Turmite

In computer science, a turmite is a Turing machine which has an orientation in addition to a current state and a "tape" that consists of an infinite two-dimensional grid of cells. The terms ant and vant are also used. Langton's ant is a well-known type of turmite defined on the cells of a square grid. Paterson's worms are a type of turmite defined on the edges of an isometric grid.

It has been shown that turmites in general are exactly equivalent in power to one-dimensional Turing machines with an infinite tape, as either can simulate the other.