Results 11 to 20 of about 9,626 (263)
Angular projections of fractal sets [PDF]
Europhysics Letters (EPL), 1997 We discuss various questions which arise when one considers the central projection of three dimensional fractal sets (galaxy catalogs) onto the celestial globe. The issues are related to how fractal such projections look. First we show that the lacunarity in the projection can be arbitrarily small.
Durrer R +7 more
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FRACTAL DIMENSIONS OF k-AUTOMATIC SETS
The Journal of Symbolic Logic, 2023 AbstractThis paper seeks to build on the extensive connections that have arisen between automata theory, combinatorics on words, fractal geometry, and model theory. Results in this paper establish a characterization for the behavior of the fractal geometry of “k-automatic” sets, subsets of $[0,1]^d$ that are recognized by Büchi automata.
Alexi Block Gorman +1 more
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Set-Valued $$\alpha $$-Fractal Functions
Constructive Approximation, 2023 In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal functions. Further, we estimate the perturbation error between the given continuous function and its $\alpha$-fractal ...
Pandey, Megha +2 more
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Fractals, 2009 The formulation of a new analysis on a zero measure Cantor set C(⊂I = [0,1]) is presented. A non-Archimedean absolute value is introduced in C exploiting the concept of relative infinitesimals and a scale invariant ultrametric valuation of the form log ε-1 (ε/x) for a given scale ε > 0 and infinitesimals 0 < x < ε, x ∈ I\C.
Raut, Santanu, Datta, Dhurjati Prasad
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From Fractal Geometry to Statistical Fractal
Recoletos Multidisciplinary Research Journal, 2013 The development from fractal geometry to fractal statistics was established in this paper. Interesting features such as self similarity, scale invariance, and the spacefilling property of objects (fractal dimension) of fractal geometry provided an ...
Roberto N. Padua, Mark S. Borres
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Fractal Curves on Banach Algebras
Fractal and Fractional, 2022 Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as ...
María A. Navascués
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Analogues to Lie Method and Noether’s Theorem in Fractal Calculus
Fractal and Fractional, 2019 In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution.
Alireza Khalili Golmankhaneh +1 more
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Fractal and Fractional, 2019 In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving
Alireza Khalili Golmankhaneh +1 more
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Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions
Mathematics, 2022 In the present paper, we try to estimate the fractal dimensions of the linear combination of continuous functions with different fractal dimensions.
Binyan Yu, Yongshun Liang
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Classifying Cantor sets by their fractal dimensions [PDF]
Proceedings of the American Mathematical Society, 2010 In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h h
Cabrelli, Carlos +2 more
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