These arrays can take on any number of dimensions, starting from a one dimensional string of cells. Each cell has its own State that can be a variable, property or other information. By receiving input from connected cells or general messages a cell uses its own set of rules to determine what its reaction should be. This reaction is a change of state and can also be a trigger to send out its own messages. These messages are passed onto other selected cells which cause them to act like wise.
Natural cells work much in the same way.
For example in an embryo messages are spread by timed releases of chemicals by cells which tell a cell which type of cell it should be. Each cell has a look up library, the code of DNA, to control its actions. A cell also has a chemical plant and chemical responses that act as its input and output devices. Different doses of chemicals and in different combinations cause a cell to act in different ways. Sometime small changes in chemical density can lead to radical changes in cell formation.