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FRAC_SD (class level)

Source: R/lsm_c_frac_sd.R
lsm_c_frac_sd.Rd

Standard deviation fractal dimension index (Shape metric)

Usage

lsm_c_frac_sd(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

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

FRAC_SD is a 'Shape metric'. The metric summarises each class as the standard deviation of the fractal dimension index of all patches belonging to class i. The fractal dimension index is based on the patch perimeter and the patch area and describes the patch complexity.

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

Units

None

Range

FRAC_SD>= 0

Behaviour

Equals FRAC_SD = 0 if the fractal dimension index is identical for all patches. Increases, without limit, as the variation of the fractal dimension indices increases.

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, sd
lsm_c_frac_mn, lsm_c_frac_cv,
lsm_l_frac_mn, lsm_l_frac_sd, lsm_l_frac_cv

Examples

landscape <- terra::rast(landscapemetrics::landscape)
lsm_c_frac_sd(landscape)
#> # A tibble: 3 × 6
#>   layer level class    id metric   value
#>   <int> <chr> <int> <int> <chr>    <dbl>
#> 1     1 class     1    NA frac_sd 0.218 
#> 2     1 class     2    NA frac_sd 0.117 
#> 3     1 class     3    NA frac_sd 0.0732