Multifractal system

（重定向自Multifractality）

$A Strange Attractor that exhibits multifractal scaling$

$Example of a multifractal electronic eigenstate at the Anderson localization transition in a system with 1367631 atoms.$

$Multifractal analysis is analogous to viewing a dataset through a series of distorting lenses to home in on differences in scaling. The pattern shown is a Hénon map$

$DQ vs Q spectra for a non-fractal circle (empirical box counting dimension = 1.0), mono-fractal Quadric Cross (empirical box counting dimension = 1.49), and multifractal Hénon map (empirical box counting dimension = 1.29).$

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 the length of coastlines, 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.

词汇	Multifractality
分类	英语词汇英语翻译词典
释义	Multifractality 英语百科 Multifractal system （重定向自Multifractality） $A Strange Attractor that exhibits multifractal scaling$ $Example of a multifractal electronic eigenstate at the Anderson localization transition in a system with 1367631 atoms.$ $Multifractal analysis is analogous to viewing a dataset through a series of distorting lenses to home in on differences in scaling. The pattern shown is a Hénon map$ $DQ vs Q spectra for a non-fractal circle (empirical box counting dimension = 1.0), mono-fractal Quadric Cross (empirical box counting dimension = 1.49), and multifractal Hénon map (empirical box counting dimension = 1.29).$ 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 the length of coastlines, 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.
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