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Fig. 10.7 Relationships between perimeters and anomalous areas using contours with different
values greater than thresholds for (a) Au, (c) Cu and (e) As. Log-log plots on right side show
relationships between estimated lengths of the perimeters of the anomalous areas for (b) Au,
(d) Cu and (f) As with variable yardstick. D 1 and D 2 are for textural and structural fractal
dimensions, respectively. All solid lines were obtained by least squares (Source: Cheng
et al. 1994 , Fig. 8)
From any two of the three fractal dimensions ( D L for perimeter; D AL for
perimeter-area relation; and D A for area), the third one can be obtained by means
of the relation D A ¼
2D L / D AL . Theoretically, D A cannot be greater than 2. In most
applications of the perimeter-area method, it is set equal to 2 so that D L ¼
D AL . The
latter relation holds approximately true for Cu and As ( D AL ¼
1.16 and D A ¼
1.96
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