## Abstract

Objects in nature are often very irregular, so that, within the constraints of Euclidean geometry, one is forced to approximate their shape grossly. A rock fragment, for example, is treated as being spherical, and a coastline straight or smoothly curved. Upon examination, however, these objects are found to be jagged, and their jaggedness does not diminish when viewed at ever finer scales. In his monumental work, Mandelbrot (1982) developed and popularized * fractal geometry * , a geometry that applies to many irregular natural objects. The analytical techniques for treating fractal geometry and their inter-relationships have undergone rapid development and broad application (Feder, 1988). Fractal geometry has been applied to a wide variety of geological and geophysical objects and phenomena: for surveys see Scholz and Mandelbrot (1989), Turcotte (1989), Turcotte (1992)), and Barton and La Pointe (1995). During this same time, there have also been revolutionary developments in understanding the types of physical processes that produce patterns described by fractal geometry. Fractal patterns have been found to arise from a wide variety of nonlinear dynamical systems, particularly those that exhibit certain types of chaotic behavior (e.g., Schuster, 1988). Examples are dissipative systems with many degrees of freedom that show self-organized criticality, such as avalanches on the surface of a sand pile and earthquakes (Bak et al., 1988; Bak and Chen, 1991).

Original language | American English |
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Title of host publication | Fractals in Petroleum Geology and Earth Processes |

DOIs | |

State | Published - Jan 1 1995 |

## Disciplines

- Earth Sciences
- Environmental Sciences
- Physical Sciences and Mathematics