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These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteratio
Computer graphics. --- Fractals. --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Dimension theory (Topology) --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Digital techniques --- Fractales y Caos (4193622) --- Bibliografía recomendada
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Computer composition --- Computer sound processing --- Fractals --- Spectrum analysis --- Analysis, Spectrum --- Spectra --- Spectrochemical analysis --- Spectrochemistry --- Spectroscopy --- Chemistry, Analytic --- Interferometry --- Optics --- Radiation --- Wave-motion, Theory of --- Absorption spectra --- Light --- Spectroscope --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Sound processing, Computer --- Electronic digital computers --- Sound --- Electronic composition --- Qualitative --- Recording and reproducing --- Digital techniques --- Theses --- Computer composition. --- Computer sound processing. --- Fractals. --- Spectrum analysis. --- Computer composition (Music) --- Spectrometry --- Analytical chemistry
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Statistical physics --- Fractals. --- Scaling laws (Statistical physics) --- Mathematical physics. --- Fractales --- Lois d'échelle (Physique statistique) --- Physique mathématique --- 536.75 --- Fractals --- Mathematical physics --- #KVIV:BB --- Ratio and proportion (Statistical physics) --- Scale invariance (Statistical physics) --- Scaling hypothesis (Statistical physics) --- Scaling phenomena (Statistical physics) --- Physical laws --- Ranking and selection (Statistics) --- Physical mathematics --- Physics --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Entropy. Statistical thermodynamics. Irreversible processes --- Mathematics --- 536.75 Entropy. Statistical thermodynamics. Irreversible processes --- Lois d'échelle (Physique statistique) --- Physique mathématique
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This book may be considered a continuation of my Springer-Verlag text Mea sure, Topology, and Fractal Geometry. It presupposes some elementary knowl edge of fractal geometry and the mathematics behind fractal geometry. Such knowledge might be obtained by study of Measure, Topology, and Fractal Ge ometry or by study of one of the other mathematically oriented texts (such as [13] or [87]). I hope this book will be appropriate to mathematics students at the beginning graduate level in the U.S. Most references are numbered and may be found at the end of the book; but Measure, Topology, and Fractal Geometry is referred to as [ MTFG]. One of the reviews of [MTFG] says that it "sacrific[es] breadth of coverage 1 for systematic development" -although I did not have it so clearly formulated as that in my mind at the time I was writing the book, I think that remark is exactly on target. That sacrifice has been made in this volume as well. In many cases, I do not include the most general or most complete form of a result. Sometimes I have only an example of an important development. The goal was to omit most material that is too tedious or that requires too much background.
Measure theory. Mathematical integration --- Fractals. --- Measure theory. --- Probability measures. --- Fractales --- Mesure, Théorie de la --- Mesures de probabilités --- 517.987 --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Mesure, Théorie de la --- Mesures de probabilités --- Fractals --- Measure theory --- Probability measures --- Measures, Normalized --- Measures, Probability --- Normalized measures --- Distribution (Probability theory) --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Fractal geometry --- Fractal sets --- Geometry, Fractal --- Sets, Fractal --- Sets of fractional dimension --- Dimension theory (Topology) --- Differential geometry. Global analysis --- Geometric measure theory --- Mesure géométrique, Théorie de la --- Fractales. --- Geometric probabilities. --- Probabilités géométriques. --- Probabilities. --- Functions of real variables. --- Probability Theory and Stochastic Processes. --- Real Functions. --- Real variables --- Functions of complex variables --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk
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