21 papers · ranked by Valyu relevance
Masato Tanaka, S. Macrae Montgomery, Liang Yue, Yaochi Wei + 3 more
'Yuyang Song' 'Tsuyoshi Nomura' 'H. Jerry Qi'] Turing patterns are self-organizing stripes or spots widely found in biological systems and nature. Although inspiring, their applications are limited. Inflatable shape-morphing structures have attracted substantial research attention. Traditional inflatable structures use…
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.…
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…
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…
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…
John J. Tyson
In a 1952 paper, Alan Turing showed that spatially distributed chemical reactions evolving in time by local kinetic rate laws and in space by unbiased molecular diffusion can develop a stable, time-independent, spatial pattern from a spatially homogeneous, steady state solution subjected to small, spatially periodic…
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…
John. TM. Campbell
—We introduce patterned numbers, a digit–divisorbased classification of integers motivated by recreational mathematics. A number is defined to be patterned if at least one of its positive divisors appears as a digit in its base-10 representation. We study the first hundred natural numbers under this definition, analyze…
Pierre Galipot
1.1.### Colour patterning and the importance of aesthetics By using Turing colour patterns as an example, we can trace the influence of aesthetics in the history of the field, in particular for the choice of model species. In our knowledge, the Turing mechanism - initially based on reaction-diffusion and theorised by…
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…
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…
Tinka Bruneau, Michael F. Whittaker
A brief history of planar aperiodic tile sets is presented, starting from the Domino Problem proposed by Hao Wang in 1961. We provide highlights that led to the discovery of the Taylor–Socolar aperiodic monotile in 2010 and the Hat and Spectre aperiodic monotiles in 2023. The Spectre tile is an amazingly simple…
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…
Dirk Frettlöh, Jan Mazáč
This short note provides two examples of aperiodic frieze patterns of the plane, supported on the rhombic Penrose tiling and the Godrèche--Lançon--Billard tiling. That is, we provide a decoration of their vertices with positive integers which satisfy the diamond rule, in analogy to the usual (in)finite frieze patterns…
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…
Marek Tyburec, Jan Zeman
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling…