patterns in nature 5 spatial patterns · 2012-09-29 · patterns in nature outline 1. introduction...
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Patterns in Nature 5Spatial patterns
Stephan Matthiesen
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Activator-Inhibitor Model(Turing 1953)
Alan Turing (1912-1954)
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Activator-Inhibitor Model
feedback: part of a system’s output influences the input positive feedback: the system responds to perturbations in the same direction as the perturbation negative feedback: it responds in opposite direction
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“Tiger bush”
100 m
Rietkerk; v.d. Koppel 2008
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Wetland ecosystems
100 m
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Savannah
200 m
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Coral reefs
20 km
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Intertidal mudflats
1 m
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Zebras
(a) Imperial zebra (Equus grevyi)(b) Mountain zebra (Equus zebra)(c) Common zebra (Equus burchelli)(d) Quagga (Equus quagga). Bard 1977
Common Zebra: week 3
Mountain Zebra: week 4Imperial Zebra: week 5A B
C D
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Leopard
2 days: spots
8 weeks: rings
Adult: rosettes
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Jaguar5 weeks: spots
3 months:irregular rings
Adult:small spots enclosed by irregular polygons
Liu, Liaw, Maini 2006
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Two-stage modelfor the Jaguar
First Stage Second stage(with different parameters)
Liu, Liaw, Maini 2006
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Hexagonal patterns
Soap bubbles
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Rayleigh-Benard convectionLane; Christensen 2000
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Polygonson Mars
Lane; Christensen 2000
http://www.coasttocoastam.com//gen/page207.html
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Martian Polygons
Lane, Christensen 2000
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Patterns inpermafrost
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Columnar jointing
de.wikipedia.org
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Giant's causeway
Jagla; Rojo (2002)
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Create your ownGiant's Causeway
• Mix cornflour with equal volume of water;add some bleach (to stop the mould)
• Not part of the experiment, but great fun: Mess around with it, try to stir it quickly and slowly, drop objects in it.
• Fill into a plastic cup, at least 3-4 cm deep• Leave open in a warm, dry place until the
stuff is completely dry (1-2 weeks)• Look at the cracks on the surface• Cut off the plastic cup, break the starch and
see the columnar jointing
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When we did the experiment...
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When we did the experiment...
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An experimentwith cornstarch
Goehring (2003); Goehring, Morris, Lin (2006)
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Maturation of crack patterns
Jagla 2004
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And honeycombs?
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Patterns in NatureOutline
1. Introduction2. Waves and oscillations3. Regularity and chaos4. Animal cooperation 5. Spatial patterns6. Aggregation and growth processes 7. Cellular automata8. Fractals9. Miscellaneous topics 10. Concluding session
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Literature
Ball, P. (1999): The self-made tapestry. Rietkerk, van de Koppel (2008). Trends in
Ecology&Evolution Jagla, Rojo (2002). Phys. Rev. E. 65, 026203 Jagla (2004). Phys. Rev. E. 69, 056212 Goehring (2003), MSc thesis; available at:
http://www.msm.cam.ac.uk/wjc/Lucas/Papers.html Goehring, Morris, Lin (2006): Phys. Rev. E. 74, 036115 Lane, Christensen (2000). JGR 105 (E7), 17617 Bard, J. B. L. 1977. J. Zool. (London) 183: 527-539