## 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).

This module generates naturally looking synthetical elevation models (DEM).

## NOTE

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

## EXAMPLE

Generate surface using fractals in selected region, set color table and display with shade.

    g.region -p raster=elevation

    r.surf.fractal output=fractals

    r.colors map=fractals color=byr
    r.relief input=fractals output=fractals_shade

    d.mon wx0
    d.shade shade=fractals_shade color=fractals b=50

Artificial surface created with fractals
Compare results when using different fractal dimensions:

    # 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

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)

## REFERENCES

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, v.surf.idw, v.surf.rst

## AUTHOR

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

Last changed: $Date: 2015-07-20 10:45:41 +0200 (Mon, 20 Jul 2015) $