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.