Contour lines of the discrete scale-invariant rough surfaces

2010/11/30 by M. Ghasemi Nezhadhaghighi, M. A. Rajabpour · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #Mathematical Dynamics and Fractals #cond-mat.other #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.83.021122

published as Phys. Rev. E 83, 021122 (2011) · 9 Pages, 12 figures

openalex publication_date 2011/02/28 · arxiv created 2011/03/08 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the fractal properties of the two-dimensional (2D) discrete scale-invariant (DSI) rough surfaces. The contour lines of these rough surfaces show clear DSI. In the appropriate limit the DSI surfaces converge to the scale-invariant rough surfaces. The fractal properties of the 2D DSI rough surfaces apart from possessing the discrete scale-invariance property follow the properties of the contour lines of the corresponding scale-invariant rough surfaces. We check this hypothesis by calculating numerous fractal exponents of the contour lines by using numerical calculations. Apart from calculating the known scaling exponents, some other new fractal exponents are also calculated.

Citations

• Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
• Fractal Geometry: Mathematical Foundations and Applications.
• The Fractal Geometry of Nature
• Discrete hierarchical organization of social group sizes
• Numerical recipes: the art of scientific computing

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