Pattern formation

Last update: 21 Apr 2025 21:17
First version: 17 August 1995

Spiral leads me to sleep

I should probably spin off reaction-diffusion models as a separate notebook.

Philip Ball, The Self-Made Tapestry: Pattern Formation in Nature [Review: The Blind Snowflake-Maker]
M. C. Cross and P. C. Hohenberg, "Pattern Formation out of Equilibrium", Reviews of Modern Physics 65 (1993) 851--1112 [Review]
Peter S. Stevens, Patterns in Nature
Ian Stewart and Golubitsky, Fearful Symmetry [Groups, symmetries, broken symmetries and pattern-formation for the non-mathematical]
D'Arcy Wentworth Thompson, On Growth and Form

Eric Bonabeau, "From Classical Models of Morphogenesis to Agent-Based Models of Pattern Formation," Artifical Life 3 (1997): 191--211
John Tyler Bonner, On Development
Janko Gravner and David Griffeath, Snowfakes [Models of snow-crystal formation]
David Griffeath, Primordial Soup Kitchen
Gemunu H. Gunaratne, David K. Hoffman and Donald J. Kouri, "Characterization of Natural Patterns," Physical Review E 57 (1998): 5146--5149
Gemunu H. Gunaratne, Anuradha Ratnaweera and K. Tennekone, "Emergence of Order in Textured Patterns," patt-sol/9809001
Lionel Harrison, Kinetic Theory of Living Form
Paul Manneville, Dissipative Structures and Weak Turbulence
Przemyslaw Prusinkiewicz and Mark Hammel, Visual Models of Morphogenesis: A Guided Tour
Thimo Rohlf and Stefan Bornholdt
- "Self-organized pattern formation and noise-induced control from particle computation", cond-mat/0312366 [Short version]
- "Morphogenesis by coupled regulatory networks", q-bio.MN/0401024 [Long version]
Satoshi Sawai, Peter A. Thomason and Edward C. Cox, "An autoregulatory circuit for long-range self-organization in Dictyostelium cell populations", Nature 433 (2005): 323--326
Vladimir K. Vanang and Irving R. Epstein, "Stationary and Oscillatory Localized Patterns, and Subcritical Bifurcations", Physical Review Letters 92 (2004): 128301
Arthur Winfree
- When Time Breaks Down
- The Geometry of Biological Time

Edward R. Abraham, "Sea urchin feeding fronts", q-bio.PE/0610004
John A. Adam, Mathematics in Nature: Modeling Patterns in the Natural World
Mark S. Alber, Yi Jiang and Maria A. Kiskowski, "Lattice gas cellular automata model for rippling and aggregation in myxobacteria", q-bio/0401014
Aris, Aronson + Swinney, Patterns and Dynamics in Reactive Media
Kenneth A. Brakke, The Motion of a Surface by Its Mean Curvature [1978]
J. Buceta, Katja Lindenberg, and J. M. R. Parrondo, "Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching," cond-mat/0110542
A. Carpio, "Wave trains, self-oscillations and synchronization in discrete media", cond-mat/0506119
Pierre-Henri Chavanis, "A stochastic Keller-Segel model of chemotaxis", arxiv:0804.4425
Elisheva Cohen, David A. Kessler and Herbert Levine, "Fluctuation-Regularized Front Propagation Dynamics in Reaction-Diffusion Systems", Physical Review Letters 94 (2005): 158302
Pierre Collet and Jean-Pierre Eckmann, Instabilities and Fronts in Extended Systems
Catherine Crawford and Hermann Riecke, "Oscillon-Type Structures and Their Interaction in a Swift-Hohenberg Model," patt-sol/9804005
Karen E. Daniels, Christian Beck and Eberhard Bodenschatz, "Defect turbulence and generalized statistical mechanics," cond-mat/0302623
Jörn Davidsen, Ronaldo Erichsen, Raymond Kapral and Hughes Chaté, "From ballistic to Brownian vortex motion in complex oscillatory media", Physical Review Letters 93 (2004): 018305 = nlin.PS/0410033
Epstein and Pojman, An Introduction to Nonlinear Chemical Dynamics
Amatzia Genin, Jules S. Jaffe, Ruth Reef, Claudio Richter, Peter J. S. Franks, "Swimming Against the Flow: A Mechanism of Zooplankton Aggregation", Science 308 (2005): 860--862
Solomon W. Golomb, Polyominoes illus. Waren Lushbaugh
Nigel Goldenfeld, Pak Yuen Chan and john Veysey, "Dynamics of Precipitation Pattern Formation at Geothermal Hot Springs", Physical Revieew Letters 96 (2006): 254501 = nlin.PS/0601028
Roman O. Grigoriev and Andreas Handel, "Nonnormality and the localized control of extended systems," nlin.PS/0207023
Ramon Grima, "Strong-coupling dynamics of a multi-cellular chemotactic system", q-bio.CB/0505004
Peter Grindrod, Theory and Application of Reaction Diffusion Equations: Patterns and Waves
Kevin Hall and Leon Glass, "How to Tell a Target from a Spiral: The Two Probe Problem," Physical Review Letters 82 (1999): 5164--5167
Rebecca Hoyle, Pattern Formation: An Introduction to Methods
Lukas Jahnke and Jan W. Kantelhardt, "Comparison of models and lattice-gas simulations for Liesegang patterns", arxiv:0803.3634
Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence [Now re-issued as a cheap Dover paperback]
Julio Largo, Piero Tartaglia, Francesco Sciortino, "Effective non-additive pair potential for lock-and-key interacting particles: the role of the limited valence", cond-mat/0703383
Men Li, Heimo Schnablegger and Stephen Mann, "Coupled Synthesis and Self-Assembly of Nanoparticles to Give Structures with Controlled Organization," Nature 402 (1999): 393--395
Markus Loecher, Noise Sustained Patterns: Fluctuations and Nonlinearities
Juan M. Lopez and Henrik J. Jensen, "Generic model of morphological changes in growing colonies of fungi," cond-mat/0110509
Paul Manneville, Instabilities, Chaos and Turbulence
Jonathan H. McCoy, Will Brunner, Werner Pesch and Eberhard Bodenschatz, "Self-Organization of Topological Defects due to Applied Constraints", Physical Review Letters 101 (2008): 254102
K. R. Mecke and D. stoyan (eds.), Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation
Girish Nathan and Gemunu Gunaratne, "Set of measures to analyze the dynamics of nonequilibrium structures", Physical Review E 71 (2005): 035101(R)
David R. Nelson, Defects and Geometry in Condensed Matter Physics
Wouter-Jan Rappel, Alastair Nicol, Armand Sarkissian, Herbert Levine and William F. Loomis, "Self-Organized Vortex State in Two-Dimensional Dictyostelium Dynamics," patt-sol/9811001
D. Reguera (ed.), Coherent Structures in Complex Systems
Hermann Riecke, "Localized Structures in Pattern-Forming Systems," patt-sol/9810002
Jori E. Ruppert-Felsot, Olivier Praud, Eran Sharon, Harry L. Swinney, "Extraction of coherent structures in a rotating turbulent flow experiment", physics/0410161
J. M. Sancho and Jordi Garcia-Ojalvo, "Noise-Induced Order in Extended Systems: A Tutorial", cond-mat/0608511
Sumithra Sankararaman, Gautam I. Menon and P. B. Sunil Kumar, "Self-organized pattern formation in motor-microtubule mixtures", Physical Review E 70 (2004): 031905
Smoller, Shock Waves and Reaction-Diffusion Equations
Swinney and Krinsky (eds). Waves and Patterns (a.k.a. Phyisca D 49)
Uwe C. Tauber, Martin Howard and Benjamin P. Vollmayr-Lee, "Applications of field-theoretic renormalization group methods to reaction-diffusion problems", Journal of Physics A 38 (2005): 79--131 = cond-mat/0501678
Steffen Trimper and Knud Zabrocki, "Memory Driven Pattern Formation", cond-mat/0406269
25 Years of Non-Equilibrium Statistical Mechanics: Proceedings, Sitges, Barcelona, 1994
Paul Umbanhowar, Pattern Formation in Granular Materials
Daniel Walgraef, Spatio-temporal Pattern Formation: with Examples from Physics, Chemistry and Materials Science
Stephen Whitelam and Phillip L. Geissler, "Cluster algorithm for pairwise-interacting particles", cond-mat/0508100 [with special application to self-assembling particle systems]
Lancelot Whyte (ed.). Aspects of Form
H. S. Wio, S. Bouzat and B. von Haeften, "Stochastic Resonance in Spatially Extended Systems: The Role of Far from Equilibrium Potentials," cond-mat/0109452