Pattern formation

December 23, 2014 — October 9, 2018

chemistry
generative art
life
photon choreography
self similar
spatial
statmech
stochastic processes
Figure 1: 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:

Figure 2: 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.

1 References

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Halsey. 2000. “Diffusion-Limited Aggregation: A Model for Pattern Formation.” Physics Today.
Kauffman, and Johnsen. 1991. “Coevolution to the Edge of Chaos: Coupled Fitness Landscapes, Poised States, and Coevolutionary Avalanches*.” Journal of Theoretical Biology.
Kim, Sewall, Sud, et al. 2007. “Fast Simulation of Laplacian Growth.” IEEE Computer Graphics and Applications.
Lomas. 2014. “Cellular Forms: An Artistic Exploration of Morphogenesis.” In SIGGRAPH Studio.
Matsushita, and Fujikawa. 1990. “Diffusion-Limited Growth in Bacterial Colony Formation.” Physica A: Statistical Mechanics and Its Applications.
Meakin. 1986. “A New Model for Biological Pattern Formation.” Journal of Theoretical Biology.
Turing. 1952. “The Chemical Basis of Morphogenesis.” Philosophical Transactions of the Royal Society B: Biological Sciences.
Vicsek, Tamás. 1983. “Fractal Models for Diffusion Controlled Aggregation.” Journal of Physics A: Mathematical and General.
Vicsek, Tamas. 1992. Fractal Growth Phenomena.
Vicsek, Tamás, and Szalay. 1987. “Fractal Distribution of Galaxies Modeled by a Cellular-Automaton-Type Stochastic Process.” Physical Review Letters.
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Zenil. 2012. “Turing Patterns with Turing Machines: Emergence and Low-Level Structure Formation.” arXiv:1210.1572.