http://bactra.org/notebooks Cosma's Notebooks en http://bactra.org/notebooks/2009/04/10#pattern-formation <blockquote><em>Spiral leads me to sleep</em></blockquote> <P>I should probably spin off reaction-diffusion models as a separate notebook. <P>See also: <a href="cellular-automata.html">Cellular Automata</a>; <a href="complexity.html">Complexity</A>; <a href="development-bio.html">Developmental Biology</a>; <a href="dissipative-structures.html">Dissipative Structures</a>; <a href="chaos.html">Nonlinear Dynamics</a>; <a href="self-organization.html">Self-Organization</a>; <a href="slime-molds.html">Slime Molds</a>; <a href="spatial-statistics.html">Spatial Statistics and Spatial Stochastic Processes</a>; <a href="winding-number.html">Winding Number</a> <ul>Recommended: <li>Philip Ball, <cite>The Self-Made Tapestry: Pattern Formation in Nature</cite> [<a href="../reviews/self-made-tapestry/">Review: The Blind Snowflake-Maker</a>] <li>Eric Bonabeau, "From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation," <cite>Artifical Life</cite> <strong>3</strong> (1997): 191--211 <li>John Tyler <a href="j-t-bonner.html">Bonner,</a> <cite>On Development</cite> <li>M. C. Cross and P. C. Hohenberg, <cite>Pattern Formation out of Equilibrium</cite> (a.k.a. <cite>Reviews of Modern Physics</cite> <strong>65</strong> (1993) 851-1112 [<a href="../reviews/cross-and-hohenberg/">Review</a>] <li>David Griffeath, <a href="http://psoup.wisc.edu/">Primordial Soup Kitchen</a> <li>Gemunu H. Gunaratne, David K. Hoffman and Donald J. Kouri, "Characterization of Natural Patterns," <cite>Physical Review E</cite> <strong>57</strong> (1998): 5146--5149 <li>Gemunu H. Gunaratne, Anuradha Ratnaweera and K. Tennekone, "Emergence of Order in Textured Patterns," <a href="http://arxiv.org/abs/patt-sol/9809001">patt-sol/9809001</a> <li>Lionel Harrison, <cite>Kinetic Theory of Living Form</cite> <li>Paul Manneville, <cite>Dissipative Structures and Weak Turbulence</cite> <li>Przemyslaw Prusinkiewicz and Mark Hammel, <cite><a href="http://www.cpsc.ucalgary.ca/projects/bmv/vmm/title.html">Visual Models of Morphogenesis: A Guided Tour</a></cite> <li>Thimo Rohlf and Stefan Bornholdt <ul> <li>"Self-organized pattern formation and noise-induced control from particle computation", <a href="http://arxiv.org/abs/cond-mat/0312366">cond-mat/0312366</a> [Short version] <li>"Morphogenesis by coupled regulatory networks", <a href="http://arxiv.org/abs/q-bio.MN/0401024">q-bio.MN/0401024</a> [Long version] </ul> <li>Satoshi Sawai, Peter A. Thomason and Edward C. Cox, "An autoregulatory circuit for long-range self-organization in <em>Dictyostelium</em> cell populations", <a href="http://dx.doi.org/10.1038/nature03228"><cite>Nature</cite> <strong>433</strong> (2005): 323--326</a> <li>Peter S. Stevens, <cite>Patterns in Nature</cite> <li>Ian Stewart and Golubitsky, <cite>Fearful Symmetry</cite> [Groups, symmetries, broken symmetries and pattern-formation for the non-mathematical] <li><a href="darcy-thompson.html">D'Arcy Wentworth Thompson</a>, <cite>On Growth and Form</cite> <li>Vladimir K. Vanang and Irving R. Epstein, "Stationary and Oscillatory Localized Patterns, and Subcritical Bifurcations", <a href="http://link.aps.org/abstract/PRL/v92/e128301"><citE>Physical Review Letters</cite> <strong>92</strong> (2004): 128301</a> <li>Arthur Winfree <ul> <li><cite>When Time Breaks Down</cite> <li><cite>The Geometry of Biological Time</cite> </ul> </ul> <ul>To read: <li>Edward R. Abraham, "Sea urchin feeding fronts", <a href="http://arxiv.org/abs/q-bio.PE/0610004">q-bio.PE/0610004</a> <li>Mark S. Alber, Yi Jiang and Maria A. Kiskowski, "Lattice gas cellular automata model for rippling and aggregation in myxobacteria", <a href="http://arxiv.org/abs/q-bio/0401014">q-bio/0401014</a> <li>Aris, Aronson + Swinney, <cite>Patterns and Dynamics in Reactive Media</cite> <li>J. Buceta, Katja Lindenberg, and J. M. R. Parrondo, "Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching," <a href="http://arxiv.org/abs/cond-mat/0110542">cond-mat/0110542</a> <li>A. Carpio, "Wave trains, self-oscillations and synchronization in discrete media", <a href="http://arxiv.org/abs/cond-mat/0506119">cond-mat/0506119</a> <li>Pierre-Henri Chavanis, "A stochastic Keller-Segel model of chemotaxis", <a href="http://arxiv.org/abs/0804.4425">arxiv:0804.4425</a> <li>Elisheva Cohen, David A. Kessler and Herbert Levine, "Fluctuation-Regularized Front Propagation Dynamics in Reaction-Diffusion Systems", <a href="http://dx.doi.org/10.1103/PhysRevLett.94.158302"><cite>Physical Review Letters</cite> <strong>94</strong> (2005): 158302</a> <li>Catherine Crawford and Hermann Riecke, "Oscillon-Type Structures and Their Interaction in a Swift-Hohenberg Model," <a href="http://arxiv.org/abs/patt-sol/9804005">patt-sol/9804005</a> <li>Karen E. Daniels, Christian Beck and Eberhard Bodenschatz, "Defect turbulence and generalized statistical mechanics," <a href="http://arxiv.org/abs/cond-mat/0302623">cond-mat/0302623</a> <li>J&ouml;rn Davidsen, Ronaldo Erichsen, Raymond Kapral and Hughes Chat&eacute;, "From ballistic to Brownian vortex motion in complex oscillatory media", <cite>Physical Review Letters</cite> <strong>93</strong> (2004): 018305 = <a href="http://arxiv.org/abs/nlin.PS/0410033">nlin.PS/0410033</a> <li>Epstein and Pojman, <citE>An Introduction to Nonlinear Chemical Dynamics</cite> <li>Amatzia Genin, Jules S. Jaffe, Ruth Reef, Claudio Richter, Peter J. S. Franks, "Swimming Against the Flow: A Mechanism of Zooplankton Aggregation", <a href="http://dx.doi.org/10.1126/science.1107834"><cite>Science</cite> <strong>308</strong> (2005): 860--862</a> <li>Solomon W. Golomb, <cite>Polyominoes</cite> illus. Waren Lushbaugh <li>Nigel Goldenfeld, Pak Yuen Chan and john Veysey, "Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs", <a href="http://dx.doi.org/10.1103/PhysRevLett.96.254501"><cite>Physical Revieew Letters</cite> <strong>96</strong> (2006): 254501</a> = <a href="http://arxiv.org/abs/nlin.PS/0601028">nlin.PS/0601028</a> <li>Roman O. Grigoriev and Andreas Handel, "Nonnormality and the localized control of extended systems," <a href="http://arxiv.org/abs/nlin.PS/0207023">nlin.PS/0207023</a> <li>Ramon Grima, "Strong-coupling dynamics of a multi-cellular chemotactic system", <a href="http://arxiv.org/abs/q-bio.CB/0505004">q-bio.CB/0505004</a> <li>Peter Grindrod, <cite>Theory and Application of Reaction Diffusion Equations: Patterns and Waves</cite> <li>Kevin Hall and Leon Glass, "How to Tell a Target from a Spiral: The Two Probe Problem," <cite>Physical Review Letters</cite> <strong>82</strong> (1999): 5164--5167 <li>Rebecca Hoyle, <cite>Pattern Formation: An Introduction to Methods</cite> [<a href="http://cambridge.org/0521817501">Blurb</a>] <li>Lukas Jahnke and Jan W. Kantelhardt, "Comparison of models and lattice-gas simulations for Liesegang patterns", <a href="http://arxiv.org/abs/0803.3634">arxiv:0803.3634</a> <li>Y. Kuramoto, <cite>Chemical Oscillations, Waves, and Turbulence</cite> [Now re-issued as a cheap Dover paperback] <li>Julio Largo, Piero Tartaglia, Francesco Sciortino, "Effective non-additive pair potential for lock-and-key interacting particles: the role of the limited valence", <a href="http://arxiv.org/abs/cond-mat/0703383">cond-mat/0703383</a> <li>Men Li, Heimo Schnablegger and Stephen Mann, "Coupled Synthesis and Self-Assembly of Nanoparticles to Give Structures with Controlled Organization," <cite>Nature</cite> <strong>402</strong> (1999): 393--395 <li>Markus Loecher, <cite>Noise Sustained Patterns: Fluctuations and Nonlinearities</cite> <li>Juan M. Lopez and Henrik J. Jensen, "Generic model of morphological changes in growing colonies of fungi," <a href="http://arxiv.org/abs/cond-mat/0110509">cond-mat/0110509</a> <li>Paul Manneville, <cite>Instabilities, Chaos and Turbulence</cite> <li>Jonathan H. McCoy, Will Brunner, Werner Pesch and Eberhard Bodenschatz, "Self-Organization of Topological Defects due to Applied Constraints", <a href="http://dx.doi.org/10.1103/PhysRevLett.101.254102"><cite>Physical Review Letters</cite> <strong>101</strong> (2008): 254102</a> <li>K. R. Mecke and D. stoyan (eds.), <cite>Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation</cite> <li>Girish Nathan and Gemunu Gunaratne, "Set of measures to analyze the dynamics of nonequilibrium structures", <a href="http://dx.doi.org/10.1103/PhysRevE.71.035101"><cite>Physical Review E</cite> <strong>71</strong> (2005): 035101(R)</a> <li>David R. Nelson, <cite>Defects and Geometry in Condensed Matter Physics</cite> [<a href="http://cambridge.org/9780521004008">blurb</a>] <li>Wouter-Jan Rappel, Alastair Nicol, Armand Sarkissian, Herbert Levine and William F. Loomis, "Self-Organized Vortex State in Two-Dimensional <em>Dictyostelium</em> Dynamics," <a href="http://arxiv.org/abs/patt-sol/9811001">patt-sol/9811001</a> <li>D. Reguera (ed.), <cite>Coherent Structures in Complex Systems</cite> <li>Hermann Riecke, "Localized Structures in Pattern-Forming Systems," <a href="http://arxiv.org/abs/patt-sol/9810002">patt-sol/9810002</a> <li>Jori E. Ruppert-Felsot, Olivier Praud, Eran Sharon, Harry L. Swinney, "Extraction of coherent structures in a rotating turbulent flow experiment", <a href="http://arxiv.org/abs/physics/0410161">physics/0410161</a> <li>J. M. Sancho and Jordi Garcia-Ojalvo, "Noise-Induced Order in Extended Systems: A Tutorial", <a href="http://arxiv.org/abs/cond-mat/0608511">cond-mat/0608511</a> <li>Sumithra Sankararaman, Gautam I. Menon and P. B. Sunil Kumar, "Self-organized pattern formation in motor-microtubule mixtures", <a href="http://dx.doi.org/10.1103/PhysRevE.70.031905"><cite>Physical Review E</cite> <strong>70</strong> (2004): 031905</a> <li>Smoller, <cite>Shock Waves and Reaction-Diffusion Equations</cite> <li>Swinney and Krinsky (eds). <cite>Waves and Patterns</cite> (a.k.a. <cite>Phyisca D</cite> <strong>49</strong>) <li>Uwe C. Tauber, Martin Howard and Benjamin P. Vollmayr-Lee, "Applications of field-theoretic renormalization group methods to reaction-diffusion problems", <a href="http://dx.doi.org/10.1088/0305-4470/38/17/R01"><cite>Journal of Physics A</cite> <strong>38</strong> (2005): 79--131</a> = <a href="http://arxiv.org/abs/cond-mat/0501678">cond-mat/0501678</a> <li>Steffen Trimper and Knud Zabrocki, "Memory Driven Pattern Formation", <a href="http://arxiv.org/abs/cond-mat/0406269">cond-mat/0406269</a> <li><cite>25 Years of Non-Equilibrium Statistical Mechanics: Proceedings, Sitges, Barcelona, 1994</cite> <li>Paul Umbanhowar, <a href="http://chaos.ph.utexas.edu/~pbu/granular.html">Pattern Formation in Granular Materials</a> <li>Daniel Walgraef, <cite>Spatio-temporal Pattern Formation: with Examples from Physics, Chemistry and Materials Science</cite> <li>Stephen Whitelam and Phillip L. Geissler, "Cluster algorithm for pairwise-interacting particles", <a href="http://arxiv.org/abs/cond-mat/0508100">cond-mat/0508100</a> [with special application to self-assembling particle systems] <li>Lancelot Whyte (ed.). <cite>Aspects of Form</cite> <li>H. S. Wio, S. Bouzat and B. von Haeften, "Stochastic Resonance in Spatially Extended Systems: The Role of Far from Equilibrium Potentials," <a href="http://arxiv.org/abs/cond-mat/0109452">cond-mat/0109452</a> </ul>