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System with multiple fractal dimensions
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;
Multifractal_system
Infinitely detailed mathematical structure
fractalPages displaying short descriptions of redirect targets Multifractal system – System with multiple fractal dimensions Newton fractal – Boundary set
Fractal
Theory of fractal structure in the universe
universe itself, is a fractal across a wide range of scales (see also: multifractal system). More generally, it relates to the usage or appearance of fractals
Fractal_cosmology
Method to detect power-law scaling in time series
FGN, thus, the exponents of their power spectra differ by 2. Multifractal system – System with multiple fractal dimensions Self-organized criticality –
Detrended fluctuation analysis
Detrended_fluctuation_analysis
French-American mathematician (1924–2010)
Mandelbrot Competition – High school mathematics competition Multifractal system – System with multiple fractal dimensions Self-similarity – Whole of an
Benoit_Mandelbrot
Continuous function that is not absolutely continuous
2307/2159830. JSTOR 2159830. Falconer, Kenneth J. (2004-01-01). "One-sided multifractal analysis and points of non-differentiability of devil's staircases".
Cantor_function
Fractal sets in complex dynamics of mathematics
{1}{2}})^{2}} on the unit interval, which is commonly used as an example of chaotic system.) The functions f and g are of the form z 2 + c {\displaystyle z^{2}+c}
Julia_set
Fractal related to the mandelbrot set
curve Pythagoras tree Weierstrass function Strange attractor Multifractal system L-system Fractal canopy Space-filling curve H tree Escape-time fractals
Douady_rabbit
Measure of the long-range dependence of a time series
{\displaystyle H(q)} is a non-linear function of q the time series is a multifractal system. In the above definition two separate requirements are mixed together
Hurst_exponent
Fractal analysis technique
analysis. It also has application in related fields such as lacunarity and multifractal analysis. Theoretically, the intent of box counting is to quantify fractal
Box_counting
French economist (born 1969)
extensions. Financial risk Fractal Markov chain Modern portfolio theory Multifractal system "EFA Executive Committee 2023 | EFA - European Finance Association"
Laurent-Emmanuel_Calvet
Fractal creation method
generating the attractor, or the fixed point, of any iterated function system (IFS). Starting with any point x0, successive iterations are formed as xk+1
Chaos_game
Absence of diffusion waves in disordered media
studies of participation numbers obtained by exact diagonalization, multifractal properties, level statistics and many others. Especially fruitful is
Anderson_localization
Continuous fractal curve obtained as the image of Cantor space
mappings of an iterated function system that produces the Sierpiński triangle. Ornstein and others describe a multifractal system, where instead of working in
De_Rham_curve
Physics problem related to laws of motion and gravity
configuration—and that regular and chaotic regions coexist at all scales with a multifractal structure. Statistical escape theories that exclude the outcomes of these
Three-body_problem
Topics referred to by the same term
639:mrw) "My reaction when", used in internet memes Multifractal random walk, a multifractal system model Magic, Ritual, and Witchcraft, a peer-reviewed
MRW
French researcher (born 1957)
the purely empirical ETAS linear model. The basic assumption of this "Multifractal stress activated" model is that, at any place and time, the local failure
Didier_Sornette
Generalization of derivative to fractals
})^{n}f(t)d_{F}^{\alpha }t} Fractional calculus Fractional-order system Multifractal system Khalili Golmankhaneh, Alireza (2022). Fractal Calculus and its
Fractal_derivative
Concept in information theory
Arimitsu, T. (2004). "The world according to Rényi: Thermodynamics of multifractal systems". Annals of Physics. 312 (1): 17–59. arXiv:cond-mat/0207707. Bibcode:2004AnPhy
Rényi_entropy
Open subset of the real–number line
Goran (28 June 2019). An overview of the theory of complex dimensions and fractal zeta functions (PDF). Dubrovnik IX - Topology & Dynamical Systems 2019.
Fractal_string
metric Fractal image compression Image differencing Metric tensor Multifractal system Drakopoulos, V.; Nikolaou, N. P. (December 2004). "Efficient computation
Hutchinson_metric
Random process independent of past history
expansions and recessions). A more recent example is the Markov switching multifractal model of Laurent E. Calvet and Adlai J. Fisher, which builds upon the
Markov_chain
French mathematical physicist
the fine structure of turbulent flows, for his early advocacy of multifractal systems in modeling physical processes, and for his research on using transportation
Uriel_Frisch
Multifractal function used in terrain modeling and simulation
of Vehicle Autonomous Systems. 10 (1/2): 3–18. doi:10.1504/IJVAS.2012.047693. Casey D. Majhor and Jeremy P. Bos. "Multifractal Terrain Generation for
Weierstrass–Mandelbrot function
Weierstrass–Mandelbrot_function
Italian physicist (born 1948)
confinement, the use of supersymmetry in statistical classical systems, the introduction of multifractals in turbulence, the stochastic differential equation for
Giorgio_Parisi
Family of probability distributions
manifest local variations in fractal dimension, they are said to be multifractals. Examples of data sequences that exhibit local variations in p like
Tweedie_distribution
Probability distribution
Calvet, L. E. (1997). A multifractal model of asset returns. 3.2 The Binomial Measure is the Simplest Example of a Multifractal Hirsch, Werner Z. (1957)
Binomial_distribution
also includes results on horocycle flows and multifractal analysis. Michael Brin Prize in Dynamical Systems (2013), "for his work on the thermodynamics
Omri_Sarig
Real-valued number of spatial dimensions
{\displaystyle D={\frac {d\log L(k)}{d\log k}}.} Lyapunov dimension Multifractal dimensions: a special case of Rényi dimensions where scaling behaviour
Fractal_dimension
Lyapunov fractal Mandelbrot set Menger sponge Minkowski–Bouligand dimension Multifractal analysis Olbers' paradox Perlin noise Power law Rectifiable curve Scale-free
Index of fractal-related articles
Index_of_fractal-related_articles
Whole of an object being mathematically similar to part of itself
Arneodo, A.; Decoster, N.; Roux, S. G. (2000). "A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and
Self-similarity
Type of software
Townsend, P.; Vince, J. A. (eds.). "Dynamic Terrain Generation Based on Multifractal Techniques". High Performance Computing for Computer Graphics and Visualisation
Scenery_generator
Process of estimating what something is worth, used in the finance industry
method for real option valuation Single-index model Markov switching multifractal Multiple factor models Damodaran, Aswath (31 January 2002). Investment
Valuation_(finance)
Irregular alternation different types of dynamics
Letters A, vol. 188, 1994, pp. 39–47 C. Meneveau and K.R. Sreenivasan, The multifractal nature of turbulent energy dissipation, Journal of Fluid Mechanics, vol
Intermittency
Mathematical technique in data science
analysis, including box counting, lacunarity analysis, mass methods, and multifractal analysis. A common feature of all types of fractal analysis is the need
Fractal_analysis
S2CID 14240006. Meakin, Paul (1987). "Diffusion-limited aggregation on multifractal lattices: A model for fluid-fluid displacement in porous media". Physical
List of fractals by Hausdorff dimension
List_of_fractals_by_Hausdorff_dimension
American financial and commodity derivative exchange
Walid; Vo, Xuan Vinh; Kang, Sang Hoon (June 1, 2022). "Upward/downward multifractality and efficiency in metals futures markets: The impacts of financial
Chicago_Mercantile_Exchange
Function for integral Fourier-like transform
speech recognition, acoustics, vibration signals, computer graphics, multifractal analysis, and sparse coding. In computer vision and image processing
Wavelet
contributions in the area of statistical physics, nonlinear physics, complex systems, and complex networks. List of physics awards "European Physical Society
EPS Statistical and Nonlinear Physics Prize
EPS_Statistical_and_Nonlinear_Physics_Prize
Prize awarded by the International Centre for Theoretical Physics
confinement, the use of supersymmetry in statistical classical systems, the introduction of multifractals in turbulence, the stochastic differential equation for
Dirac_Medal_(ICTP)
Stochastically generated naturalistic terrain
Continuity". General Systems Yearbook. 6: 139–187. van Lawick van Pabst, Joost; Jense, Hans (2001). "Dynamic Terrain Generation Based on Multifractal Techniques"
Fractal_landscape
Fundamental quantity in physics
of information entropy production, of a system. Mandelbrot introduces intrinsic time in his book Multifractals and 1/f noise. Khemani, Moessner, and Sondhi
Time_in_physics
All of space observable from the Earth at the present
744M. doi:10.1086/497125. Mureika, J. R.; Dyer, C. C. (2004). "Review: Multifractal Analysis of Packed Swiss Cheese Cosmologies". General Relativity and
Observable_universe
Generalization of the standard Boltzmann–Gibbs entropy
Lyra, M.; Tsallis, C. (1998). "Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems". Physical Review Letters. 80 (1): 53–56. arXiv:cond-mat/9709226
Tsallis_entropy
Chinese-American mechanical engineer
dissertation was titled Analytical modeling of bifurcations, chaos and multifractals in nonlinear dynamics (1996). From 1996 to 1998, Luo was an NSERC (Natural
Albert_C.J._Luo
French-Chilean born American fluid dynamicist
and his advisor Prof. K. R. Sreenivasan established the fractal and multifractal theory for turbulent flows and confirmed the theory using experiments
Charles_Meneveau
Tendency of software to fail due to external changes or prolonged operation
Liu (2003). "Software aging and multifractality of memory resources". 2003 International Conference on Dependable Systems and Networks, 2003. Proceedings
Software_aging
Argentine mathematician
English) de Spinadel, Vera W. (June 1999). "The metallic means family and multifractal spectra". Nonlinear Analysis: Theory, Methods & Applications. 36 (6):
Vera_W._de_Spinadel
Portuguese mathematician (born 1968)
articles, predominantly in Differential Equations, Dynamic Systems, Ergodic Theory and Multifractal Analysis. Barreira got his degree in 1991 in Applied Mathematics
Luís_Barreira
Signal with equal energy per octave
convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality" (PDF). Phys. Rev. E. 84 (6) 066120. Bibcode:2011PhRvE..84f6120K. doi:10
Pink_noise
Algorithm
not consisting of only one defined fractal, it is characterized by a multifractal complex network. This means that on different scales, the defined fractal
Head/tail_breaks
Sequence of data points over time
switching multifractal (MSMF) techniques for modeling volatility evolution. A hidden Markov model (HMM) is a statistical Markov model in which the system being
Time_series
experimental, theoretical, and numerical research on the nonlinear and multifractal foundations of turbulent flows. 2023 Itamar Procaccia The Weizmann Institute
Leo_P._Kadanoff_Prize
Features that do not change if length or energy scales are multiplied by a common factor
convergence: A mathematical basis for Taylor's power law, 1/f noise, and multifractality" (PDF). Phys. Rev. E. 84 (6) 066120. Bibcode:2011PhRvE..84f6120K. doi:10
Scale_invariance
Russian-Mexican scientist (born 1958)
new concept of multifractal elasticity and has developed the theory of mechanical behaviour and fracture of composites with multifractal structures. In
Alexander_Balankin
Professor of Aerospace Engineering
of turbulent thermoacoustic systems from combustion noise to instability. His research has also explored the multifractal nature of combustion noise and
R._I._Sujith
Indian physicist
collaborators include the phase transition analogs of the thermodynamics of multifractals, the method of impulsive synchronisation and the enhancement of the
Neelima_Gupte
Functional relationship between two quantities
convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality" (PDF). Phys. Rev. E. 84 (6) 066120. Bibcode:2011PhRvE..84f6120K. doi:10
Power_law
Interacting particle system Jump diffusion M/M/1 model M/M/c model Mark V Shaney Markov chain Monte Carlo Markov switching multifractal Oscillator linewidth
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Fossilized evidence of wildfires on Earth
(2019-12-14). "The Classification of Inertinite Macerals in Coal Based on the Multifractal Spectrum Method". Applied Sciences. 9 (24): 5509. doi:10.3390/app9245509
Fossil_record_of_fire
Motion characterized by chaotic changes in pressure and flow velocity
ISBN 978-0-521-57066-4. Meneveau, C.; Sreenivasan, K.R. (1991). "The multifractal nature of turbulent energy dissipation". J. Fluid Mech. 224: 429–484
Turbulence
explain the origin of the variance to mean power law, 1/f noise and multifractality, features associated with self-similar processes. Ethernet traffic
Self-similar_process
Category of denial-of-service attack
Liyuan; Yue, Meng (2015). "Low-Rate DoS Attacks Detection Based on Network Multifractal". IEEE Transactions on Dependable and Secure Computing. 13 (5): 559–567
Slow_DoS_attack
Italian physicist
completed her Ph.D. at Boston University in 1986; her dissertation, Multifractality in Percolation: the Voltage Distribution, was supervised by Sidney
Lucilla_de_Arcangelis
Signal analysis tool
Muyi; Huang, Yongxiang (July 2014). "Hilbert–Huang Transform based multifractal analysis of China stock market". Physica A: Statistical Mechanics and
Hilbert–Huang_transform
Branch of geophysics, primarily seismology
of statistical physics, i.e., detrended fluctuation analysis (DFA), multifractal DFA and wavelet transform revealed that SES are clearly distinguished
Earthquake_prediction
Least variables needed to represent data
1. World Scientific. pp. 1–107. ISBN 9810213530. Harte, D. (2001). Multifractals — Theory and Applications. Chapman and Hall/CRC. ISBN 9781584881544
Intrinsic_dimension
Art style
W.H. Freeman, 1982. Print.] J.R. Mureika, C.C. Dyer, G.C. Cupchik, “Multifractal Structure in Nonrepresentational Art”, Physical Review E, vol. 72, 046101-1-15
Fractal_expressionism
currently lack in experimental data. Lebyodkin, M.A.; Estrin, Y. (2005). "Multifractal analysis of the Portevin–Le Chatelier effect: General approach and application
Dislocation_avalanches
American physicist and applied mathematician
; DelSordo, F.; Wettlaufer, J. S. (2017). "Exoplanetary detection by multifractal spectral analysis". The Astronomical Journal. 153 (1): 12. arXiv:1609
John_Wettlaufer
German astronomer
The Case for Dwarf K Stars (2016) (incl. E. F. Guinan). Fractal and Multifractal Analysis of the Rise of Oxygen in Earth's Early Atmosphere (2015) (incl
Manfred_Cuntz
Struzik. (2004). "Econophysics vs Cardiophysics: the Dual Face of Multifractality". In Hideki Takayasu (ed.). The Application of Econophysics. Japan:
Cardiophysics
Indian physicist (1956–2021)
classical and quantum problems in random media and physics of mesoscopic systems. High temperature superconductors, thermal ratchets and molecular motors
A._M._Jayannavar
Danish statistician
distributions in natural systems. They can be used to explain the origin of Taylor's law as well as 1/f noise and multifractality. Consequent to Jørgensen's
Bent_Jørgensen_(statistician)
Italian professor and engineer (born 1952)
"Size effects on nominal tensile strength of concrete structures: multifractality of material ligaments and dimensional transition from order to disorder"
Alberto_Carpinteri
Cell-free DNA profiling method
Karri, Sirish; Firer, Michael A.; Minnes, Refael (2 November 2023). "Multifractal analysis of cellular ATR-FTIR spectrum as a method for identifying and
EPIC-Seq
Azerbaijani petroleum scientist and academic (1959–2026)
and recoverable resources was developed; Based on the use of fractal, multifractal dimensions and Fisher-Shannon indicators, new methods of oil field development
Baghir_Suleimanov
António (2003). "Modeling Network Traffic with Multifractal Behavior" (PDF). Telecommunication Systems. 24 (2/4): 339–362. doi:10.1023/a:1026183318200
History of network traffic models
History_of_network_traffic_models
German theoretical physicist
analysis, employing profitably Elsasser variables, and analyzed the multifractal nature of fluctuations and their dissipation in turbulent energy cascades
Eckart_Marsch
Empirical law on the variance of species in a habitat
convergence: a mathematical basis for Taylor's power law, 1/f noise and multifractality". Physical Review E. 84 (6) 066120. Bibcode:2011PhRvE..84f6120K. doi:10
Taylor's_law
Claimed earthquake prediction method
of statistical physics, i.e., detrended fluctuation analysis (DFA), multifractal DFA and wavelet transform revealed that SES are clearly distinguished
VAN_method
travel, tourism, insurance
MULTIFRACTAL SYSTEM
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travel, tourism, insurance