A new fractal model for anisotropic surfaces

A new fractal-based functional model for anisotropic rough surfaces is used to devise and test two methods for the approximate computation of the fractal dimension of surfaces, and as an instrument for simulating the topography of engineering surfaces. A certain type of statistical self-affinity is proved for the model, and this property serves as the basis for one of the methods of approximating fractal dimension. The other technique for calculating fractal dimension is derived from a Hölder type condition satisfied by the model. Algorithms for implementing both of these new schemes for computing approximate values of fractal dimension are developed and compared with standard procedures. Both the functional model and its corresponding modified Gaussian height distribution are used for simulating fractal surfaces and several examples are adduced that strongly resemble some common anisotropic engineering surfaces.