Contour lines of the discrete scale invariant rough surfaces

TL;DR

This paper investigates the fractal properties of 2D discrete scale invariant rough surfaces and their contour lines, revealing both known and new fractal exponents through numerical analysis.

Contribution

It introduces a detailed numerical study of the fractal properties of 2D DSI rough surfaces and their contour lines, including the calculation of new fractal exponents.

Findings

Contour lines exhibit clear discrete scale invariance

Fractal exponents of contour lines are consistent with scale invariant surfaces

New fractal exponents for contour lines are identified

Abstract

We study the fractal properties of the 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.