Training Cellular Automata

A complex material or physical system can behave in several different ways: (1) it can settle into a stable state (Class I behavior), (2) it can exhibit simple periodic behavior or oscillation (Class II), (3) it can act chaotically, like a turbulent fluid (Class III), or (4), most importantly, it can exhibit behavior between Classes II and III, that is, more complex than simple oscillation but more orderly that chaos; therefore this class of behavior is often called the “edge of chaos” (Class IV).  Class IV systems are considered suitable for computation because they exhibit long-range interactions (which can be used for communication), numerous semi-stable states (which can be used for memory), and other desirable characteristics.

Therefore, the search for new computational technologies concentrates on Class IV systems, and nanotechnology is developing many new materials and structures that exhibit complex (Class IV) behavior, which might be suitable for computation. Unfortunately, just because a physical system exhibits Class IV behavior does not imply that we know how to use it for useful computation. Given a material or physical system with sufficiently rich behavior, how can we apply it to specific computational problems?

The purpose of this project is to develop software to test one particular approach to using a complex material for useful computation.  We will use cellular automata (similar to the familiar “Game of Life”) to model Class IV materials, and use a variant of a neural net learning algorithm in order to determine how to initialize a CA (cellular automaton) to accomplish a specified task.  You will need to program the simulator for the CA, implement the learning algorithm (which I will provide), and test it on several simple computational tasks.

For more information on this project, please send me mail or make an appointment to discuss it.

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Last updated: 2006-08-27.