Cellular Automata (CA) processors are a physical, not software only, implementation of CA concepts, which can process information computationally. Processing elements are arranged in a regular grid of identical cells. The grid is usually a square tiling, or tessellation, of two or three dimensions; other tilings are possible, but not yet used. Each cell is in one of a finite number of states, determined only by interactions with the small number of adjoining cells. Cells interact, communicate, directly only with adjoining, adjacent, neighbor cells. No means exists to communicate directly with cells farther away. Cell interaction can be via electric charge, magnetism, vibration (phonons at quantum scales), or any other physically useful means. This can be done in several ways so no wires are needed between any elements.
This is very unlike processors used in most computers today, von Neumann designs, which are divided into sections with elements that can communicate with distant elements, over wires.