Finding paths in a labyrinth based on reaction–diffusion media

Abstract

During the past few decades, many proposals were made on how to take an effective solution for finding a path in a labyrinth, one of the most well known problems of high computational complexity inherent in information processing by biomolecular and biological entities. In particular, attempts were made to use a technique attractive enough for solving this problem based on wave processes in reaction–diffusion media. Trigger waves in reaction–diffusion systems spread simultaneously through all paths of the labyrinth in a highly parallel mode. Regretfully, the velocity of these waves is extremely low which gave no way for the practical implementation of this technique until now. An effective ‘hardware’ system was designed which was capable of finding a path in a labyrinth using fast phase waves. Three principal points were assumed as a basis for this design, i.e. (1) hybrid architecture that combined an information processing reaction–diffusion medium which performs operations of high computational complexity with a digital computer carrying out supplementary image processing operations; (2) light-sensitive information processing media of Belousov–Zhabotinsky type that enables the simulation of the labyrinth and spreading wave evolution by their images stored in the medium and reduces the problem to the image processing operations; (3) fast light-induced phase wave processes that spreads through the labyrinth in several seconds instead of hours which is typical for trigger waves inherent in reaction–diffusion media. These fundamentals along with the additional procedure of testing for labyrinth fragment connectness provided us with the opportunity to solve labyrinth problems.