** r.mandelbrot** - A Perl-script to compute the
mandelbrot set within a XY-location.

**r.mandelbrot**

**r.mandelbrot **map=result [-2rp] [iterations=255] [cols=3000] [rows=3000]

The *r.mandelbrot* script computes the
Mandelbrot set.

If no parameters are provided, *r.mandelbrot* calculates the
generic Mandelbrot set using a minimum number of iterations (15)
for a default region displaying the whole mandelbrot-set.

The iterations-parameter defines the number of iterations for the
current mandelbrot (sub-)set.

The cols- and rows-parameters define the resolution to be used.

Without the *raster_name*-parameter the script defaults to
write its results to the raster map "mandelbrot".

The script can be used in several runs to interactively zoom into the
mandelbrot set. Once an image has been calculated, use d.zoom to zoom in on
interesting features. The regions' setting will be kept for the next run of
r.mandelbrot. Alternatively, the -r flag can be used to return to the
original settings.
Previous content will be overwritten.

*-r*- Reset to default region and number of iterations.

*-p*- Print the current settings and exit.

*-2*- Double the number of iterations.

*map*- Name of the raster to be used. If no name is provided, the default is 'mandelbrot'.
*iterations*- Number of iterations to be calculated for the current region.
*cols*- Number of columns.
*rows*- Number of rows.

The script can only be executed in a xy-location.

A GRASS monitor is crucial to judge the computations progress since
this is an excercise in visual mathematics and requires the use of d.zoom.

Navigating within the Mandelbrot-set tends to be an iterative
process by itself. The following procedure is recommended:

(1) Initialize a session by using *r.mandelbrot* without any
parameters. The Mandelbrot set will be displayed in sufficent
resolution in the monitor.

(2) Use *d.zoom *to choose* *an area of interest.

(3) Now re-run *r.mandelbrot*, but provide the iteration
parameter and possibly also a specific name for the raster file.

Repeat steps (2) and (3) as necessary.

It is always possible to revisit previous mandelbrot-regions,
as the ** raster_name**-parameter stores both the raster
map and its region.

So to re-use the

The NVIZ tool is quite handy to visualize the resulting
maps of the Mandelbrot-set.

The described script is an excercise in things GRASS was not
originally ment for. So do not expect it to match the speed of
C code.

Publications by Benoit Mandelbrot, Peitgen et al., etc. etc.

Peter Löwe

*Last changed: $Date: 2007/07/16 05:45:34 $*