Calc Fractal Dimensions

Description

This submodel calculates the fractal dimensions per map category and r2 from regressing patch areas on their edges.

Inputs

Name	Type	Description
Landscape	Categorical Map	Map of classes or categories output from an execution pipeline.

Outputs

Name	Type	Description
Fractal Dimensions	Table	Table

Group

Landscape Metrics

Notes

The fractal dimension is an index used to assess the complexity of the geometry of the landscape patches, which is evaluated using the area-perimeter relationship (LOVEJOY, 1982; MAMDELBROT, 1983). P ~ AD / 2 The total fractal dimension (D) of a landscape can be estimated by regressing the log (P) in the log (A) and evaluating D, as twice the slope of the regression line (LOVEJOY, 1982), where P is the perimeter and A the area of each patch. In a landscape, composed of simple geometric shapes such as rectangles and squares, the fractal dimension will be small, approaching 1.0. In a landscape with many patches with convoluted and complex shapes, the perimeter begins to fill in the plane and P ~ A with D -> 2. (KRUMMEL et al. 1987). Therefore, substantial changes in the shape of landscape patches must reflect changes in the fractal dimension.

LOVEJOY, S. Area-perimeter relation for rain and cloud areas. Science, v.216, p.185-87, 1982. MANDELBROT, B. The fractal geometry of nature. New York, W.H. Freeman, 1983. RIPPLE, W; BRADSHAW, G.A.; SPIES, T.A. Measuring forest landscape patterns in Cascade range of Oregon, U.S.A. Biological Conservation, v. 57, p. 73-88, 1991.