The stress-strain behavior of fractal networks possesses self-affine scaling associated with statistical scale invariance of damage patterns. We found that the damage part of stress-strain curve of fractal network and the corresponding rupture line are characterized by the same scaling (Hurst) exponent, H , which is not universal, rather it depends on the network fractal dimension as H =DB − 1....

A new and improved model of red sprites is presented. Emphasis is placed in accounting for the puzzling observation of the spatial structure in the red sprite's optical emissions. The model relies upon a horizontal fractal lightning discharge, which generates the EMPs that excites the optical emissions in the lower ionosphere. It is shown that the fractal model may account for the observed spri...

A series of three experiments was conducted with the aim of determining the processing nature of the fractal rotation stimulus introduced by C. P. Benton, J. M. O'Brien, and W. Curran (2007). This stimulus has been proposed to be invisible to first-order sensitive mechanisms considering it is drift-balanced. Rather, motion perception would require the analysis of spatial structure (orientation)...

So far, several implementations of the Fractal specifications have been proposed. These implementations propose frameworks for programming with Fractal in a target language (Java, C, Smalltalk, C++). The general principles of implementing the specifications are common to all these frameworks. However, as far as we know, no concrete piece of software or no common set of internal interfaces have ...

Inheriting from a long experience about modules, objects and interfaces, component programming has emerged as a programming methodology ensuring both re-usability and composability. Among the components models, Fractal [6] provides hierarchical composition for a better structure, and specification of control interfaces for dynamic management. Fractal defines a highly extensible component model ...

BACKGROUND Tumor grading, PSA concentration, and stage determine a risk of prostate cancer patients with accuracy of about 70%. An approach based on the fractal geometrical model was proposed to eliminate subjectivity from the evaluation of tumor aggressiveness and to improve the prediction. This study was undertaken to validate classes of equivalence for the spatial distribution of cancer cell...

The Farey sequences can be used to create the Euler totient function, by identifying the fractions for number n that did not occur in all Farey sequences up to n – 1. This function creates, when divided by n – 1, what is here called the primety measure, which is a measure of how close to being a prime number n is. The quality of a number sequence can be determined using the primety, which is fu...

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the ‘‘fractional’’ continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier–Stokes and Euler equations are considered. We derive the eq...