Discrete multifractals |
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Authors: | Qiuming Cheng |
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Institution: | (1) Department of Earth and Atmospheric Science, Department of Geography, York University, M3J 1P3 North York, Ontario, Canada |
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Abstract: | The concept of multifractal modeling has been used intensively in various fields of science for characterizing measures with
self- similarity. It has been shown that multifractal modeling provides powerful tools for characterizing patterns in the
spatial distribution of geological quantities and objects. Existing multifractal models were proposed for the purpose of handling
spatially intertwined fractals with continuous fractal spectrum f(α) (or continuous codimension function C(γ)). In this paper, these conventional multifractals are termed “continuous multifractals” whereas multifractals with discrete
fractal dimensions are termed “discrete multifractals.” The properties of discrete multifractals are investigated. It is shown
by various artificial examples and a case study of stratigraphy of Ocean Drilling Program (ODP) site 645 that spatially intertwined
fractals/multifractals indeed can have discrete fractal dimensions. Histogram-and moment-based techniques are proposed for
discrete multifractal modeling and illustrated using the artificial examples. The new concept of discrete multifractals and
associated multifractal modeling yields not only techniques for characterizing multifractals with discrete fractal dimensions
but it also provides insight into the relationships between fractals, bifractals, and multifractals. |
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Keywords: | discrete multifractals fractal spectrum discrete multiplicative cascade model Ocean Drilling Program |
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