Turing systems as models of complex pattern formation

Abstract

Half a century ago a reaction-diffusion system of two chemicals was introduced by Alan Turing to account for morphogenesis, i.e., the development of patterns, shapes and structures found in nature. Here we will discuss the formation of patterns and structures obtained through numerical simulation of the Turing mechanism in two and three dimensions. The forming patterns are found to depend strongly on the initial and boundary conditions as well as system parameters, showing a rich variety of patterns, e.g. stripes and spots (2D), and lamellae and spherical droplets (3D) arranged in structures of high symmetry, with or without defects or distortions.

Highly Ordered Anodic Porous Alumina Formation by Self‐Organized Anodizing

“…One very promising approach to the anodic porous alumina description seems to be a fractal model of the porous layer formation [400], and the appearance of hexagonally ordered patterns as a result of Turing systems modeling [401,402].…”

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

“…Turing patterns in a chemical reactor were first experimentally observed by De Kepper's group in a chlorite-iodide-malonic acid (CIMA) reaction [18] and later confirmed by Ouyang and Swinney who observed striped as well as spotty patterns [53]. The chance to experimentally detect Turing structures has produced a renewed interest in these systems as shown by the large number of theoretical [35,58], computational [43,44,67] and experimental studies in the field [6,42,52].…”

Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction–diffusion systems

“…Examples include the synthesis and processing of materials, intracellular signaling in biology, and morphogenic processes in the development of tissues [38,[49][50][51][52][53]70,73]. In many reactiondiffusion systems, the most interesting features are exhibited only in a sub-region of the spatial domain, such as in a chemically active front or in a layer near boundaries.…”