A Class of Rough Surfaces and Their Fractal Dimensions

Based on a function represented by the Cantor series and a binary fraction of real numbers, a class of rough surfaces is constructed in this paper. The method used completely differs from those previously developed. In addition, the fractal dimensions, as an indicator of the roughness of such surfaces, are also investigated. The calculating formulas for the box-counting and packing dimensions are derived, and the upper and lower bounds of the Hausdorff dimension are estimated.