The Bichromatic Excitable Schrodinger Metamedium

In this work, we apply quantum cellular automata (QCA) to study pattern formation and image processing in quantum-di usion Schrodinger systems (QDSS) with generalized complex di usion coe cients. Generalized complex numbers have the real part and imaginary part with the imaginary unit i = −1 (classical case), i = +1 (double numbers) and i = 0 (dual numbers). They form three 2-D complex algebras. Discretization of the Schrodinger equation gives lattice based metamaterial models with various complex valued physical parameters. The process of excitation in these media is described by the Schrodinger equations with the wave functions that have values in algebras of the complex, dual, double numbers. If a traditional computer is thought of as a programmable object , QDSS in the form of QCA is a computer of new kind and is better visualized as a programmable material . The purpose of this work is to introduce new metamedium in the form of cellular automata. The cells are placed in a 2-D array and they are capable of performing basic complex operating (in di erent complex algebras) and exchanging messages about their state. Cellular automata like architectures have been successfully used for computer vision problems and grey-level image processing. Such media possess large opportunities in processing of bichromatic images in comparison with the ordinary di usion media with the real-valued di usion coe cients. The latter media are used for creation of the eye-prosthesis (so called the silicon eye ). The medium suggested can serve as the prosthesis prototype for perception of the bichromatic images.