One idea: every point claims the ground nearest to it.
Scatter some points on a plane. For each one, mark every location that is closer to it than to any other point. That region is its Voronoi cell, and together the cells carve the plane into tiles that look organic because they are. The same rule governs cracked mud, giraffe markings, foam and the grain structure of metals.
The structure is named after Georgy Voronoy, though John Snow had already drawn one by hand in 1854 to work out which water pump was causing a cholera outbreak in Soho.
Delaunay triangulation connects points whose cells share an edge. The two structures are duals of each other: compute one and you have effectively computed the other.
Delaunay also maximises the smallest angle across all its triangles, which is why it produces well-shaped meshes and why low-poly artwork leans on it so heavily.
Randomly scattered points give uneven cells with awkward slivers in them. Lloyd's algorithm, worked out at Bell Labs in 1957, moves each point to the centre of its own cell and recomputes, over and over.
A few passes give you evenly sized rounded cells. Keep going and it converges towards something close to a hexagonal grid. The iteration count is effectively a dial between chaos and order, and the useful settings are usually at the low end.