Fractals in ScienceArmin Bunde, Shlomo Havlin The fractal concept has become an important tool for understanding irregular complex systems in various scientific disciplines. This book discusses in great detail fractals in biology, heterogeneous chemistry, polymers, and the earth sciences. Beginning with a general introduction to fractal geometry it continues with eight chapters on self-organized criticality, rough surfaces and interfaces, random walks, chemical reactions, and fractals in chemistry, biology, and medicine. A special chapter entitled "Computer Exploration of Fractals, Chaos, and Cooperativity" presents computer demonstrations of fractal models. |
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analysis approximation asymptotic avalanche average Avnir behavior calculated chain Chap characteristic function Chem cluster coding concentration corresponds critical CTRW D.E. Wolf defined density dependence deterministic diffusion dimensional discussed displacement dissolution distance distribution DNA sequences DNA walk domain dynamics equation example exponent finite fluctuations fractal dimension G.H. Weiss growth H.E. Stanley Havlin ideal chain initial interaction interface Ising model iteration Julia set Kertész kinetic Laplace Laplace transform lattice length scales Lett linear long-range correlations Macromolecules Mandelbrot Meakin mean-field monomers motion neighbors noise nucleotide obtained one-dimensional P.G. de Gennes parameter particle percolation Phys physical polymers power law probability properties radius random walk reactants reaction zone recursive regime regions roughening S.V. Buldyrev self-affine self-organized criticality self-similar semi-dilute simulations solution spatial species step structure surface transform transition two-species annihilation variable Vicsek walker