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On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм. / Pustovoit, P. M. ; Yashina, E. G. ; Pshenichnyi, K. A. ; Grigoriev, S. V. .

In: Journal of Surface Investigation X-Ray, Synchrotron and Neutron Techniques, Vol. 14, 2020, p. 1232-1239.

Research output: Contribution to journal › Article › peer-review

Harvard

Pustovoit, PM, Yashina, EG, Pshenichnyi, KA & Grigoriev, SV 2020, 'On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм', Journal of Surface Investigation X-Ray, Synchrotron and Neutron Techniques, vol. 14, pp. 1232-1239.

APA

Pustovoit, P. M., Yashina, E. G., Pshenichnyi, K. A., & Grigoriev, S. V. (2020). On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм. Journal of Surface Investigation X-Ray, Synchrotron and Neutron Techniques, 14, 1232-1239.

Vancouver

Pustovoit PM, Yashina EG, Pshenichnyi KA, Grigoriev SV. On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм. Journal of Surface Investigation X-Ray, Synchrotron and Neutron Techniques. 2020;14:1232-1239.

Author

Pustovoit, P. M. ; Yashina, E. G. ; Pshenichnyi, K. A. ; Grigoriev, S. V. . / On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм. In: Journal of Surface Investigation X-Ray, Synchrotron and Neutron Techniques. 2020 ; Vol. 14. pp. 1232-1239.

BibTeX

@article{725dead94fee4781995c6b4e13c4f331,
title = "On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм",
abstract = "The method of numerical Fourier analysis is used to investigate the fractal properties of 2D objects with micrometer–centimeter sizes. This numerical method simulates the small-angle light scattering experiment. Different geometric 2D-regular fractals, such as the Sierpinski carpet, Sierpinski triangle, Koch snowflake, and Vishek snowflake, are studied. We can divide 2D fractals, by analogy with 3D fractals, into “plane” and “boundary” fractals with fractal dimensions lying in the intervals from 1 to 2 and from 2 to 3, respectively. For an object with a smooth boundary, i.e., a circle, the model small-angle scattering curve decreases according to the power law q–3, where q is the momentum transferred.",
keywords = "Fractals, Fourier analysis, small-angle light scattering, 2D space",
author = "Pustovoit, {P. M.} and Yashina, {E. G.} and Pshenichnyi, {K. A.} and Grigoriev, {S. V.}",
note = "Pustovoit, P.M., Yashina, E.G., Pshenichnyi, K.A. et al. On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space. J. Synch. Investig. 14, 1232–1239 (2020). https://doi.org/10.1134/S1027451020060415",
year = "2020",
language = "English",
volume = "14",
pages = "1232--1239",
journal = "ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ",
issn = "1027-4510",
publisher = "МАИК {"}Наука/Интерпериодика{"}",

}

RIS

TY - JOUR

T1 - On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Spaceм

AU - Pustovoit, P. M.

AU - Yashina, E. G.

AU - Pshenichnyi, K. A.

AU - Grigoriev, S. V.

N1 - Pustovoit, P.M., Yashina, E.G., Pshenichnyi, K.A. et al. On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space. J. Synch. Investig. 14, 1232–1239 (2020). https://doi.org/10.1134/S1027451020060415

PY - 2020

Y1 - 2020

N2 - The method of numerical Fourier analysis is used to investigate the fractal properties of 2D objects with micrometer–centimeter sizes. This numerical method simulates the small-angle light scattering experiment. Different geometric 2D-regular fractals, such as the Sierpinski carpet, Sierpinski triangle, Koch snowflake, and Vishek snowflake, are studied. We can divide 2D fractals, by analogy with 3D fractals, into “plane” and “boundary” fractals with fractal dimensions lying in the intervals from 1 to 2 and from 2 to 3, respectively. For an object with a smooth boundary, i.e., a circle, the model small-angle scattering curve decreases according to the power law q–3, where q is the momentum transferred.

AB - The method of numerical Fourier analysis is used to investigate the fractal properties of 2D objects with micrometer–centimeter sizes. This numerical method simulates the small-angle light scattering experiment. Different geometric 2D-regular fractals, such as the Sierpinski carpet, Sierpinski triangle, Koch snowflake, and Vishek snowflake, are studied. We can divide 2D fractals, by analogy with 3D fractals, into “plane” and “boundary” fractals with fractal dimensions lying in the intervals from 1 to 2 and from 2 to 3, respectively. For an object with a smooth boundary, i.e., a circle, the model small-angle scattering curve decreases according to the power law q–3, where q is the momentum transferred.

KW - Fractals

KW - Fourier analysis

KW - small-angle light scattering

KW - 2D space

UR - https://link.springer.com/article/10.1134/S1027451020060415

M3 - Article

VL - 14

SP - 1232

EP - 1239

JO - ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ

JF - ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ

SN - 1027-4510

ER -

ID: 85656433