## NAME

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

## KEYWORDS

raster, surface, fractal

## SYNOPSIS

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

### Flags:

--overwrite
  Allow output files to overwrite existing files
--help
  Print usage summary
--verbose
  Verbose module output
--quiet
  Quiet module output
--ui
  Force launching GUI dialog

### Parameters:

output=name [required]
  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).

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

## SOURCE CODE

Available at: r.surf.fractal source code (history)

Accessed: Thursday Oct 30 22:17:22 2025

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