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Simulates a midpoint displacement neutral landscape model.

Usage

nlm_mpd(
  ncol,
  nrow,
  resolution = 1,
  roughness = 0.5,
  rand_dev = 1,
  torus = FALSE,
  rescale = TRUE,
  verbose = TRUE
)

Arguments

ncol

[numerical(1)]
Number of columns forming the raster.

nrow

[numerical(1)]
Number of rows forming the raster.

resolution

[numerical(1)]
Resolution of the raster.

roughness

[numerical(1)]
Controls the level of spatial autocorrelation (!= Hurst exponent)

rand_dev

[numerical(1)]
Initial standard deviation for the displacement step (default == 1), sets the scale of the overall variance in the resulting landscape.

torus

[logical(1)]
Logical value indicating wether the algorithm should be simulated on a torus (default FALSE)

rescale

[logical(1)]
If TRUE (default), the values are rescaled between 0-1.

verbose

[logical(1)]
If TRUE (default), the user gets a warning that the functions changes the dimensions to an appropriate one for the algorithm.

Value

RasterLayer

Details

The algorithm is a direct implementation of the midpoint displacement algorithm. It performs the following steps:

  • Initialization: Determine the smallest fit of max(ncol, nrow) in n^2 + 1 and assign value to n. Setup matrix of size (n^2 + 1)*(n^2 + 1). Afterwards, assign a random value to the four corners of the matrix.

  • Diamond Step: For each square in the matrix, assign the average of the four corner points plus a random value to the midpoint of that square.

  • Diamond Step: For each diamond in the matrix, assign the average of the four corner points plus a random value to the midpoint of that diamond.

At each iteration the roughness, an approximation to common Hurst exponent, is reduced.

Examples


# simulate midpoint displacement
midpoint_displacememt <- nlm_mpd(ncol = 100,
                                 nrow = 100,
                                 roughness = 0.3)
#> Warning: nlm_mpd changes the dimensions of the RasterLayer if even ncols/nrows are choosen.
if (FALSE) {
# visualize the NLM
landscapetools::show_landscape(midpoint_displacememt)
}