(P9) Fractal Dimension Index 


p_{ij} = perimeter (m) of patch ij. a_{ij} = area (m^{2}) of patch ij. 

Description 
FRAC equals 2 times the logarithm of patch perimeter (m) divided by the logarithm of patch area (m^{2}); the perimeter is adjusted to correct for the raster bias in perimeter. 

Units 
None 

Range 
1 ≤ FRAC ≤ 2 A fractal dimension greater than 1 for a 2dimensional patch indicates a departure from Euclidean geometry (i.e., an increase in shape complexity). FRAC approaches 1 for shapes with very simple perimeters such as squares, and approaches 2 for shapes with highly convoluted, planefilling perimeters. 

Comments 
Fractal dimension index is appealing because it reflects shape complexity across a range of spatial scales (patch sizes). Thus, like the shape index (SHAPE), it overcomes one of the major limitations of the straight perimeterarea ratio as a measure of shape complexity. 