Turing/Turing-like patterns: Products of random aggregation of spatial components

Abstract Turing patterns are typical spatiotemporal ordered structures in various systems driven far from thermodynamic equilibrium. Turing’s reaction-diffusion theory, containing a long-range inhibiting agent and a local catalytic agent, has provided an explanation for the formation of some patterns in nature. Numerical, experimental and theoretical studies about Turing/Turing-like patterns have been generally focused on systems driven far from thermodynamic equilibrium. The local dynamics of these systems are commonly very complex, which brings great difficulties to the understanding of the formation of patterns. Here, we investigated a type of Turing-like patterns in a near-equilibrium thermodynamic system experimentally and theoretically, and put forward a new formation mechanism and a quantitative method for Turing/Turing-like patterns. Specifically, we observed a type of Turing-like patterns in starch solutions, and studied the effect of concentration on the structure of patterns. The experimental results show that, with the increase of concentration, patterns change from spots to inverse spots, and labyrinthine stripe patterns appear in the region of intermediate concentration. We analyzed and modeled the formation mechanism of these patterns observed in experiments, and the simulation results are agreed with the experimental results. Our conclusion indicates that the random aggregation of spatial components leads to the formation of these patterns, and the proportion of spatial components determines the structures. Our findings shed light on the formation mechanism for Turing/Turing-like patterns.