In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoret...

An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal brane...

This paper is an attempt to attain a new and profound model of the nature’s structure using a vortex-fractal theory (VFT). Scientists try to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-fractal modeling of vortex-ring fractal structure of atoms, molecules, and a creation of elements in the Mendeleev’s periodic table with vortex-ring p...

Fractal geometry has proven to be a useful tool in quantifying the structure of a wide range of idealized and naturally occurring objects, from pure mathematics, through physics and chemistry, to biology and medicine. In the past few years fractal analysis techniques have gained increasing attention in signal and image processing, especially in medical sciences, e.g. in pathology, neuropsychiat...

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimensi...