FRACTAL ANALYSIS OF TOPOGRAPHIC DATA BY THE PATCHWORK METHOD

A new, fractal-based method is described for analyzing topographic data sets from engineering surfaces. The method, which we call the patchwork method, is analogous to the well-known coastline method of fractal analysis, which uses line segments to estimate the length of a jagged line as a function of the segment length. The patchwork method uses triangular patches to estimate surface area as a function of patch area. The patch area can be interpreted either as the scale of observation, or as the scale of interaction for morphologically dependent phenomena. Using the patchwork method one can identify the crossover, or threshold, in scale which separates the relatively large scales, where the surface is smooth and best described by Euclidean geometry, from those smaller scales where the surface is rough and best described by fractal geometry. One also obtains a parameter that characterizes the complexity, or intricacy, of the topography, below the threshold. These parameters, combined with the concept of characterizing topographically dependent phenomena by their scales of interaction, appear to have good potential for elucidating mechanisms of surface interactions. These parameters can also serve as a tool for supporting design processes for surfaces and for their manufacture.