The incorporation of fractal concepts into the natural sciences, especially physics, has been swift. This growth has also occurred, albeit at a much slower pace, in the earth sciences, including geomorphology, sedimentology, stratigraphy, and petroleum geology (Korvin, 1992; Turcotte, 1992, 1994a; Barton and LaPointe 1995a,b). Nevertheless, many earth scientists remain unfamiliar with fractal concepts and applications and are perhaps even suspicious that it is a fad. In this chapter we will demonstrate that fractal models and methods allow the geologist to quantify many concepts that have long been intuitive, while also providing new and fruitful ways of looking at data. In addition, as we will show in later chapters, fractals are important in the interpretation of chaos and nonlinear dynamics. We believe that fractal methods will eventually become part of the standard toolkit of any quantitatively oriented geologist, to the same extent that calculus or statistics are currently.
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The intention of these notes is to provide sedimentary geologists with an introduction to the new techniques for analyzing experimental and observational data provided by the rapid development of those disciplines generally known as Fractals and Nonlinear Dynamics (chaos theory). A general introduction to a minimum of theory is given, but most of the space is devoted to show how these ideas are useful for interpreting sedimentary data. The main applications are likely to be time series or spatial profiles or two-dimensional maps or images. Sedimentary geologists deal every day with actual time series, such as measurements of current velocity or suspended concentration at a station, or with virtual time series, such as stratigraphic sections, well logs, or topographic profiles yet few geologists know much about the new numerical techniques available to analyze such data.