ssa2d: Site cluster on Square Anisotropic 2D lattice with...

In SPSL: Site Percolation on Square Lattices (SPSL)

Description

ssa2d() function provides sites labeling of the anisotropic cluster on 2D square lattice with Moore (1,d)-neighborhood.

Usage

ssa2d(x=33, p0=runif(4, max=0.8), 
            p1=colMeans(matrix(p0[c(
               1,3, 2,3, 1,4, 2,4)], nrow=2))/2,
            set=(x^2+1)/2, all=TRUE, shape=c(1,1))

Arguments

x	a linear dimension of 2D square percolation lattice.
p0	a vector of relative fractions (0<p0)&(p0<1) of accessible sites (occupation probability) for lattice directions: (-x,+x,-y,+y).
p1	averaged double combinations of p0-components weighted by Minkowski distance: p1=colMeans(matrix(p0[c(1,3,...)], nrow=2))/rhoMe1.
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.

Details

The percolation is simulated on 2D square lattice with uniformly weighted sites acc and the vectors p0 and p1, distributed over the lattice directions, and their combinations.

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

To form the cluster the condition acc[set+eN[n]]<pN[n] is iteratively tested for sites of the Moore (1,d)-neighborhood eN for the current cluster perimeter set, where eN is equal to e0 or e1 vector; pN is equal to p0 or p1 vector; n is equal to direction in 2D square lattice.

Moore (1,d)-neighborhood on 2D square lattice consists of sites, at least one coordinate of which is different from the current site by one: e=c(e0,e1), where
e0=c(-1, 1, -x, x);
e1=colSums(matrix(e0[c(1,3, 2,3, 1,4, 2,4)], nrow=2)).

Minkowski distance between sites a and b depends on the exponent d:
rhoM <- function(a, b, d=1)
if (is.infinite(d)) return(apply(abs(b-a), 2, max))
else return(apply(abs(b-a)^d, 2, sum)^(1/d)).

Minkowski distance for sites from e1 subset with the exponent d=1 is equal to rhoMe1=2.

Forming cluster ends with the exhaustion of accessible sites in Moore (1,d)-neighborhood of the current cluster perimeter.

Value

acc	an accessibility matrix for 2D square percolation lattice: if acc[e]<pN[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.

Author(s)

Pavel V. Moskalev

References

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

See Also

fssa2d, ssa3d, ssa20, ssa30, ssi2d, ssi3d

Examples

set.seed(20120507)
x <- y <- seq(33)
image(x, y, ssa2d(), zlim=c(0,2), 
main="Anisotropic (1,1)-cluster")
abline(h=17, lty=2); abline(v=17, lty=2)

SPSL documentation built on May 2, 2019, 12:34 p.m.