The Color Excitable Schrodinger Metamedium

Abstract

In this work, we apply quantum cellular automata (QCA) to study pattern formation and image processing in quantum-diffusion Schrodinger systems (QDSS) with triplet-valued (color-valued) diffusion coefficients. Triplet numbers have the real part and two imaginary parts (with two imaginary units). They form 3-D triplet algebra. Discretization of the Schrodinger equation gives “lattice based metamaterial models” with various triplet–valued physical parameters. The process of excitation in these media is described by the Schrodinger equations with the wave functions that have values in triplet algebras. 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 arithmetic operating in the triplet algebra and exchanging massages about their state. Cellular automata like architectures have been successfully used for computer vision problems and color image processing. Such metamedia possess large opportunities in processing of color images in comparison with the ordinary diffusion media with the real-valued diffusion coefficients. The latter media are used for creation of the eye-prosthesis (so called the “silicon eye”). The color metamedium suggested can serve as the prosthesis prototype for perception of the color images.