Again, this quantity forms a straight curve on a log-log plot with the 
inclination a-1. 
The constant a, may be related to the mathematical concept of dimension 
D. While the well known topological dimension may only assume integer 
values (D = 1 for a Straight line and D = 2 for a plane), other dimen- 
sion concepts, like the Haussdorf dimension, can describe the transi- 
tion of a line to a plane-filling curve (Peano curve; cf. figure 4), 
by allowing also non-integer values for D, 1 « D <2. We may thus use 
D, directly as a measure of the roughness of à curve. 
    
   
   
   
   
   
    
   
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Figure 4. The Peano curve: A plane-filling curve of dimension 2 
(Peano, 1890). 
Our example of Figure 3, has a Haussdorf dimension D - log 4/log 3 
~ 1.2618. According to Berry (Berry, 1980), it holds in general that 
Let us now illustrate the above ideas in a terrain located south-east 
of Oslo, in Norway. 
Seven profiles were measured photogrammetrically in the area, using 
aerial photos at scale 1:15.000 and a point spacing of 15 m. An example 
of one profile of 500 points is shown in figure 5. 
The spectrum and variogram of this profile, and average spectra and 
variogram for al] profiles, were derived, cf. figure 6 and 7. 
7:262.