Reaction diffusion equations, and diffusion limited aggregation and other models for pretty blobs and swirls.
How the leopard got its spots.
- Reaction diffusion equations
- Turing, the Brusselator, morphogenesis etc.
- Can I file Lichtenberg figures here?
- Diffusion-limited aggregation?
- Lapalacian growth?
- …abolutely any such model involving PDEs?
- random fields
Thanks Royal Society:
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.
- Meak86: Paul Meakin (1986) A new model for biological pattern formation. Journal of Theoretical Biology, 118(1), 101–113. DOI
- ErCM07: Radek Erban, Jonathan Chapman, Philip Maini (2007) A practical guide to stochastic simulations of reaction-diffusion processes. ArXiv:0704.1908 [Physics, q-Bio].
- Loma14: Andy Lomas (2014) Cellular forms: an artistic exploration of morphogenesis. In SIGGRAPH Studio (pp. 1–1). ACM Press DOI
- KaJo91: Stuart A Kauffman, Sonke Johnsen (1991) Coevolution to the edge of chaos: Coupled fitness landscapes, poised states, and coevolutionary avalanches*. Journal of Theoretical Biology, 149, 467–505. DOI
- Hals00: Thomas C Halsey (2000) Diffusion-limited aggregation: a model for pattern formation. Physics Today, 53(11), 36–41. DOI
- MaFu90: M Matsushita, H Fujikawa (1990) Diffusion-limited growth in bacterial colony formation. Physica A: Statistical Mechanics and Its Applications, 168(1), 498–506.
- KSSL07: T. Kim, J. Sewall, A. Sud, M.C. Lin (2007) Fast Simulation of Laplacian Growth. IEEE Computer Graphics and Applications, 27(2), 68–76. DOI
- ViSz87: Tamás Vicsek, Alexander S Szalay (1987) Fractal distribution of galaxies modeled by a cellular-automaton-type stochastic process. Physical Review Letters, 58(26), 2818–2821. DOI
- Vics92: Tamas Vicsek (1992) Fractal Growth Phenomena. World Scientific Pub Co Inc
- Vics83: Tamás Vicsek (1983) Fractal models for diffusion controlled aggregation. Journal of Physics A: Mathematical and General, 16, 647. DOI
- Ball12: Philip Ball (2012) Pattern Formation in Nature: Physical Constraints and Self-Organising Characteristics. Architectural Design, 82(2), 22–27. DOI
- Wolf83: Stephen Wolfram (1983) Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3), 601–644. DOI
- Turi52: Alan Mathison Turing (1952) The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B: Biological Sciences, 237(641), 37–72. DOI
- Zeni12: Hector Zenil (2012) Turing Patterns with Turing Machines: Emergence and Low-level Structure Formation. ArXiv:1210.1572.
- ElKl09: Iddo Eliazar, Joseph Klafter (2009) Universal Generation of Statistical Self-Similarity: A Randomized Central Limit Theorem. Physical Review Letters, 103(4), 040602. DOI