LatticeAnimals.jl

LatticeAnimals.jl - Generate random lattice animals (polyforms) from the percolation model using the Metripolis algorithm

LatticeAnimals.jl

This packages generates random lattice animals (or sometimes called polyforms) from the standard percolation model using the Metropolis-Hasting algorithm.

The polyform is specified by its lattice basis matrix and a list of neighbours, where each entry is a linear combination of basis vectors leading to a neighbouring lattice point. So for example the square tesselation of the polyomino squares has the basis matrix $B$ and neighbours $N$:

$$B = \begin{pmatrix}1 & 0 \\0 & 1 \end{pmatrix} \quad \quad \quad N = \left\{\begin{pmatrix}1 \\0 \end{pmatrix}, \begin{pmatrix}0 \\1 \end{pmatrix}, \begin{pmatrix}-1 \\0 \end{pmatrix}, \begin{pmatrix}0 \\-1 \end{pmatrix}\right\}$$

The following functions are exported:

Poly(n, p, basis, neighbours): Generate a random polyform - specified in the basis-neighbours notation - of size n and percolation factor p
Polyomino(n, p): Generate a random polyomino of size n and percolation factor p
Polyhex(n, p): Generate a random polyhex of size n and percolation factor p
polyPlot(tiles, basis, path): Draw the polyform as a scatter plot and save to path
setDimension(d): Change the number of dimensions (default value: 2), a Julia restart is required afterwards