Abstract
Scale-invariant structures originating from growth processes have been found to be extremely widespread in nature.1 This observation have led to a number of careful experiments, and various growth models have been suggested to describe the fractal outcome; but why did they become fractal in the first place? To answer this question we must understand the spatio-temporal evolution. Dynamically, the interface is observed to be unstable, and the system eventually reaches a statistically stationary state where a rich ramified pattern is created. A major observation is that this state can be described by power laws — the pattern becomes scale invariant.
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References
See e.g. B. B. Mandelbrot, “The Fractal Geometry of Nature” (Freeman, San Fransisco, 1982); R. Pynn and T. Riste, eds., “Time-Dependent Effects in Disordered Materials” (Plenum, New York, 1987); H. E. Stanley and N. Ostrowsky, eds., “Random Fluctuations and Pattern Growth: Experiments and Models” (Kluwer, Dordrecht, 1988); J. Feder, “Fractals” (Plenum, New York, 1988).
P. Alstrøm, Phys. Rev. A 38, 4905 (1988). P. Alstrøm, preprint.
T. E. Harris, “The Theory of Branching Processes” (Springer, Berlin, 1963).
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© 1989 Plenum Press, New York
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Alstrøm, P., Trunfio, P., Stanley, H.E. (1989). New Critical Exponents for Spatial and Temporal Fluctuations in Stochastic Growth Phenomena. In: Riste, T., Sherrington, D. (eds) Phase Transitions in Soft Condensed Matter. NATO ASI Series, vol 211. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0551-4_37
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DOI: https://doi.org/10.1007/978-1-4613-0551-4_37
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