Results 11 to 20 of about 538,685 (145)
A Study on the Curves of Scaling Behavior of Fractal Cities [PDF]
arXiv, 2021 The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. This paper is devoted to researching a set of basic problems of the scaling behavior curves in urban studies by using mathematical reasoning and empirical
arxiv
Fractal Properties and Characterizations [PDF]
arXiv, 2020 There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic transformation-periodic properties. The properties that remain unchanged under the structural multi scale transformation-
arxiv
Closed Contour Fractal Dimension Estimation by the Fourier Transform [PDF]
Chaos, Solitons and Fractals, Volume 44, Issue 10, October 2011,
Pages 851--861, 2012 This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform.
arxiv +1 more source
Fractal Dimension and Retinal Pathology: A Meta-analysis [PDF]
arXiv, 2021 Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current scientific evidence regarding the relationship between fractal dimension and retinal pathology and thus assess the ...
arxiv
Deterministic fractals: extracting additional information from small-angle scattering data [PDF]
Phis. Rev. E 84, 036203 (2011), 2011 The small-angle scattering curves of deterministic mass fractals are studied and analyzed in the momentum space. In the fractal region, the curve I(q)q^D is found to be log-periodic with a good accuracy, and the period is equal to the scaling factor of the fractal.
arxiv +1 more source
Small-angle scattering from the Cantor surface fractal on the plane and the Koch snowflake [PDF]
Phys. Chem. Chem. Phys. 19, 2261-2268 (2017), 2016 The small-angle scattering (SAS) from the Cantor surface fractal on the plane and Koch snowflake is considered. We develop the construction algorithm for the Koch snowflake, which makes possible the recurrence relation for the scattering amplitude.
arxiv +1 more source
On Bivariate Fractal Interpolation for Countable Data and Associated Nonlinear Fractal Operator [PDF]
arXiv, 2020 We provide a general framework to construct fractal interpolation surfaces (FISs) for a prescribed countably infinite data set on a rectangular grid. Using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function.
arxiv
The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data [PDF]
, 2019 Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS data: the fractal dimension, and the lower and upper limits of the fractal range.
arxiv +1 more source
Local Fractal Interpolation On Unbounded Domains [PDF]
arXiv, 2015 We define fractal interpolation on unbounded domains for a certain class of topological spaces and construct local fractal functions. In addition, we derive some properties of these local fractal functions, consider their tensor products, and give conditions for local fractal functions on unbounded domains to be elements of Bochner-Lebesgue spaces.
arxiv
The dynamics of the angular and radial density correlation scaling exponents in fractal to non-fractal morphodynamics [PDF]
arXiv, 2018 Fractal/non-fractal morphological transitions allow for the systematic study of the physics behind fractal morphogenesis in nature. In these systems, the fractal dimension is considered a non-thermal order parameter, commonly and equivalently computed from the scaling of the two-point radial- or angular-density correlations.
arxiv