A fractal (power-law) distribution is the only statistical distribution applicable to a scale-invariant process. One of the major problems in petrology is the distribution of trace elements in the Earth’s crust. Extreme values of this distribution result in ore deposits. There is accumulating observational evidence that tonnage–grade statistics of ore deposits are often fractal (powerlaw). Rayl...

In this study, 115 samples taken from the stream sediments were analyzed for concentrations of As, Co, Cr, Cu, Ni, Pb, W, Zn, Au, Ba, Fe, Mn, Sr, Ti, U, V and Zr. In order to outline mineralization-derived stream sediments, various mapping techniques including fuzzy factor score, geochemical halos and fractal model were used. Based on these models, concentrations of Co, Cr, Ni, Zn, Ba, Fe, Mn, ...

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure with prede®ned stati...

There are several methods to estimate fractal dimension in fractional Brownian motion model. In this paper, one of methods, the variance method, is analyzed detailedly, and some problems in the method are pointed out. To resolve the problems, an improved method is proposed. To validate the method, a comparing experiment of two methods is designed. In the experiment, a SPOT image is selected and...

We introduce fractal liquids by generalizing classical liquids of integer dimensions d = 1, 2, 3 to a fractal dimension df . The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid drop...

Fluctuations in the concentration of Brownian particles in one and two dimensions, or any reasonable measurement of the concentration such as in fluorescence correlation spectroscopy, is shown to be a stochastic fractal with a long tail. Being singular at omega = 0, the power spectrum of the fluctuation S(omega) approximately omega-1/2 for diffusion in one dimension, approximately log omega in ...