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

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

In: Journal of Surface Investigation, Vol. 14, No. 6, 11.2020, p. 1232-1239.

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

BibTeX

@article{548636a32ef84a4e9d196b92c83bf5ac,

title = "On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space",

abstract = "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 = "2D space, : fractals, Fourier analysis, small-angle light scattering",

author = "Pustovoit, {P. M.} and Yashina, {E. G.} and Pshenichnyi, {K. A.} and Grigoriev, {S. V.}",

note = "Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd.",

year = "2020",

month = nov,

doi = "10.1134/S1027451020060415",

language = "English",

volume = "14",

pages = "1232--1239",

journal = "ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ",

issn = "1027-4510",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "6",

}

RIS

TY - JOUR

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

AU - Pustovoit, P. M.

AU - Yashina, E. G.

AU - Pshenichnyi, K. A.

AU - Grigoriev, S. V.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - 2D space

KW - : fractals

KW - Fourier analysis

KW - small-angle light scattering

UR - http://www.scopus.com/inward/record.url?scp=85098287293&partnerID=8YFLogxK

U2 - 10.1134/S1027451020060415

DO - 10.1134/S1027451020060415

M3 - Article

AN - SCOPUS:85098287293

VL - 14

SP - 1232

EP - 1239

JO - ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ

JF - ПОВЕРХНОСТЬ. РЕНТГЕНОВСКИЕ, СИНХРОТРОННЫЕ И НЕЙТРОННЫЕ ИССЛЕДОВАНИЯ

SN - 1027-4510

IS - 6

ER -

ID: 86426707