Pattern formation


Diffusion limited aggregation in cheap industrial hand soap

Reaction diffusion equations, and diffusion limited aggregation and other models for pretty blobs and swirls arising from a small number of parameters.

How the leopard got its spots and other special cases in morphogenesis.

To mention:

  • Reaction diffusion equations
  • hallucinations
  • Turing, the Brusselator etc.
  • Can I file Lichtenberg figures here?
  • Diffusion-limited aggregation?
  • Lapalacian growth?
  • …abolutely any such model involving PDEs?

The Royal Society, Induction discharge

Patterns produced by electrical discharges on surfaces revealed by dusting with powdered red lead and sulphur. Sometimes termed ‘Lichtenberg figures’. These experiments were conducted at Cragside in Northumberland, England, using a Wimshurst machine (electrostatic generator) and two 10-gallon Leiden jars. Current was conveyed to two rod conductors with a spark gap at which coated wires discs or plates were positioned. Lord Armstrong exhibited figures of the type produced at the Royal Society soiree at Burlington House in London on 16 June 1897.

Team Prigogene have something to say about this presumably.

Ball, Philip. 2012. “Pattern Formation in Nature: Physical Constraints and Self-Organising Characteristics.” Architectural Design 82 (2): 22–27. https://doi.org/10.1002/ad.1375.
Eliazar, Iddo, and Joseph Klafter. 2009. “Universal Generation of Statistical Self-Similarity: A Randomized Central Limit Theorem.” Physical Review Letters 103 (4): 040602. https://doi.org/10.1103/PhysRevLett.103.040602.
Erban, Radek, Jonathan Chapman, and Philip Maini. 2007. “A Practical Guide to Stochastic Simulations of Reaction-Diffusion Processes.” April 15, 2007. http://arxiv.org/abs/0704.1908.
Halsey, Thomas C. 2000. “Diffusion-Limited Aggregation: A Model for Pattern Formation.” Physics Today 53 (11): 36–41. https://doi.org/10.1063/1.1333284.
Kauffman, Stuart A, and Sonke Johnsen. 1991. “Coevolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Coevolutionary Avalanches*.” Journal of Theoretical Biology 149: 467–505. https://doi.org/10.1016/S0022-5193(05)80094-3.
Kim, T., J. Sewall, A. Sud, and M. C. Lin. 2007. “Fast Simulation of Laplacian Growth.” IEEE Computer Graphics and Applications 27 (2): 68–76. https://doi.org/10.1109/MCG.2007.33.
Lomas, Andy. 2014. “Cellular Forms: An Artistic Exploration of Morphogenesis.” In SIGGRAPH Studio, 1–1. ACM Press. https://doi.org/10.1145/2619195.2656282.
Matsushita, M, and H Fujikawa. 1990. “Diffusion-Limited Growth in Bacterial Colony Formation.” Physica A: Statistical Mechanics and Its Applications 168 (1): 498–506.
Meakin, Paul. 1986. “A New Model for Biological Pattern Formation.” Journal of Theoretical Biology 118 (1): 101–13. https://doi.org/10.1016/S0022-5193(86)80011-X.
Turing, Alan Mathison. 1952. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society B: Biological Sciences 237 (641): 37–72. https://doi.org/10.1098/rstb.1952.0012.
Vicsek, Tamas. 1992. Fractal Growth Phenomena. 2 Sub. World Scientific Pub Co Inc.
Vicsek, Tamás. 1983. “Fractal Models for Diffusion Controlled Aggregation.” Journal of Physics A: Mathematical and General 16: –647. https://doi.org/10.1088/0305-4470/16/17/003.
Vicsek, Tamás, and Alexander S Szalay. 1987. “Fractal Distribution of Galaxies Modeled by a Cellular-Automaton-Type Stochastic Process.” Physical Review Letters 58 (26): 2818–21. https://doi.org/10.1103/PhysRevLett.58.2818.
Wolfram, Stephen. 1983. “Statistical Mechanics of Cellular Automata.” Reviews of Modern Physics 55 (3): 601–44. https://doi.org/10.1103/RevModPhys.55.601.
Zenil, Hector. 2012. “Turing Patterns with Turing Machines: Emergence and Low-Level Structure Formation.” October 4, 2012. http://arxiv.org/abs/1210.1572.