Resampling a raster for use in a fractal analysis?

Discussion created by dhyman on Feb 21, 2012
So for a project for a class, I have decided to attempt to determine the fractal dimension of a small ravine on Hamilton College's property: The Root Glen.
Hypothetically, this surface should have a fractal dimension between 2 and 3 as it is a highly irregular surface.  To compute it, I will need to follow standard box counting methodology, except, since we are talking a grid in 3-space, I will need to count cubes. 
I have a LiDAR DEM for this area with a pixel resolution of 1m.
The easiest way to do this it seems would be to resample the DEM several times to get several DEMs with pixel sizes that are exponentially larger than the previous one ie: I want rasters with pixel size 2m, 4m, 8m, 16m, 32m, 64m, 128m, 256m, etc.  

I have never done a resampling so this is new to me.
Does anyone know which resampling technique is most appropriate for this analysis?  Does it matter?

If you need any more info please say so.

Thanks so much!