21 papers · ranked by Valyu relevance
Philip Ball
Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate…
Lewis Grozinger, Ángel Goñi-Moreno
Turing patterns are a key theoretical foundation for understanding organ development and organization. While they have been found to occur in natural systems, implementing new biological systems that form Turing patterns has remained challenging. To address this, Tica et al.1 used synthetic genetic networks to engineer…
Soha Ben Tahar, Jose J Muñoz, Sandra J Shefelbine, Ester Comellas
Reaction-diffusion systems have been widely used to model pattern formation in biological systems. However, the emergence of Turing patterns in three-dimensional (3D) domains remains relatively unexplored. A few studies on this topic have shown that extending pattern formation from 2D to 3D is not straightforward.…
Tom Leyshon, Elisa Tonello, David Schnoerr, Heike Siebert + 1 more
The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic…
Shubham Shinde, Archishman Raju
Turing patterns are a well-studied model of reaction-diffusion equations for developmental patterning. Their applicability has often been limited by the difficulty in identifying candidate molecules that satisfy the requisite criteria for patterning. Here, we build on recent work on geometric models to describe Turing…
Laura Regueira López de Garayo, Luciano Marcon
Understanding how genetic networks can drive different self-organizing spatial behaviors remains a significant challenge. Here, we use an automated algebraic method to systematically screen for Turing networks capable of generating diverse spatial patterns from noise, including periodic static waves, traveling waves…
Thurston C. Lacalli
This is a brief account of Turing’s ideas on biological pattern and the events that led to their wider acceptance by biologists as a valid way to investigate developmental pattern, and of the value of theory more generally in biology. Periodic patterns have played a key role in this process, especially 2D arrays of…
Thomas E. Woolley, Andrew L. Krause, Eamonn A. Gaffney
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…
Pierre Galipot
Evidenced in zebrafishes skin and Mimulus petal, Turing-like mechanisms are suspected to be responsible for many periodic colour patterns of Eukaryotes. They are characterised by the mathematical relationships linking their cellular or molecular actors, the periodicity and the geometrical range of the patterns they…
Martina Oliver Huidobro, Robert G. Endres
Turing patterns are a fundamental concept in developmental biology, describing how homogeneous tissues develop into self-organized spatial patterns. However, the classical Turing mechanism, which relies on linear stability analysis, often fails to capture the complexities of real biological systems, such as…
Pierre Galipot, Hualin Fu
Evidenced in zebrafishes skin and Mimulus petal, Turing-like mechanisms are probably responsible for many periodic color patterns of Eukaryotes. They are characterized by the mathematical relationships linking their cellular or molecular actors, the periodicity and the geometrical range of the patterns they produce…
Andrew L. Krause, Eamonn A Gaffney, Philip K. Maini, Václav Klika
Elucidating pattern forming processes is an important problem in the physical, chemical and biological sciences. Turing's contribution, after being initially neglected, eventually catalysed a huge amount of work from mathematicians, physicists, chemists and biologists aimed towards understanding how steady spatial…
Neetu ., Aman Saini, Rishi Ram Mahato, Priyanka . + 1 more
The theory behind origin of life to Darwinian evolution considers emergence of dissipative structures driven by the flow of energy across all length scales. To this end, developing and deeper understanding of non-equilibrium self-assembly processes under continuous supply of energy is a demanding matter, both in…
Ioannis Tamvakis
Here we show how reversible computation processes, like Margolus diffusion[1], can be envisioned as physical turning operations on a 2 dimensional rigid surface that is cut by a regular pattern of intersecting circles. We then briefly explore the design-space of these patterns, and report on the discovery of an…
Authors not listed
Laser modification of polymer surfaces is critical in many contexts including self-cleaning materials, microelectronics, and biomedical research. Despite their utility, accessing these modified polymers requires expensive or complex materials and multi-step fabrication, masking, and washing processes. Here, we present…
James R. Smith
These notes derive aperiodic monotiles from a set of rhombuses with matching rules. This dual construction is used to simplify the proof of aperiodicity by considering the tiling as a colouring game on a Rhombille tiling. A simple recursive substitution system is then introduced to show the existence of a non-periodic…
Darren C. Ong
Aperiodic order refers to a mathematical structures that are not periodic, but are nevertheless highly ordered and close to periodic in some way. Aperiodically ordered patterns gained increased interest among physicists and mathematicians upon the discovery of the quasicrystal in 1982, since these structures were…
Veronika Irvine, Thérèse Biedl, Craig S. Kaplan
Bobbin lace is a fibre art form in which threads are braided together to form a fabric, often with a very detailed and complex design. In traditional practice, each region of the fabric is filled with a periodic texture. We establish the groundwork for non-periodic lace patterns and present three new quasiperiodic…
Authors not listed
The discovery of quasicrystals, characterized by unique, non-repeating atomic arrangements and forbidden rotational symmetries, has significantly expanded our understanding of crystalline materials. However, controlling quasiperiodic length scales remains challenging because the quasiperiodic arrangements are often…
Karen E. Daniels, Charles Emmett Maher, Katherine A. Newhall, Mason A. Porter + 1 more
Karen E. Daniels, Department of Physics, North Carolina State University Charles Emmett Maher, Department of Mathematics, University of North Carolina at Chapel Hill Katherine Newhall, Department of Mathematics, University of North Carolina at Chapel Hill Mason A. Porter, Department of Mathematics, University of…
Howard L. Resnikoff
It introduces a generalization of inflationary tessellations to equivalence classes of tiles. Two tiles belong to the same class if they share a defined geometric property, such as equivalence under a group of isometries, having the same measure, or having the same 'decoration'. Some properties of ordinary…