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NAME

r.surf.fractal - Creates a fractal surface of a given fractal dimension.

KEYWORDS

raster

SYNOPSIS

r.surf.fractal
r.surf.fractal help
r.surf.fractal output=string [dimension=float] [number=integer] [--verbose] [--quiet]

Parameters:

output=string
Name for output raster map
dimension=float
Fractal dimension of surface (2 < D < 3)
Default: 2.05
number=integer
Number of intermediate images to produce
Default: 0

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
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

Last changed: $Date: 2012-11-26 16:18:53 -0800 (Mon, 26 Nov 2012) $


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