There isn’t really any perfect choice for images with a square lattice of sample points. With a one-dimensional signal you don’t get the same annoying patterns

There isn’t really any perfect choice for images with a square lattice of sample points. With a one-dimensional signal you don’t get the same annoying patterns from the interaction of the two grids along different dimensions. If you use a equilateral triangle grid (if you like, think of hexagonal pixels) you can do better.