# lsm_p_frac: FRAC (patch level) In r-spatialecology/landscapemetrics: Landscape Metrics for Categorical Map Patterns

## Description

Fractal dimension index (Shape metric)

## Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 lsm_p_frac(landscape, directions) ## S3 method for class 'RasterLayer' lsm_p_frac(landscape, directions = 8) ## S3 method for class 'RasterStack' lsm_p_frac(landscape, directions = 8) ## S3 method for class 'RasterBrick' lsm_p_frac(landscape, directions = 8) ## S3 method for class 'stars' lsm_p_frac(landscape, directions = 8) ## S3 method for class 'list' lsm_p_frac(landscape, directions = 8) 

## Arguments

 landscape Raster* Layer, Stack, Brick or a list of rasterLayers. directions The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).

## Details

FRAC = \frac{2 * \ln * (0.25 * p_{ij})} {\ln a_{ij}}

where p_{ij} is the perimeter in meters and a_{ij} is the area in square meters

FRAC is a 'Shape metric'. The index is based on the patch perimeter and the patch area and describes the patch complexity. Because it is standardized, it is scale independent, meaning that increasing the patch size while not changing the patch form will not change the ratio.

None

1 <= FRAC <= 2

#### Behaviour

Approaches FRAC = 1 for a squared patch shape form and FRAC = 2 for a irregular patch shape.

tibble

## References

McGarigal, K., SA Cushman, and E Ene. 2012. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical and Continuous Maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. Available at the following web site: http://www.umass.edu/landeco/research/fragstats/fragstats.html

Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company.

lsm_p_area, lsm_p_perim,
lsm_c_frac_mn, lsm_c_frac_sd, lsm_c_frac_cv,
lsm_l_frac_mn, lsm_l_frac_sd, lsm_l_frac_cv
 1 lsm_p_frac(landscape)