EFFECT OF RESOLUTION ON THE APPARENT FRACTAL DIMENSION OF JAGGED FORCE-DISPLACEMENT RELATIONSHIPS AND OTHER IRREGULAR SIGNATURES

The apparent fractal dimension of computer simulated and experimental jagged force-displacement curves was determined using the Richardson a nd Kolmogorov algorithms. The curves analyzed had a wide range of ampl itudes and a variety of temporal resolutions. Despite the fact that cu rves whose points are uniformly spaced (i.e. recorded at a constant sa mpling rate) are not truly fractal, both algorithms could be successfu lly employed, as judged by the linearity of their corresponding plots. The apparent Kolmogorov dimension of the simulated curves was general ly smaller than that calculated from the Richardson plot. There was ho wever a good agreement between the two in the experimental curves. Bot h dimensions increased in unison with the curve fluctuation's amplitud e and resolution, indicating that the apparent fractal dimension is a consistent measure of jaggedness. In all the cases, the relationship b etween the apparent fractal dimension and the resolution could be desc ribed by simple empirical models which could be used interchangeably t o calculate the asymptotic apparent fractal dimension at infinite reso lution. Consequently, the record of real instruments with a finite res olution determined by technical and physical considerations could be u sed to estimate the 'ultimate jaggedness' of the force-displacement re lationship or any other digitized signature. The same method can be us ed, through interpolation, to estimate the curve's jaggedness at any d esired resolution for the sake of comparison. Without such an adjustme nt, the jaggedness of different curves when expressed in terms of thei r apparent dimension is meaningful only if they have been recorded at the same resolution. (C) 1997 Elsevier Science Limited.