locally-disconnected or locally-connected. It is shown that, in each case, transitions occur via an accessible point on the boundary. The complicated structure of paths inside the locally-disconnected fractal boundary is ...

We use fractional integrals to generalize the description of hydrodynamic accretion in fractal media. The fractional continuous medium model allows the generalization of the equations of balance of mass density and momentum density. These make it possible to consider the general case of spherical hydrodynamic accretion onto a gravitating mass embedded in a fractal medium. The general nature of ...

In this report, we present a complete theory for the fractal that is obtained when applying Newton's Method to nd the roots of a complex cubic. We show that a modiied Newton's Method improves convergence and does not yield a fractal, but basins of attraction with smooth borders. Extensions to higher-order polynomials and the numerical relevance of this fractal analysis are discussed. M. Drexler...