Description Usage Arguments Details Value Author(s) References See Also Examples

`ssa2d()`

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

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`x` |
a linear dimension of 2D square percolation lattice. |

`p0` |
a vector of relative fractions |

`p1` |
averaged double combinations of |

`set` |
a vector of linear indexes of a starting sites subset. |

`all` |
logical; if |

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

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.

`acc` |
an accessibility matrix for 2D square percolation lattice: |

Pavel V. Moskalev

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

fssa2d, ssa3d, ssa20, ssa30, ssi2d, ssi3d

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