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NAME - Creates a fractal surface of a given fractal dimension.


raster, surface, fractal

SYNOPSIS --help output=name [dimension=float] [number=integer] [--overwrite] [--help] [--verbose] [--quiet] [--ui]


Allow output files to overwrite existing files
Print usage summary
Verbose module output
Quiet module output
Force launching GUI dialog


output=name [required]
Name for output raster map
Fractal dimension of surface (2 < D < 3)
Default: 2.05
Number of intermediate images to produce
Default: 0

Table of contents

DESCRIPTION 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).


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


Generate surface using fractals in selected region, set color table and display with shade.
g.region -p raster=elevation 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
Artificial surface created with fractals
Compare results when using different fractal dimensions:
# D=2.0005
g.region -dp out=dem_d2_0005 dim=2.0005 -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 out=dem_d2_90 dim=2.90 -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
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)


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.



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


Available at: source code (history)

Latest change: Monday Feb 27 13:45:25 2023 in commit: a82501dc85294207e8e58437c3ec7f1056465ed4

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