Related papers: A universal route to pattern formation
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous…
We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
Nature is a blossoming of regular structures, signature of self-organization of the underlying microscopic interacting agents. Turing theory of pattern formation is one of the most studied mechanisms to address such phenomena and has been…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
In his seminal paper on morphogenesis (1952), Alan Turing demonstrated that different spatio-temporal patterns can arise due to instability of the homogeneous state in reaction-diffusion systems, but at least two species are necessary to…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…