FRAC (patch level)

Fractal dimension index (Shape metric)

Usage

lsm_p_frac(landscape, directions = 8)

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).

Value

tibble

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.

Because the metric is based on distances or areas please make sure your data is valid using check_landscape.

Units

None

Range

1 <= FRAC <= 2

Behaviour

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

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.

See also

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

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