Fractal Heterogeneous Media

Abstract

A method is proposed for generating compact fractal disordered media, by generalizing the random midpoint displacement algorithm. The obtained structures are invasive stochastic fractals, with the Hurst exponent varying as a continuous parameter, as opposed to lacunar deterministic fractals, such as the Menger sponge. By employing the Detrending Moving Average algorithm [Phys. Rev. E 76, 056703 (2007)], the Hurst exponent of the generated structure can be subsequently checked. The fractality of such a structure is referred to a property defined over a three dimensional topology rather than to the topology itself. Consequently, in this framework, the Hurst exponent should be intended as an estimator of compactness rather than of roughness. Applications can be envisaged for simulating and quantifying complex systems characterized by self-similar heterogeneity across space. For example, exploitation areas range from the design and control of multifunctional self-assembled artificial nano and micro structures, to the analysis and modelling of complex pattern formation in biology, environmental sciences, geomorphological sciences, etc.

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• Detrending Moving Average Algorithm: Frequency Response and Scaling Performances
• Effects of polynomial trends on detrending moving average analysis
• Information Measures for Long-Range Correlated Sequences: the Case of the 24 Human Chromosome Sequences
• Direct determination approach for the multifractal detrending moving average analysis
• Snow metamorphism: a fractal approach
• Linear and nonlinear correlations in order aggressiveness of Chinese stocks
• Probabilistic properties of detrended fluctuation analysis for Gaussian processes
• Inelastic rotations and pseudo-turbulent plastic avalanches in crystals
• Complexity Aided Design: the FuturICT Technological Innovation Paradigm