Lattice geometries

The geometry determines the coordinate system, velocity channels and propagation neighbourhood. Pass a geometry name or alias to lgca.get_lgca().

Geometry	Common aliases	Velocity channels	Coordinates
1D linear	"1d", "lin", "linear"	2	x
2D square	"square", "sq", "rect", "rectangular"	4	(x, y)
2D hexagonal	"hex", "hx", "hexagonal"	6	(x, y)
3D cubic	"cubic", "cb"	6	(x, y, z)
3D Moore	"moore", "moore3d"	26	(x, y, z)

1-dimensional lattice

Nodes are arranged on a line. The two velocity channels represent motion to the left and right. Integer dims values create a lattice of that length.

2-dimensional square lattice

Nodes form a rectangular grid. Four velocity channels point to the orthogonal neighbours. Optional rest channels can be appended after the velocity channels.

2-dimensional hexagonal lattice

Nodes are arranged on a hexagonal tiling. Six velocity channels point to adjacent hexagons, giving a more isotropic planar neighbourhood than the square lattice.

3-dimensional cubic lattice

Nodes occupy a regular cube grid. Six velocity channels point along the positive and negative coordinate axes.

3-dimensional Moore lattice

The Moore lattice extends the cubic neighbourhood to all 26 surrounding nodes: all combinations of (dx, dy, dz) in {-1, 0, 1} except the origin.

Example

from lgca import get_lgca

lgca = get_lgca(geometry="moore", dims=(10, 10, 10), seed=1)