---
name: "r.surf.fractal"
section: "1grass"
platform: "linux"
package: "grass-doc"
version: "8.4.1-1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/r.surf.fractal"
---

# r.surf.fractal(1grass)

Creates a fractal surface of a given fractal dimension.

## 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: Monday Feb 24 17:50:54 2025

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