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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.

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.

• Square 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)
}
``````