More importantly, this idea doesn't work in the context of space dilation. Per special relativity, the distance between objects is arbitrarily different for different observers, so any grid you draw will be wrong for me if I'm moving at a different velocity than you. This is especially bad because it doesn't just depend on the magnitude of the velocity, but also the direction - space is compressed in the direction of motion. So two observers moving at an angle to each other will have very different views of the grid.