One important contribution has been made by Benoit Mandelbrot, the famous father of fractals who proposed a multi-fractal model of asset returns (MMAR), a theory which inherits all the hallmarks of Mandelbrot’s earlier work that has emerged since the 1970s. As a new formalization of stochastic models for the volatility dynamics of asset prices, it preserves the hierarchical multiplicative struc...

Identification of the vertical and horizontal distributions for elemental grades is of an important sign in different mineral exploration stages. The main aim of this work is to determine the vertical distribution directional properties of Cu values in the Milloieh Cu porphyry deposit, Kerman (SE Iran) using the power-law frequency fractal model. This work is carried out based on four mineraliz...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...

This paper presents a method for fast encoding and decoding of image sequences based on fractal coding theory and the hybrid coding concept. The DPCM-loop accounts for statistical dependencies of natural image sequences in temporal direction. Those regions of the original image where the prediction, i.e. motion estimation and compensatio, fails are encoded using an advanced fractal coding schem...

Shape is one of the most important visual attributes used to characterize objects, playing a important role in pattern recognition. There are various approaches to extract relevant information of a shape. An approach widely used in shape analysis is the complexity, and Fractal Dimension and Multi-Scale Fractal Dimension are both well-known methodologies to estimate it. This papers presents a co...

We numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x(t+1)=1-a/x(t)/(z(i)) (i=1,2 correspond to x(t)>0 and x(t)<0, respectively, z(i)>1, 0<a< or =2, t=0,1,2,...) at the edge of chaos. We employ three distinct algorithms to characterize the power-law sensitivity to initial conditions at the edge of chaos, namely: direct measure of the divergence of initia...

Multi-fractal patterns occur widely in nature. In developing new algorithms to determine multi-fractal spectra of experimental data I am lead to the conclusion that generalised dimensions Dq of order q ≤ 0, including the Hausdorff dimension, are effectively irrelevant. The reason is that these dimensions are extraordinarily sensitive to regions of low density in the multi-fractal data. Instead,...

Multi-fractal scaling in the transition to the dissipative regime for compressible turbulence is considered. The multi-fractal power law scaling behavior breaks down for very small length scales thanks to viscous effects. However, the effect of compressibility is found to extend the single-scaling multi-fractal regime further into the dissipative range. This result appears to be consistent with...

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV(s) = U/d(s), where d(s) is the spectral dimension and V(s) defines the "spectral volume." For regular manifolds, V(s) coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. T...

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based” algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuz...