What are cellular automata?

      From Wikipedia: A cellular automaton (plural: cellular automata) is a discrete model studied in mathematics, and theoretical biology. It consists of an infinite, regular grid of cells, each in one of a finite number of states. The grid can be in any finite number of dimensions. Time is also discrete, and the state of a cell at time t is a function of the states of a finite number of cells (called its neighborhood) at time t-1. These neighbors are a selection of cells relative to the specified cell, and do not change. (Though the cell itself may be in its neighborhood, it is not usually considered a neighbor.) Every cell has the same rule for updating, based on the values in this neighbourhood. Each time the rules are applied to the whole grid a new generation is created.

What does that mean? 

      Basically, a cellular automata is a set of rules about how a grid of cells should updated. The updates are carried out in steps called generations. Usually, the cells are squares (or cubes in three-dimensional cellular automata) and are coloured according to their state. The rules for the cellular automaton dictate how many states their are, and what cells change state under what conditions. Amazingly complex behavior can arise in these extremely simple machines.

What is significant about them?

      Cellular automata occur in natural processes like some chemical chemical reactions, and the pigmentation of the shells of some sea creatures. Many provide us with models for a plethora of scientific and mathematic phenomena as well as harbor simple artificial life capable of reproduction and evolution. Many are powerful enough to act as fully-fledged computers. Some are tools for investigating the properties of other cellular automata. They have been used in the creation of art and computer animation.

    Some research (particularily by Stephen Wolfram) suggests that simple computational processes like cellular automata may be a better way to model the nature of our universe than mathematical equations.

Where can I learn more about them?

      Wikipedia is always a good place to start. Googling will also lead you to many interesting sites. My links page is here. There are links to specific cellular automata concepts in the side bar at the top left of these pages.

Can I explore them on my home computer?

      Absolutely. I have found inventing and exploring cellular automata an amusing and engaging way to spend time. Furthermore, I think there are important insights to be obtained through the study of these (relatively) simple worlds. There are a few good freeware programs for implementing cellular automata, mostly for Microsoft's Windows operating system, though programs for Unix-like operating systems are also available. I list the software I'm aware of at my links page.