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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