====== 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 Type | Categorical Map]] | Map of classes or categories output from an execution pipeline. |

===== Outputs =====

^ Name ^ Type                                       ^ Description                  ^
| Fractal Dimensions  | [[Table | 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.