![]() ![]() A discontinuous time series is defined if a variable y i is specified at equally spaced times t i, examples would be mean annual temperatures or daily maximum river flows. Self-affine fractals are self-similar time series. Self-affine fractals are also often found in geophysics. When a site has four particles they are redistributed Fractional noises and walks and applications In this model a square grid of sites is considered, a particle is added to a randomly selected site at each time step. These models have a steady input and an output that is characterized by a fractal (power-law) distribution of “avalanches.” The original model in this class was the “sandpile” model proposed by Bak et al. In its standard form, DLA consists of a seed “particle” at the center of a region, random walkers are introduced randomly on the boundaries of the region and are allowed to migrate until they either attach to the seed particle (or the dendritic network that Self-organized criticality––landslides and earthquakesĪ number of simple cellular automata models have been proposed that are said to exhibit self-organized criticality. One of the best examples of how a relatively simple cellular automata model can be related to an important geological (geophysical) problem is the application of diffusion limited aggregation (DLA) to the evolution of drainage networks. More recently a similarity solution to the heat Drainage networks In geophysical applications expansions in special functions have found wide use, i.e., expansions in Legendre functions were used for the earth’s gravitational field. During the 19th century, a wide range of solutions to these equations were obtained. Section snippets Discrete versus continuum geophysicsĬontinuum geophysics utilizes partial differential equations, in particular, LaPlace’s equation, the wave equation, the heat equation, Maxwell’s equations, and the Navier–Stokes equations. Several specific models will be considered below which will illustrate the cellular automata approach. Usually, but not always, interactions are only with nearest neighbors. In many applications a square grid of points is considered. It must be a discretized system, i.e., a one-, two-, three-, or higher dimensional grid of points. There is no absolute definition of what is and what is not a cellular automata. I will then discuss several cellular automata simulations that are applicable to problems in geology and geophysics. In this paper I will first consider the role of cellular automata solutions versus solutions of partial differential equations in geophysics. This book is a best seller, but is also extremely controversial. Topics addressed include general relativity, computability, turbulence, genetic coding, and many others. Stephen Wolfram’s recent book A New Kind of Science argues that cellular automata simulations, broadly interpreted, will lead to a new scientific revolution. ![]()
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