Spirals in nature, in lab, and in simulations
1. Seashell spiral patterns
Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 ...
2. Spiral waves in the Belousov-Zhabotinsky reaction
3. Spiral waves and target patterns in the catalytic CO-oxidation on Pt(110)
(J CHEM PHYS 98 (12): 9977(1993))
4. Spirals in colonies of microorganism:cAMP spiral wave formation in Dyctiostelium discodeum
The most familiar strategy of cooperative behavior among such microorganism is attractive chemotaxis.
Colonies of the slime mold Dictyostelium discoideum bacteria,
when deprived of heat or moisture, start up their cross-talk,
this communication allows them to aggregate into multicellular bodies
that are more fit survive hardship. Certain cells, called pioneer cells,
release pulse of the compound cyclic adenosine monophosphate (cAMP),
and nearby cells then follow this chemical trail to its source.
Once a cell has emitted a burst of the chemoattractant,
it falls silence for several minute, as if recuperating from the exertion.
This refractory period means that, when a slime mold colony starts to undergo chemotaxis,
it behaves as an excitable medium, then there is no surprise that the slime mold shows
target and spiral patterns as BZ retraction.
cAMP spiral waves and target patterns
5. Inwardly rotating spiral waves (antispirals) in BZ-AOT
V.K. Vanag and I.R. Epstein, Science 294, 835-837 (2001)
6. Antispirals in a complex Ginzburg-Landau equation and more ...
KLEVECZ RR, PILLIOD J, BOLEN J,CHRONOBIOLOGY INTERNATIONAL 8 (1): 6-13 1991
BOLEN JL, DURAN O, KLEVECZ RR,PHYSICA D 67 (1-3): 245-256 AUG 15 1993
Klevecz RR,PHYSICA D 124 (1-3): 1-10 DEC 1 1998
WU XG, KAPRAL R,PHYSICAL REVIEW LETTERS 70 (13): 1940-1943 MAR 29 1993
Goryachev A, Chate H, Kapral R, PHYSICAL REVIEW LETTERS, 80 (4): 873-876 JAN 26 1998