Perimeter-area method

Fractal Dimensions of Self-Affine Fractal Electrodes Determined by the Perimeter-Area Method (2nd Column), the Peak-Current Method (3rd Column), and the Triangulation... 

In their works,51"54 the self-similar fractal dimension dF>ss of the two-dimensional distribution of the pits was determined by the analysis of the digitized SEM images using the perimeter-area method. The value of dF>ss increased with increasing solution temperature,51 and it was inversely proportional to the pit shape parameter and the pit growth rate parameter.53 Keeping in mind that dr>ss is inversely proportional to the increment of the pit area density, these results can be accounted for in terms of the fact that the increment of the pit area density is more decelerated with rising solution temperature. 

On the other hand, for the microporous carbons with pore size distribution (PSD) with pore fractality, the pore fractal dimensions56,59,62 which represent the size distribution irregularity can be theoretically calculated by non-linear fitting of experimental adsorption isotherm with Dubinin-Astakhov (D-A) equation in consideration of PSD with pore fractality.143"149 The image analysis method54,151"153 has proven to be also effective for the estimation of the surface fractal dimension of the porous materials using perimeter-area method.154"159... 

The surface fractal dimension d uif of the porous materials can be determined from the TEM image by using perimeter-area method " " . If the scaling property of the porous materials is undoubtedly isotropic, the 3-D pore surface is simply related to the projection of the 3-D pore surface onto the 2-D surface. It is well known " that the areaH and the perimeter P of the self-similar lakes are related to their self-similar fractal dimension d by... 

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