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Abstract <p>The paper proposes a numerical algorithm for synthesizing a random relief surface of a given fractal dimension using the fractional Riemann–Liouville integro-differential operator. A two-dimensional field of Gaussian white noise is used as the initial random field. The Fourier transform of the sought field is obtained by applying a fractional order operator to the two-dimensional spectrum of white noise. The random surface relief is obtained by the inverse two-dimensional fast Fourier transform. The work uses the mutual relationships of the fractal dimension <i>D</i> of the relief surface with the order ν of fractional integration and the Hurst exponent, as well as the power exponent α of the spectral density decay.</p>

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Algorithm for Synthesis of Relief Surface with Given Fractal Dimension Based on Fractional Dimension Operators

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Yu. K. Evdokimov,
  • L. Yu. Fadeeva,
  • D. V. Shakhturin

摘要

Abstract

The paper proposes a numerical algorithm for synthesizing a random relief surface of a given fractal dimension using the fractional Riemann–Liouville integro-differential operator. A two-dimensional field of Gaussian white noise is used as the initial random field. The Fourier transform of the sought field is obtained by applying a fractional order operator to the two-dimensional spectrum of white noise. The random surface relief is obtained by the inverse two-dimensional fast Fourier transform. The work uses the mutual relationships of the fractal dimension D of the relief surface with the order ν of fractional integration and the Hurst exponent, as well as the power exponent α of the spectral density decay.