Cellular automata are often simulated on a finite grid rather than an infinite one. In two dimensions, the universe would be a rectangle instead of an infinite plane. The obvious problem with finite grids is how to handle the cells on the edges. How they are handled will affect the values of all the cells in the grid. One possible method is to allow the values in those cells to remain constant. Another method is to define neighborhoods differently for these cells. One could say that they have fewer neighbors, but then one would also have to define new rules for the cells located on the edges. These cells are usually handled with a "toroidal" arrangement: when one goes off the top, one comes in at the corresponding position on the bottom, and when one goes off the left, one comes in on the right. (This essentially simulates an infinite periodic tiling, and in the field of partial differential equations is sometimes referred to as "periodic" boundary conditions.) This can be visualized as taping the left and right edges of the rectangle to form a tube, then taping the top and bottom edges of the tube to form a torus (doughnut shape). Universes of other dimensions are handled similarly. This solves boundary problems with neighborhoods, but another advantage is that it is easily programmable using modular arithmetic functions. For example, in a 1-dimensional cellular automaton like the examples below, the neighborhood of a cell "xit" is {"x""i"−1"t"−1, "x""i""t"−1, "x""i"+1"t"−1}, where "t" is the time step (vertical), and "i" is the index (horizontal) in one generation.