Comparison of two fractal surface modeling methods

Abstract

Fractal surface modeling methods that provide effective and spatially continuous information over natural object surfaces and parts surfaces of precise manufacturing have become increasingly important in monitoring the features of the natural images and refinement of industrial manufacturing techniques. Numerous fractal methods have been generated during the last decades, but they differ substantially in terms of the form features and statistical properties. In this study, we simulated one-dimensional and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and analyzed the statistical characteristics and autocorrelation features of the two methods. The results showed that the simulations of the midpoint displacement method is not periodic, and its randomness is more prominent, suitable for the simulation of aperiodic alpine surface. While the simulations of the Weierstrass-Mandelbrot fractal function method has strong periodicity, the simulated surface is relatively stable, suitable for the simulation of uniform fluctuant surface.