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

NAME  KEYWORDS  SYNOPSIS  Flags:  Parameters:  DESCRIPTION  NOTE  EXAMPLE  REFERENCES  SEE ALSO  AUTHOR  SOURCE CODE 

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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)

Latest change: Friday Oct 25 16:16:09 2024 in commit: 4ea983fff87951516b6e4578a0527e3b10f04643

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