the substrate surface intended to be in the range of contact with the traction surface this set of data is then used to develop a relationship between the length of the variations in surface with their frequency of occurrence such that in some embodiments of the invention the relative number of elements in each size group in the tread design pattern corresponds to the relative number of elements in a corresponding size group in the substrate intended for contact with the traction surface see literature references 1 u2013 3 cited below another way to measure the topography of the surface is described in u s pat no 5 859 919 the disclosure of which is incorporated herein by reference the data is then represented in a log log power spectrum the power spectrum is then subjected to a logarithmic transformation followed by a waveform transformation typically a fourier transform thus providing the frequency of occurrence of each class of length on a log log scale the fourier transform procedure reduces a complex measured u2018 waveform u2019 into a sinusoidal equation that simulates the characteristics of the measured waveform the measured waveform is a measurement of the variation in the height or z dimension with distance along either the width x or depth y dimensions both would give equivalent results a natural consequence of the analytical technique is that it results in a sinusoidal function with fractal characteristics in both the x y and z dimensions the characteristics of these distributions of surface amplitudes relative to the linear dimensions are then simulated by a surface of the tread having fractal characteristics the substrate surface profile is typically an irregular waveform with the surface represented as a function of height.