AbstractAnalysing terrain profiles of fields, roads, and other terrains, it was determined that terrain profiles are random and non-periodical. Mandelbrot has defined non-scaling, self-similar figures as fractals, and many investigators have tried to characterize natural forms and structures using fractal geometry. The work here investigates whether terrain profiles can be defined as fractals. Fractal dimensions of profiles were calculated. These were compared with a locus of Brownian motion further to investigate characteristics of terrain profiles. Fractals are defined to be self-similar and irregular. Measuring and analysing terrain profiles, it was established that the statistical characteristics of any part of a terrain profile are similar and that the statistical characteristics of profiles of any kind of terrain are similar irrespective of roughness. This means that terrain profiles are self-similar, and irregular. From these results, it was determined that terrain profiles are fractals. The fractal dimensions were calculated with a coarse-graining method and by Power Spectral Densities (PSD), and fractal dimensions by Scaling were between 1.1 and 1.8 and by PSD between 1.3 and 1.5. Using the locus of Brownian motion, fractal dimensions were 1.5 or slightly larger than those of the terrain profiles. Fractal dimensions for the locus of smoothed Brownian motion were nearly equal to terrain profiles. Therefore terrain profiles could be artificially generated from the locus of smoothed Brownian motion. It appears that terrain roughness is formed by random and non-periodical force.


    Access

    Check access

    Check availability in my library

    Order at Subito €


    Export, share and cite



    Title :

    Fractal dimensions of terrain profiles


    Contributors:

    Published in:

    Journal of Terramechanics ; 28 , 2-3 ; 155-165


    Publication date :

    1991-01-01


    Size :

    11 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English



    Fractal dimensions of terrain profiles

    Ohmiya,K. / Hokkaido Univ.,Fac.of Agriculture,JP | Automotive engineering | 1990


    Calculating fractal parameters from low-resolution terrain profiles

    Goodin, Christopher / Stevens, Maria / Villafañe Rosa, Francisco J. et al. | Elsevier | 2017


    Fractal terrain generation for vehicle simulation

    Dawkins,J.J. / Bevly,D.M. / Jackson,R.L. et al. | Automotive engineering | 2012


    Fractal terrain generation for vehicle simulation

    Dawkins, Jeremy J. | Online Contents | 2012


    Evaluation of fractal dimension of soft terrain surface

    Jiang, Chunxia | Online Contents | 2017