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- Multifractal_system abstract "A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed.Multifractal systems are common in nature, especially geophysics. They include fully developed turbulence, stock market time series, real world scenes, the Sun’s magnetic field time series, heartbeat dynamics, human gait, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed to mathematical convergence effects related to the central limit theorem that have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models as well as the geometric Tweedie models. The first convergence effect yields monofractal sequences and the second convergence effect is responsible for variation in the fractal dimension of the monofractal sequences.From a practical perspective, multifractal analysis uses the mathematical basis of multifractal theory to investigate datasets, often in conjunction with other methods of fractal analysis and lacunarity analysis. The technique entails distorting datasets extracted from patterns to generate multifractal spectra that illustrate how scaling varies over the dataset. The techniques of multifractal analysis have been applied in a variety of practical situations such as predicting earthquakes and interpreting medical images.".
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- Multifractal_system wikiPageExternalLink abstract.
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- Multifractal_system wikiPageWikiLink Box_counting.
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- Multifractal_system wikiPageWikiLink Capacity_dimension.
- Multifractal_system wikiPageWikiLink Cardiac_cycle.
- Multifractal_system wikiPageWikiLink Category:Dimension_theory.
- Multifractal_system wikiPageWikiLink Category:Fractals.
- Multifractal_system wikiPageWikiLink Central_limit_theorem.
- Multifractal_system wikiPageWikiLink Continuous_cascade.
- Multifractal_system wikiPageWikiLink Correlation_dimension.
- Multifractal_system wikiPageWikiLink Detrended_fluctuation_analysis.
- Multifractal_system wikiPageWikiLink Ecological_niche.
- Multifractal_system wikiPageWikiLink Fluid_dynamics.
- Multifractal_system wikiPageWikiLink Fractal.
- Multifractal_system wikiPageWikiLink Fractal_analysis.
- Multifractal_system wikiPageWikiLink Fractal_dimension.
- Multifractal_system wikiPageWikiLink Fractal_set.
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- Multifractal_system wikiPageWikiLink Fractional_Brownian_motion.
- Multifractal_system wikiPageWikiLink Gaussian.
- Multifractal_system wikiPageWikiLink Geophysics.
- Multifractal_system wikiPageWikiLink Hausdorff_dimension.
- Multifractal_system wikiPageWikiLink Information_dimension.
- Multifractal_system wikiPageWikiLink Lacunarity.
- Multifractal_system wikiPageWikiLink Legendre_transform.
- Multifractal_system wikiPageWikiLink Legendre_transformation.
- Multifractal_system wikiPageWikiLink List_of_things_named_after_Carl_Friedrich_Gauss.
- Multifractal_system wikiPageWikiLink Lognormal_cascade.
- Multifractal_system wikiPageWikiLink Mandelbrot_cascade.
- Multifractal_system wikiPageWikiLink Markov_switching_multifractal.
- Multifractal_system wikiPageWikiLink Mathematical_singularity.
- Multifractal_system wikiPageWikiLink Metacommunity.
- Multifractal_system wikiPageWikiLink Minkowski–Bouligand_dimension.
- Multifractal_system wikiPageWikiLink Multifractal_Model_of_Asset_Returns.
- Multifractal_system wikiPageWikiLink Multifractal_Random_Walk_model.
- Multifractal_system wikiPageWikiLink Multiplicative_cascade.
- Multifractal_system wikiPageWikiLink Power_law.
- Multifractal_system wikiPageWikiLink Regular.
- Multifractal_system wikiPageWikiLink Regularity.
- Multifractal_system wikiPageWikiLink Relative_species_abundance.
- Multifractal_system wikiPageWikiLink Singularity_(mathematics).
- Multifractal_system wikiPageWikiLink Singularity_exponent.
- Multifractal_system wikiPageWikiLink Singularity_spectrum.
- Multifractal_system wikiPageWikiLink Stock_market.
- Multifractal_system wikiPageWikiLink Turbulence.
- Multifractal_system wikiPageWikiLink Tweedie_distribution.
- Multifractal_system wikiPageWikiLink Tweedie_distributions.
- Multifractal_system wikiPageWikiLink Unified_neutral_theory_of_biodiversity.
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- Multifractal_system wikiPageWikiLink File:Dqvsq.png.
- Multifractal_system wikiPageWikiLink File:Karperien_Strange_Attractor_200.gif.
- Multifractal_system wikiPageWikiLink File:WF111-Anderson_transition-multifractal.jpeg.
- Multifractal_system wikiPageWikiLinkText "Multifractal system".
- Multifractal_system wikiPageWikiLinkText "multifractal system".
- Multifractal_system wikiPageWikiLinkText "multifractal".
- Multifractal_system wikiPageWikiLinkText "multifractality".
- Multifractal_system wikiPageWikiLinkText "multifractals".
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- Multifractal_system subject Category:Dimension_theory.
- Multifractal_system subject Category:Fractals.
- Multifractal_system hypernym Generalization.
- Multifractal_system type Article.
- Multifractal_system type Article.
- Multifractal_system type Function.
- Multifractal_system comment "A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed.Multifractal systems are common in nature, especially geophysics.".
- Multifractal_system label "Multifractal system".
- Multifractal_system sameAs Análisis_multifractal.
- Multifractal_system sameAs سامانه_چندبرخالی.
- Multifractal_system sameAs Multifractale.
- Multifractal_system sameAs Multifractal.
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- Multifractal_system sameAs Мультифрактал.
- Multifractal_system sameAs Мультифрактал.
- Multifractal_system sameAs Q2629238.
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- Multifractal_system wasDerivedFrom Multifractal_system?oldid=681735758.
- Multifractal_system depiction Karperien_Strange_Attractor_200.gif.
- Multifractal_system isPrimaryTopicOf Multifractal_system.