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Explicit Spectral Decimation for a Class of Self-Similar Fractals [PDF]
Abstract and Applied Analysis, 2013 The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very ...
Sergio A. Hernández +1 more
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Perceptual and Physiological Responses to Jackson Pollock's Fractals
Frontiers in Human Neuroscience, 2011 Fractals have been very successful in quantifying the visual complexity exhibited by many natural patterns, and have captured the imagination of scientists and artists alike.
Richard P Taylor
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On the construction of recurrent fractal interpolation functions using Geraghty contractions
Electronic Research Archive, 2023 The recurrent iterated function systems (RIFS) were first introduced by Barnsley and Demko and generalized the usual iterated function systems (IFS). This new method allowed the construction of more general sets, which do not have to exhibit the strict ...
Najmeddine Attia , Hajer Jebali
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Fractals: An Eclectic Survey, Part-I
Fractal and Fractional, 2022 Fractals are geometric shapes and patterns that may repeat their geometry at smaller or larger scales. It is well established that fractals can describe shapes and surfaces that cannot be represented by the classical Euclidean geometry.
Akhlaq Husain +3 more
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The mutual singularity of the relative multifractal measures
Nonautonomous Dynamical Systems, 2021 M. Das proved that the relative multifractal measures are mutually singular for the self-similar measures satisfying the significantly weaker open set condition. The aim of this paper is to show that these measures are mutually singular in a more general
Douzi Zied, Selmi Bilel
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Regular, Singular and Hypersingular Integrals over Fractal Contours
Mathematics, 2023 The paper is devoted to the approximate calculation of Riemann definite integrals, singular and hypersingular integrals over closed and open non-rectifiable curves and fractals.
Ilya Boykov +2 more
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ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
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Fractal Calculus on Fractal Interpolation Functions [PDF]
Fractal and Fractional, 2021 In this paper, fractal calculus, which is called Fα-calculus, is reviewed. Fractal calculus is implemented on fractal interpolation functions and Weierstrass functions, which may be non-differentiable and non-integrable in the sense of ordinary calculus.
Gowrisankar, Arulprakash +2 more
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Incomplete fractal showers and restoration of dimension [PDF]
EPJ Web of Conferences, 2019 The S ePaC and BC methods are used in the fractal analysis of mixed events containing incomplete fractals. The reconstruction of the event distribution by the dimension DF is studied.
Dedovich Tatiana, Tokarev Mikhail
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