SPSL (version 0.1-9)

ssa20: Site cluster on Square Anisotropic 2D lattice with (1,0)-neighborhood

Description

ssa20() function provides sites labeling of the anisotropic cluster on 2D square lattice with von Neumann (1,0)-neighborhood.

Usage

ssa20(x=33, p=runif(4, max=0.9), 
      set=(x^2+1)/2, all=TRUE, shape=c(1,1))

Arguments

x

a linear dimension of 2D square percolation lattice.

p

a vector of relative fractions (0<p)&(p<1) of accessible sites (occupation probability) for lattice directions: (-x,+x,-y,+y).

set

a vector of linear indexes of a starting sites subset.

all

logical; if all=TRUE, mark all sites from a starting subset; if all=FALSE, mark only accessible sites from a starting subset.

shape

a vector with two shape parameters of beta-distributed random variables, weighting the percolation lattice sites.

Value

acc

an accessibility matrix for 2D square percolation lattice: if acc[e]<p[n] then acc[e] is accessible site; if acc[e]==1 then acc[e] is non-accessible site; if acc[e]==2 then acc[e] belongs to a sites cluster.

Details

The percolation is simulated on 2D square lattice with uniformly weighted sites acc and the vector p, distributed over the lattice directions.

The anisotropic cluster is formed from the accessible sites connected with the initial subset, and depends on the direction in 2D square lattice.

To form the cluster the condition acc[set+e[n]]<p[n] is iteratively tested for sites of the von Neumann (1,0)-neighborhood e for the current cluster perimeter set, where n is equal to direction in 2D square lattice.

Von Neumann (1,0)-neighborhood on 2D square lattice consists of sites, only one coordinate of which is different from the current site by one: e=c(-1, 1, -x, x).

Forming cluster ends with the exhaustion of accessible sites in von Neumann (1,0)-neighborhood of the current cluster perimeter.

References

[1] Moskalev, P.V. Percolation modeling of porous structures. Moscow: URSS, 2018. 240 pp; in Russian.

See Also

fssa20, ssa30, ssi20, ssi30, ssa2d, ssa3d

Examples

# NOT RUN {
set.seed(20120507)
x <- y <- seq(33)
image(x, y, ssa20(), zlim=c(0,2), 
main="Anisotropic (1,0)-cluster")
abline(h=17, lty=2); abline(v=17, lty=2)
# }