Perimeter-Area Fractal Dimension (Shape metric)
lsm_c_pafrac(landscape, directions = 8, verbose = TRUE)tibble
Raster* Layer, Stack, Brick, SpatRaster (terra), stars, or a list of rasterLayers.
The number of directions in which patches should be connected: 4 (rook's case) or 8 (queen's case).
Print warning message if not sufficient patches are present
$$PAFRAC = \frac{2}{\beta}$$ where \(\beta\) is the slope of the regression of the area against the perimeter (logarithm) \(n_{i}\sum \limits_{j = 1}^{n} \ln a_{ij} = a + \beta n_{i}\sum \limits_{j = 1}^{n} \ln p_{ij}\)
PAFRAC is a 'Shape metric'. It describes the patch complexity of class i while being scale independent. This means that increasing the patch size while not changing the patch form will not change the metric. However, it is only meaningful if the relationship between the area and perimeter is linear on a logarithmic scale. Furthermore, if there are less than 10 patches in class i, the metric returns NA because of the small-sample issue.
None
1 <= PAFRAC <= 2
Approaches PAFRAC = 1 for patches with simple shapes and approaches PAFRAC = 2 for irregular shapes
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: https://www.umass.edu/landeco/
Burrough, P. A. 1986. Principles of Geographical Information Systems for Land Resources Assessment. Monographs on Soil and Resources Survey No. 12. Clarendon Press, Oxford
lsm_p_area,
lsm_p_perim,
lsm_l_pafrac