Fractal dimension

This tool can be used to calculate the fractal dimension (Mcgarigal et al. 2002) for polygons. It will work for either raster or vector input files. If a raster file is input, the grid should contain polygons with unique identifiers. Raster input files also require the name of the output raster file (where the fractal dimension will be assigned to each feature in the input file), the specified option of outputting text, and whether or not zero values should be treated as background values. If a vector shapefile is specified as the input file, the only required input is the name of the file. The fractal dimension values calculated for each vector polygon feature will be placed in the accompanying database file (.dbf) as a fractal dimension field (FRACTAL_D). The resulting database file will be automatically displayed after the tool has completed.

The fractal dimension (F) is:

F = 2lnP / lnA

Where P is the polygon's perimeter, A is its area, and ln is the natural logarithm. For raster-based perimeter estimation, the tool uses the accurate, anti-aliasing algorithm of Prashker (2009).

Theoretically, F approaches 1 for shapes with very simple boundaries, such as circles, and approaches 2 for shapes with highly convoluted, plane-filling boundaries. In practice, however, F tends to display a very restricted range of values for a wide variety of shapes. For many applications, the Shape Complexity Index is better suited to expressing polygon irregularity and overall shape complexity.

See Also:



The following is an example of a Python script that uses this tool:

wd = pluginHost.getWorkingDirectory()
inputFile = wd + "polygons.shp" # vector input
outputFile = "" # ignored for vector input
textOutput = "false" # also ignored
zerosAreBackground = "false" # also ignored
args = [inputFile, outputFile, textOutput, zerosAreBackground]
pluginHost.runPlugin("FractalDimension", args, False)

This is a Groovy script also using this tool:

def wd = pluginHost.getWorkingDirectory()
def inputFile = wd + "polygons.dep" // raster input
def outputFile = wd + "output.dep"
def textOutput = "true"
def zerosAreBackground = "true"
String[] args = [inputFile, outputFile, textOutput, zerosAreBackground]
pluginHost.runPlugin("FractalDimension", args, False)