Fractal geometries : theory and applications
著者
書誌事項
Fractal geometries : theory and applications
Penton Press, c1991
- タイトル別名
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Les géometries fractales
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注記
Translation of: Les géometries fractales
Includes bibliographical references and index
内容説明・目次
内容説明
Fractal geometry, based on recursive mathematical schemas, provides a means for modelling a great number of natural phenomena, and for this reason is of increasing interest to physicists, chemists, biologists and geographers, amongst others. A major quality of fractality is that not only does it unify in a single theoretical framework phenomena thought previously to be anomalous or disparate, but it also promotes a return to graphical treatment, which had been almost completely banished from scientific thought in favour of analysis. This book casts a new light on scientific territories still not fully explored. It is addressed to research workers, engineers and experimentalists faced with problems of measurement and action in heterogeneous materials and environments.
目次
- Part 1 The discovery of fractal geometry: the surveyor's task - rectifiable curves, measuring by arc lengths
- a journey into pathology - the search for lost rectifiability
- what is a measure?
- from line to surface, a simple expression of fractality - self-similarity
- fractal closed curves (loops) - perimeter, area, density, fractal mass dimension, the concept of co-dimension
- scaling laws with variable ratios
- from self-similarity to self-affinness. Part 2 Measures of dimension - time in fractal geometry
- practical methods - different measures of dimension
- two methods for measuring the fractal dimension
- relation between time and measure, parametrization of fractal curves
- case where the geometry is a transfer function, physical analysis and non-integral derivation
- an irregularity parameter for continuous non-derivation of non-integral order
- spectral analysis and non-integral derivation
- an irregularity parameter for continuous non-derivable functions - the maximum-order of derivation. Part 4 Composition of fractal geometries: statistical aspects - multifractality - the combination of several fractal dimensions
- hyperfractality - combination of derivations of different orders. Part 5 Applications: measure and uncertainty
- fractal morphogenesis
- from fractal geometry to irreversibility
- complexity.
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