# isc3s: Isotropic set cover on the 3D square lattice In SECP: Statistical Estimation of Cluster Parameters (SECP)

## Description

`isc3s()` function calculates the boundary coordinates for the isotropic set cover on the 3D square lattice with a fixed point in the lattice center.

## Usage

 `1` ```isc3s(k=12, x=rep(95, times=3), o=(x+1)/2, r=min(o-2)^(seq(k)/k)) ```

## Arguments

 `k` a maximal set cover size: `k>2`. `x` a vector of lattice sizes: `all(x>5)`. `o` a fixed point of set cover elements: `all((0

## 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 isotropic set cover with a fixed point in the lattice center.

The isotropic set cover on 3D square lattice is formed from scalable cubes with variable sizes `2r+1` and a fixed point in the lattice center.

## Value

A list of boundary coordinates and sizes for the isotropic set cover on a 3D square lattice with a fixed point in the lattice center.

## Author(s)

Pavel V. Moskalev

fdc2s, fds2s, fds3s

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# # # # # # # # # # # # # # # # # # Example: Isotropic set cover # # # # # # # # # # # # # # # # # pc <- .311608 p2 <- pc + .03 lx <- 33; ss <- (lx+1)/2 set.seed(20120627); ac2 <- ssi30(x=lx, p=p2) bnd <- isc3s(k=9, x=dim(ac2)) x <- z <- seq(lx); y2 <- ac2[,ss,] image(x, z, y2, cex.main=1, main=paste("Isotropic 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(h=ss, lty=2); abline(v=ss, lty=2) ```

### Example output

```Loading required package: SPSL
```

SECP documentation built on May 1, 2019, 10:51 p.m.