isc2s | R Documentation |

`isc2s()`

function calculates the boundary coordinates for the isotropic set cover on the 2D square lattice with a fixed point in the lattice center.

isc2s(k=12, x=rep(95, times=2), o=(x+1)/2, r=min(o-2)^(seq(k)/k))

`k` |
a maximal set cover size: |

`x` |
a vector of lattice sizes: |

`o` |
a fixed point of set cover elements: |

`r` |
a variable radius of set cover elements: |

The percolation is simulated on 2D 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 isotropic set cover with a fixed point in the lattice center.

The isotropic set cover on 2D square lattice is formed from scalable squares with variable sizes `2r+1`

and a fixed point in the lattice center.

A list of boundary coordinates and sizes for the isotropic set cover on a 2D square lattice with a fixed point in the lattice center.

Pavel V. Moskalev

Moskalev, P.V., Grebennikov, K.V. and Shitov, V.V. (2011),
Statistical estimation of percolation cluster parameters.
*Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies*, No.1 (January-June), pp.29-35, arXiv:1105.2334v1; in Russian.

fdc3s, fds2s, fds3s

# # # # # # # # # # # # # # # # # # Example: Isotropic set cover # # # # # # # # # # # # # # # # # pc <- .592746 p2 <- pc + .03 lx <- 33; ss <- (lx+1)/2 set.seed(20120627); ac2 <- ssi20(x=lx, p=p2) bnd <- isc2s(k=9, x=dim(ac2)) x <- y <- seq(lx) image(x, y, ac2, cex.main=1, main=paste("Isotropic set cover and a 2D cluster of\n", "sites with (1,0)-neighborhood and p=", round(p2, digits=3), sep="")) rect(bnd["x1",], bnd["y1",], bnd["x2",], bnd["y2",]) abline(h=ss, lty=2); abline(v=ss, lty=2)

SECP documentation built on May 11, 2022, 9:05 a.m.

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