asc3s {SECP}

Anisotropic set cover on the 3D square lattice

Description

asc3s() function calculates the boundary coordinates for the anisotropic set cover on the 3D square lattice with a fixed face along the lattice boundary.

Usage

asc3s(k=12, x=rep(95, times=3), dir=3, r=(x[dir]-3)^(seq(k)/k))

Arguments

k

a maximal set cover size: k>2.

x

a vector of lattice sizes: all(x>5).

dir

a variable component index: x) dir=1; y) dir=2; z) dir=3.

r

a variable lenght of set cover elements: all((0<r)&(r<x)).

Details

The percolation is simulated on 3D square lattice with uniformly weighted sites and the constant parameter p.

The percolation cluster is formed from the accessible sites connected with initial sites subset.

If an initial cluster subset in the lattice center, to estimate the mass fractal dimension requires an anisotropic set cover with a fixed face along the lattice boundary.

The anisotropic set cover on 3D square lattice is formed from scalable cuboids with a variable length r+1 and a fixed face along the lattice boundary.

Value

A list of boundary coordinates and sizes for the anisotropic set cover on a 3D square lattice with a fixed face along the lattice boundary.

Author(s)

Pavel V. Moskalev

See Also

fdc2s, fds2s, fds3s

Examples

# # # # # # # # # # # # # # # # #
# Example: Anisotropic set cover, dir=3
# # # # # # # # # # # # # # # # #
pc <- .311608
p2 <- pc + .03
lx <- 33; ss <- (lx+1)/2; ssz <- seq(lx^2+lx+2, 2*lx^2-lx-1)
set.seed(20120627); ac2 <- ssi30(x=lx, p=p2, set=ssz, all=FALSE)
bnd <- asc3s(k=9, x=dim(ac2), dir=3)
x <- z <- seq(lx); y2 <- ac2[,ss,]
image(x, z, y2, cex.main=1,
      main=paste("Anisotropic set cover and\n",
                 "a 3D cluster of sites in the y=",ss," slice with\n",
                 "(1,0)-neighborhood and p=", 
                 round(p2, digits=3), sep=""))
rect(bnd["x1",], bnd["z1",], bnd["x2",], bnd["z2",])
abline(v=ss, lty=2)