Fractal dimension index (Shape metric)
Arguments
- landscape
A categorical raster object: SpatRaster; Raster* Layer, Stack, Brick; stars or a list of SpatRasters.
- 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.
References
McGarigal K., SA Cushman, and E Ene. 2023. FRAGSTATS v4: Spatial Pattern Analysis Program for Categorical Maps. Computer software program produced by the authors; available at the following web site: https://www.fragstats.org
Mandelbrot, B. B. 1977. Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company.
Examples
landscape <- terra::rast(landscapemetrics::landscape)
lsm_p_frac(landscape)
#> # A tibble: 28 × 6
#> layer level class id metric value
#> <int> <chr> <int> <int> <chr> <dbl>
#> 1 1 patch 1 1 frac 1
#> 2 1 patch 1 2 frac 1.37
#> 3 1 patch 1 3 frac 1.27
#> 4 1 patch 1 4 frac 1
#> 5 1 patch 1 5 frac 1
#> 6 1 patch 1 6 frac 1.29
#> 7 1 patch 1 7 frac 1.23
#> 8 1 patch 1 8 frac 1.67
#> 9 1 patch 1 9 frac 1.14
#> 10 1 patch 2 10 frac 1.28
#> # ℹ 18 more rows