A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. ...

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...

Gazestan magnetite-apatite deposit is located in Central Iran and Bafq region, which has been occurred in form of veins, veinlets, and small apatite lenses as well as magnetite in metasomatic rock types such as green chlorite-actinolite rock units. These rocks are situated in the carbonate-volcanic complex of Upper Precambrian-Lower Cambrian Rizo formation. In this study, staged factor analysis...

Different strands of research show that natural form has a positive influence on human emotional states. Although preliminary, evidence is converging that the fractal geometry characteristic of natural elements can induce similar responses. It is argued that, due to their artful nature, fractal patterns are ideally suited to integrate in art therapy. Art therapists are thereby presented an addi...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

The discovery of normal galaxies and heavy elements at the fringes of the observable universe is one of the sources of crisis in modern cosmology. The real universe unfolding is essential for progress in all scientific fields because the origin of chemical elements and space bodies creates the fundamental framework for understanding of everything. The big bang universe is believed to come due t...

This paper presents a case study in the generic design of Grid component models. It defines a framework allowing two component systems, one running in a CCA environment, and another running in a Fractal environment, to interact as if they were elements of the same system. This work demonstrates the openness of both Fractal and CCA component models. It also gives a very generic and exhaustive ov...

The concept of atomic weights (relative atomic masses) of chemical elements and molecular weights (relative molecular masses) of chemical compounds is fundamental to chemistry and the problem to determine their values has captured attention of chemists for a long time. On the other hand, fractal ideas of Mandelbrot have been extended to studies of various forms in nature on a wide range of leng...

Assuming that the motions of a complex system structural units take place on continuous, but non-differentiable curves of a space-time manifold, the scale relativity model with arbitrary constant fractal dimension (the hydrodynamic and wave function versions) is built. For non-differentiability through stochastic processes of the Markov type, the non-differentiable entropy concept on a space-ti...