Turing Patterns in Deserts

Sherratt, Jonathan A.

doi:10.1007/978-3-642-30870-3_67

Cited by 6 publications

(3 citation statements)

References 48 publications

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“…Turing-type patterning is also studied in a variety of other settings, such as in nonlinear optics (Oppo 2009;Ardizzone et al 2013;Chembo et al 2017), geochemistry (Baurmann et al 2004;McBride and Picard 2004), astrophysics (Smolin 1996), reaction-advection-diffusion systems (Klika et al 2018;Krause et al 2018a;Van Gorder et al 2019), network-organised media (Nakao and Mikhailov 2010;Asllani et al 2014), spatial ecology (Sherratt 2012;Hata et al 2014;Taylor et al 2020), and social dynamics (Wakano et al 2009). Whilst it has been known for decades that chemical systems can be engineered to produce specific Turing patterns (Vanag and Epstein 2001), recently Tan et al (2018) employed such designed Turing systems to manufacture a porous filter for use in water purification.…”

Section: Introductionmentioning

confidence: 99%

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Bespoke Turing Systems

2021

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Reaction–diffusion systems are an intensively studied form of partial differential equation, frequently used to produce spatially heterogeneous patterned states from homogeneous symmetry breaking via the Turing instability. Although there are many prototypical “Turing systems” available, determining their parameters, functional forms, and general appropriateness for a given application is often difficult. Here, we consider the reverse problem. Namely, suppose we know the parameter region associated with the reaction kinetics in which patterning is required—we present a constructive framework for identifying systems that will exhibit the Turing instability within this region, whilst in addition often allowing selection of desired patterning features, such as spots, or stripes. In particular, we show how to build a system of two populations governed by polynomial morphogen kinetics such that the: patterning parameter domain (in any spatial dimension), morphogen phases (in any spatial dimension), and even type of resulting pattern (in up to two spatial dimensions) can all be determined. Finally, by employing spatial and temporal heterogeneity, we demonstrate that mixed mode patterns (spots, stripes, and complex prepatterns) are also possible, allowing one to build arbitrarily complicated patterning landscapes. Such a framework can be employed pedagogically, or in a variety of contemporary applications in designing synthetic chemical and biological patterning systems. We also discuss the implications that this freedom of design has on using reaction–diffusion systems in biological modelling and suggest that stronger constraints are needed when linking theory and experiment, as many simple patterns can be easily generated given freedom to choose reaction kinetics.

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Section: Introductionmentioning

confidence: 99%

“… 2019 ), network-organised media (Nakao and Mikhailov 2010 ; Asllani et al. 2014 ), spatial ecology (Sherratt 2012 ; Hata et al. 2014 ; Taylor et al.…”

Section: Introductionmentioning

confidence: 99%

Bespoke Turing Systems

2021

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“…has produced stimulating research in the field of non-linear dynamics [46,47,51]. As a matter of fact, Turing's diffusion-driven instability is now universally recognized as one of the leading mechanisms of spatial pattern formation in reaction-diffusion systems and the related Turing patterns have been the subject of extensive studies in a variety of applied contexts [20,21,25,28,32,46,48,51,65].…”

Section: Introductionmentioning

confidence: 99%

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

2014

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In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013 J. Solid State Electr. 17, 467-479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, spatially uniform dynamics is discussed and the occurrence of a supercritical Hopf bifurcation for the local kinetics is proved. In the spatial case, initiation of morphological patterns induced by diffusion is shown to occur in a suitable region of the parameter space. The intriguing interplay between Hopf and Turing instability is also considered, by investigating the spatio-temporal behaviour of the system in the neighbourhood of the codimensiontwo Turing-Hopf bifurcation point. An ADI (Alternating Direction Implicit) scheme based on high-order finite differences in space is applied to obtain numerical approximations of Turing patterns at the steady state and for the simulation of the oscillating Turing-Hopf dynamics.

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‘Turingalila’ Visual Music on the Theme of Morphogenesis

Trickett

2016

Evolutionary and Biologically Inspired Music, Sound, Art and Design

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Turing Patterns in Deserts

Cited by 6 publications

References 48 publications

Bespoke Turing Systems

Bespoke Turing Systems

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

‘Turingalila’ Visual Music on the Theme of Morphogenesis

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