## DESCRIPTION

r.surf.fractal creates a fractal surface of a given fractal dimension. It uses the spectral synthesis method. The module can create intermediate layers showing the build up of different spectral coefficients (see Saupe, pp.106-107 for an example of this).

Use this module to generate naturally looking synthetical elevation models (DEM).

## NOTE

This module requires the FFTW library for computing Discrete Fourier Transforms.

## EXAMPLE

    # D=2.0005
    g.region -dp
    r.surf.fractal out=dem_d2_0005 dim=2.0005
    r.info -r dem_d2_0005
    r.mapcalc "dem_d2_0005_final = 1.0 * dem_d2_0005 + abs(min(dem_d2_0005))"
    r.colors dem_d2_0005_final color=terrain
    r.slope.aspect dem_d2_0005_final aspect=dem_d2_0005_final_as

    # D=2.90
    r.surf.fractal out=dem_d2_90 dim=2.90
    r.info -r dem_d2_90
    r.mapcalc "dem_d2_90_final = 1.0 * dem_d2_90 + abs(min(dem_d2_90))"
    r.colors dem_d2_90_final color=terrain
    r.slope.aspect dem_d2_90_final aspect=dem_d2_90_final_as

    d.mon x0
    d.erase -f
    d.split.frame
    d.frame -s uno
    d.rast dem_d2_0005_final
    d.frame -s dos
    d.rast dem_d2_0005_final_as
    d.frame -s tres
    d.rast dem_d2_90_final
    d.frame -s cuatro
    d.rast dem_d2_90_final_as

Artificial DEMs created with fractals:
top: fractal dimension d=2.0005 (left: elevation map, right: aspect map)
top: fractal dimension d=2.90 (left: elevation map, right: aspect map)

## REFERENCE

Saupe, D. (1988) Algorithms for random fractals, in Barnsley M., Devaney R., Mandelbrot B., Peitgen, H-O., Saupe D., and Voss R. (1988) The Science of Fractal Images, Ch. 2, pp.71-136. London: Springer-Verlag.

## SEE ALSO

r.surf.contour, r.surf.idw, r.surf.gauss, r.surf.random, r.surf.idw2, v.surf.idw, v.surf.rst

## AUTHOR

Jo Wood, Midlands Regional Research Laboratory (ASSIST), University of Leicester

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