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FRAC_MN (landscape level)

Source: R/lsm_l_frac_mn.R
lsm_l_frac_mn.Rd

Mean fractal dimension index (Shape metric)

Usage

lsm_l_frac_mn(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

$$FRAC_{MN} = mean(FRAC[patch_{ij}])$$ where \(FRAC[patch_{ij}]\) equals the fractal dimension index of each patch.

FRAC_MN is a 'Shape metric'. The metric summarises the landscape as the mean of the fractal dimension index of all patches in the landscape. The fractal dimension index is based on the patch perimeter and the patch area and describes the patch complexity. The Coefficient of variation is scaled to the mean and comparable among different landscapes.

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

Units

None

Range

FRAC_MN > 0

Behaviour

Approaches FRAC_MN = 1 if all patches are squared and FRAC_MN = 2 if all patches are irregular.

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_frac, mean,
lsm_c_frac_mn, lsm_c_frac_sd, lsm_c_frac_cv,
lsm_l_frac_sd, lsm_l_frac_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_l_frac_mn(landscape)
#> # A tibble: 1 × 6
#>   layer level     class    id metric  value
#>   <int> <chr>     <int> <int> <chr>   <dbl>
#> 1     1 landscape    NA    NA frac_mn  1.19