# Box Counting Method

Agustin Lobo alobo at ija.csic.es
Tue Sep 7 05:03:50 EDT 1999

```I did something similar to study the sprectral response of
a high reolution sensor for each cell of a coarse resolution
sensor.

I just made an script (I think that I actually contributed to Markus N.)
that produces a numbered image, i.e., like r.clump but each pixel has
an individual integer value.

You could run a similar process for each given resolution and create a
suite of rasters (numbered.1, numbered.2, numbered.3 ...) that would
match as:

numbered.1:
1  2  3  4  5  6  7  8  9
10 11 12 13 14 15 16 17 18
19 20 21 22 23 24 25 26 27
....

numbered.2

1  1  2  2  3  3  4  4  5  5
1  1  2  2  3  3  4  4  5  5
6  6  7  7  8  8  9  9 10 10
....

Then you select the resolution of your fracture maps
(0: no fracture; 1: fracture; if you have different types
of fractures, just add more categories) and use
r.stats with each numbered.x map and your fracture map,
to obtain, for each numbered.x, a file with 2 columns:

numbered.1  fracture
1             0
2             0
3             1
4             1
5             6

etc.

Export to your stats program and count the number of "1"
for each numbered.x. From this series you can calculate
the fractal dimension.

It might seem complicated, but it's not.

Agus

****NOTE NEW PHONE NUMBER*****
Dr. Agustin Lobo
Instituto de Ciencias de la Tierra (CSIC)
Lluis Sole Sabaris s/n
08028 Barcelona SPAIN
tel 34 93409 5410
fax 34 93411 0012
alobo at ija.csic.es
http://pangea.ija.csic.es/alobo

On Mon, 6 Sep 1999, Michael Schulz wrote:

> Dear List!
>
> Together with a diploma student, we are trying to use GRASS to
> perform calculations with the Box Counting Method. The box method is used
> here to measure the fractal dimension of the spatial and scaling
> distribution of fractures.
>
> A sequence of grids, each with a different cell size is placed over maps
> of fracture traces and the number of cells intersected by the fractures
> is counted.
>
> We used scanned maps of the fracture traces, imported them into GRASS and
> tried to run r.reports on the same mapset with varying resolutions. this
> did not work. We thought about using r.mapcalc to do some kind of
> neighborhood analysis, but the problem seems to be the varying cell sizes.
>
> Is it possible to use r.mapcalc within one location but different
> resolutions of raster maps ? Could it be done with several locations (
> r.mapcalc takes input from location 1 with res 1 and analyzes this grid
> with neighborhood-sizes of location 2 with res 2 and writes the result to
> location 2 ) ?
>
> Any comments or ideas would be appreciated !
>
> Cheers, Michael
>
>
> ==============================================================
> Michael Schulz
>
> Christoph-Mang-Str.5       Geologisches Institut
> 79100 Freiburg             Universitaet Freiburg
>                            Albertstr. 23b
>                            79104 Freiburg
>
>
>

```