Understanding of tissue growth is in its nature multidisciplinary, since it varies from cancer diagnostics, image processing, fractal analysis to regular and non-regular heat flows. By medical sciences it was requested to better understood the tissue grow relation to mathematical modelling (stochastic geometry, fractal growth, diffusions). It is clear, that deterministic fractal is not an appro...

Noise-free stochastic resonance is investigated in two chaotic maps with periodically modulated control parameter close to a boundary crisis: the Hénon map and the kicked spin model. Response of the maps to the periodic signal at the fundamental frequency and its higher harmonics is examined. The systems show noise-free stochastic multiresonance, i.e. multiple maxima of the signal-to-noise rati...

We consider the binary fragmentation problem in which, at any breakup event, one of daughter segments either survives with probability $p$ or disappears $1\!-\!p$. It describes a stochastic dyadic Cantor set that evolves time, and eventually becomes fractal. investigate this phenomenon, through analytical methods Monte Carlo simulation, for generic class models, where segment points follow symm...

Asynchronous nonlinear fractal operators were considered in order to implement fractal applications by massive parallel asynchronous computing system as recurrent neural networks. Assuming the convergence of the synchronous fractal operator to an element ~ f which is an approximation of the original image f , it is proved that any asynchronous deterministic realization of local fractal operator...

The main component of a cryptographic system that allows us to ensure its strength against attacks, is the substitution box. this can be validated by various metrics, one them being nonlinearity. To end, it essential develop design for boxes guarantee compliance with metric. In work, we implemented hybrid between stochastic fractal search algorithm in conjunction opposition-based learning. This...

Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the “eternal...