In recent work, various fractal image coding methods are reported, which adopt the selfsimilarity of images to compress the size of images. However, till now, no solutions for the security of fractal encoded images have been provided. In this paper, a secure fractal image coding scheme is proposed and evaluated, which encrypts some of the fractal parameters during fractal encoding, and thus, pr...

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter q. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which ar...

subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. water flow in these systems is described by the boussinesq equation, and the advection-dispersion equation coupled with the boussinesq equation is used to study the solute transport. the objective of this study was to propose a finite difference solution of the advection-dispersi...

In this paper we address two issues in modeling natural terrain using fractal geometry: estimation of fractal dimension, and fractal surface reconstruction. For estimation of fractal dimension, we extend the fractal Brownian function approach to accommodate irregularly sampled data, and we develop methods for segmenting sets of points exhibiting self-similarity over only certain scales. For fra...

We study the invariant measure or the stationary density of a coupled discrete dynamical system as a function of the coupling parameter ǫ (0 < ǫ < 1/4). The dynamical system considered is chaotic and unsynchronized for this range of parameter values. We find that the stationary density, restricted on the synchronization manifold, is a fractal function. We find the lower bound on the fractal dim...

A hybrid wavelet-fractal coder (WFC) for image compression is proposed. The WFC uses the fractal contractive mapping to predict the wavelet coefficients of the higher resolution from those of the lower resolution and then encode the prediction residue with a bitplane wavelet coder. The fractal prediction is adaptively applied only to regions where the rate saving offered by fractal prediction j...

Alzheimer's disease (AD) represents one major health concern for our growing elderly population. It accounts for increasing impairment of cognitive capacity followed by loss of executive function in late stage. AD pathogenesis is multifaceted and difficult to pinpoint, and understanding AD etiology will be critical to effectively diagnose and treat the disease. An interesting hypothesis concern...

Deterministic diffusion is studied in simple, parameter-dependent dynamical systems. The diffusion coefficient is often a fractal function of the control parameter, exhibiting regions of scaling and self-similarity. Firstly, the concepts of chaos and deterministic diffusion are introduced in the context of dynamical systems. The link between deterministic diffusion and physical diffusion is mad...

The reflectance of corrugated surfaces with a fractal distribution of grooves is investigated. Triadic and polyadic Cantor fractal distributions are considered, and the reflected intensity is compared with that of the corresponding periodic structure. The self-similarity property of the response is analyzed when varying the depth of the grooves and the lacunarity parameter. The results confirm ...

cation exchange capacity and specific surface area are among some of the important soil characteristics the direct measurement of which is laborious, costly and time consuming. therefore, fractal dimension of particle size distribution has been widely studied in relation with many such dynamic and static processes as transmission of water and solutes, water holding capacity, heat storage and co...