It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a one-parameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value ...

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional array of scatterers with moving point particles. The particles move from one scatterer to the next according to a piecewise linear, expanding, deterministic map on unit intervals. The microscopic chaotic scattering process of the map can be changed by a control parameter. The macroscopic diffusion coef...

Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network traffic models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally efficient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fr...

We investigate chaotic and multi-fractal properties of a two parameter map of the unit interval onto itself – the Kim-Kong map. These results are compared with similar properties in well known one parameter maps of the unit interval onto itself.

The origin of log-periodic oscillations around the power-law trend of the escape probability from a precritical attractor and of the noise-free stochastic multiresonance, found in numerical simulations in chaotic systems close to crises is discussed. It is shown that multiple maxima of the spectral power amplification vs. the control parameter result from a fractal structure of a precritical at...

We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range of length scales. We focus on the dynamics of these systems during the relaxation from a long-range ordered initial state to the disordered fractal-domain s...

Self-similar processes based on fractal point processes (FPPs) provide natural and attractive network traac models. We show that the point process formulation yields a wide range of FPPs which in turn yield a diversity of parsimonious, computationally eecient, and highly practical asymptotic second-order self-similar processes. Using this framework, we show that the relevant second-order fracta...

A Fractal Evolutionary Particle Swarm Optimization (FEPSO) is proposed based on the classical particle swarm optimization (PSO) algorithm. FEPSO applies the fractal Brownian motion model used to describe the irregular movement characteristics to simulate the optimization process varying in unknown mode, and include the implied trends to go to the global optimum. This will help the individual to...

This paper presents steps towards creating a general model for aggregated traffic streams. We show that fitting the mean, variance and Hurst parameter is insufficient to consistently model a long range dependent traffic stream. A fourth parameter, the “level of aggregation,” is required. We also show that with increased aggregation, the behaviour of a traffic stream tends towards that of a frac...

Fourier analysis has shown that human electroencephalography (EEG) signals mainly consist of frequencies below 80 Hz. Waves with a frequency below 13Hz are dominant during sleep. Here we find that the fractal dimensions of sleep EEG results in a frequency range of 2Hz to 13Hz have potential to be used as a continuous parameter to characterize sleep status. Our results show that during sleep, th...