Chaos and Fractals

By H. Peitgen, H. Jürgens, Dietmar Saupe. 2004

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Multifractal analysis of Hg pore size distributions of tectonically deformed coals (2015, background): “These complex distributions can be attributed to the underlying nonlinear dynamics, as superposition of different processes acting simultaneously along a wide range of length scale (Peitgen et al., 1992).”
Permutation Entropy and Its Main Biomedical and Econophysics Applications: A Review (2012, methodology): “On the contrary, suppose that we are studying the output of the logistic map [18], defined as:”
Chaotic harmony search algorithms (2010, methodology): “Gauss map The Gauss map is used for testing purpose in the literature [33] and is represented by:”
Nonplanar Faults: Mechanics of Slip and Off-fault Damage (2009, methodology): “The simulations employ faults with surface profiles that have a random fractal roughness, which are generated using the random mid-point displacement method (FOURNIER et al., 1982; PEITGEN et al., 1992).”
Chaotic sequences to improve the performance of evolutionary algorithms (2003, background): “Before giving a definition of chaos, the following definitions are required [24].”