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Testing Turing's theory of morphogenesis in chemical cells

N. Tompkins, N. Li, C. Girabawe, M. Heymann, G. B. Ermentrout, I. R. Epstein, S. Fraden
2014 Proceedings of the National Academy of Sciences of the United States of America  
S1 ) consists of a monodisperse emulsion of drops of aqueous BZ solution, whose diameter ranges from 20 to 200 μm dispersed in a continuous phase of oil (17, 18) .  ...  Our experiments verify Turing's thesis of the chemical basis of morphogenesis and reveal a pattern, not previously predicted by theory, which we explain by extending Turing's model to include heterogeneity  ... 
doi:10.1073/pnas.1322005111 pmid:24616508 pmcid:PMC3970514 fatcat:vjpd4gbcxve43lfydhezgspofu

Computability and the morphological complexity of some dynamics on continuous domains

Mathieu Hoyrup, Arda Kolçak, Giuseppe Longo
2008 Theoretical Computer Science  
Crucial dynamical properties are transferred to it, while allowing an investigation of stability and chaoticity, in terms of computability, in particular in the presence of singularities.  ...  (Preliminary or revised versions of Longo's papers are downloadable from: or Search: Google: Giuseppe Longo).  ...  Unfortunately when Ruelle, in the '70s, proposed this very effective -and popular -name for Turing's exponential drift, he was not aware of Turing's morphogenesis paper.  ... 
doi:10.1016/j.tcs.2008.01.048 fatcat:pbesijwghngjzioblranl242ty

Adding continuous components to L-systems [chapter]

A. Lindenmayer
1974 Lecture Notes in Computer Science  
It ~S proposed that we can make use of some of the L-system results for these continuous component models.  ...  Constructions are shown for cellular developmental models with continuous parameters~ such as concentration of nutrients or inhibitors~ size and age of cells or compartments.  ...  Turing's diffusion-reaction model i for morphogenesis, a considerable number of developmental models have been published with computer instructions and partly based on the production~ diffusion~ and decomposition  ... 
doi:10.1007/3-540-06867-8_3 fatcat:u53im546m5b4hnvr5ucsh4schm

Pattern formation on networks with reactions: A continuous-time random-walk approach

C. N. Angstmann, I. C. Donnelly, B. I. Henry
2013 Physical Review E  
We derive the generalized master equation for reaction-diffusion on networks from an underlying stochastic process, the continuous time random walk (CTRW).  ...  Here we focus attention on CTRWs with exponential waiting times for two cases; one in which the rate parameter is constant for all vertices and the other where the rate parameter is proportional to the  ...  That is to say the particles will jump from vertex to vertex on the network according to the edges present.  ... 
doi:10.1103/physreve.87.032804 fatcat:kdumwkdujjbbndp3sqdfnk7lnm

Complexity and self-organization in Turing [article]

Jean Petitot
2015 arXiv   pre-print
We comment on Alan Turing's celebrated paper "The Chemical Basis of Morphogenesis" published in 1952 in the "Philosophical Transactions of the Royal Society of London".  ...  We will first do them for the continuous model and then return to Turing's own discrete model.  ...  Turing's foresightedness In his 1990 paper "Turing's theory of morphogenesis.  ... 
arXiv:1502.05328v1 fatcat:qqvglgengbanxo4kzjy44jqroy

Modifying Reaction Diffusion: A Numerical Model for Turing Morphogenesis, Ben Jacob Patterns, and Cancer Growth [article]

Kai Trepka
2018 bioRxiv   pre-print
Here, applications of such an approach to a few model problems are presented - morphogenesis, bacterial growth, and cancer treatment.  ...  Often, complex systems of development or signaling pathways can be explained and modeled to a high degree of accuracy with only a few simplifying assumptions.  ...  based on the previous timepoint, the diffusion constant, and a discretized version of the Laplacian from the diffusion equation.  ... 
doi:10.1101/370304 fatcat:mqdm5rkppne57bz6u7ckcctn2q

Alan Turing: His Work and Impact, A Book Review

Jeremy Avigad
2014 Notices of the American Mathematical Society  
Acknowledgments I am grateful to Thomas Hales and Robert Lewis for very helpful comments.  ...  "Intelligent machinery" in and of itself inaugurated the field of artificial intelligence, distinguished clearly between discrete and continuous models of computation, and even foreshadowed the study of  ...  Part II also devotes seven pages to excerpts from Turing's ninety-page programmer's handbook for a successor to the Baby, known as the Ferranti Mark I.  ... 
doi:10.1090/noti1160 fatcat:zfa7r42cbrgj5ellguokh23xua

Towards an integrated experimental-theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis

K. J. Painter, G. S. Hunt, K. L. Wells, J. A. Johansson, D. J. Headon
2012 Interface Focus  
test the theory and, encouragingly, a number of systems have emerged that appear to conform to some of Turing's fundamental ideas.  ...  In his seminal 1952 paper, 'The Chemical Basis of Morphogenesis', Alan Turing lays down a milestone in the application of theoretical approaches to understand complex biological processes.  ...  We acknowledge funding from the Leverhulme Trust (RF-2011-045) and BBSRC.  ... 
doi:10.1098/rsfs.2011.0122 pmid:23919127 pmcid:PMC3363042 fatcat:5spwgk5c4feuvpkiv6gcwpdkvi

Incomputability after Alan Turing

S. Barry Cooper
2012 Notices of the American Mathematical Society  
As we move up the informational-type structure from discrete to continuous data, we lose the sure footholds but identify emergent controls at higher levels.  ...  in morphogenesis.  ... 
doi:10.1090/noti866 fatcat:4mtlv6oddzec3kr2gvta542w2i

Laplace, Turing and the "Imitation Game" Impossible Geometry [chapter]

Giuseppe Longo
2009 Parsing the Turing Test  
We shortly compare this tentative imitation with Turing's mathematical modelling of morphogenesis (his 1952 paper, focusing on continuous systems, as he calls non-linear dynamics, which are sensitive to  ...  From the physico-mathematical view point, the imitation game between man and machine, proposed by Turing in his 1950 paper for the journal "Mind", is a game between a discrete and a continuous system.  ...  A question from Jean Petitot and his interest have encouraged me to clarify  ... 
doi:10.1007/978-1-4020-6710-5_23 fatcat:tbybvft3tzfjzhwb3t3xilti4q

Experimental visually-guided investigation of sub-structures in three-dimensional Turing-like patterns [article]

Martin Skrodzki, Ulrich Reitebuch, Eric Zimmermann
2020 arXiv   pre-print
Young proposed a discretization of Turing's model, reducing it to an activator/inhibitor process on a discrete domain.  ...  From this model, the concept of three-dimensional Turing-like patterns was derived. In this paper, we consider this generalization to pattern-formation in three-dimensional space.  ...  The structures obtained from Young's discretizations of Turing's work are consequentially referred to as Turinglike patterns.  ... 
arXiv:2006.16676v1 fatcat:xhqtjyd5yrbgno5poek6ogrgme

Doing Justice to the Imitation Game [chapter]

Jean Lassègue
2009 Parsing the Turing Test  
Therefore, doing justice to the Imitation Game implies showing first that the formalist interpretation misses some crucial points in Turing's line of thought and secondly that the 1950 paper should not  ...  Interpreted from a formalist point of view, the Imitation game set up by Turing in his 1950 world-famous article amounts therefore to a test that would show, on a statistical basis, that the discrimination  ...  The computable framework was therefore, to Turing's own mind, not powerful enough to tackle the general morphogenetic problem of how it is possible for a discrete form to emerge from a shapeless continuous  ... 
doi:10.1007/978-1-4020-6710-5_11 fatcat:2ihhd6igzvcy5fep4cavzp42ua

Incomputability after Alan Turing [article]

S. Barry Cooper
2013 arXiv   pre-print
This article takes a Turing centenary look at how the interface between the computable world and the incomputable formed a central theme in Turing's work - from the early establishment of the standard  ...  Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s.  ...  As we move up the informational type structure from discrete to continuous data, we lose the sure footholds, but identify emergent controls at higher levels.  ... 
arXiv:1304.6363v1 fatcat:nh5lsf23pvedleymkatyjksivi

Turing Patterns with Turing Machines: Emergence and Low-level Structure Formation [article]

Hector Zenil
2012 arXiv   pre-print
However, his treatment of morphogenesis, and in particular a difficulty he identified relating to the uneven distribution of certain forms as a result of symmetry breaking, are key to connecting his theory  ...  But instead the approach developed here captures Turing's initial concern and provides a low-level solution to a more general question by way of the concept of algorithmic probability, thus bridging two  ...  But one of Turing's two approaches was very close to the current model of CA, at least with respect to some of its most basic properties (and not far from modern variations of continuous Cellular Automata  ... 
arXiv:1210.1572v1 fatcat:mcz7kd2uezgshdwze2mgkzq2ci

Page 21 of Geographical Analysis Vol. 28, Issue 1 [page]

1996 Geographical Analysis  
It should be noted that these competition/niche models—usually represented by interrelated logistics like the Lotka-Volterra type of equations—are related to the family of Turing’s model of biological  ...  morphogenesis, in which two cells interact via diffusion through a thin membrane.  ... 
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