Turing patterns on rotating spiral growing domains

Abstract

We investigate the emergence of Turing patterns in a system growing as a rotating spiral in two dimensions, utilizing the photosensitivity of the chlorine dioxide–iodine–malonic acid (CDIMA) reaction to control the growth process. We observe the formation of single and multiple (double and triple) stationary spiral patterns as well as transitional patterns. From numerical simulations of the Lengyel–Epstein model with an additional term to account for the effects of illumination on the reaction, we analyze the relationship between the final morphologies and the radial and angular growth velocities, identify conditions conducive to the formation of transitional structures, examine the importance of the size of the initial nucleation site in determining the spiral's multiplicity, and evaluate the stability and robustness of these Turing patterns. Our results indicate how inclusion of rotational degrees of freedom in the growth process may lead to the formation of a diverse new class of patterns in chemical and biological systems.