Organizing centres for three-dimensional chemical waves

Excitable media propagate periodic waves of chemical activity. In three dimensions, they resemble scrolls rotating about axes where reactions are not periodic. These axes close in rings which may be linked and knotted, in ways limited by an exclusion principle.

[1]  A. Winfree.  Spiral Waves of Chemical Activity , 1972, Science.

[2]  A. Winfree,et al.  Scroll-Shaped Waves of Chemical Activity in Three Dimensions , 1973, Science.

[3]  M. Strutt,et al.  Die folgen einiger elektronenträgheitseffekte in elektronenrohren II: Anwendungen und numerische ergebnisse , 1942 .

[4]  Sir William Thomson F.R.S..  II. On vortex atoms , 1867 .

[5]  John Tyler Bonner,et al.  The Cellular Slime Molds. , 1967 .

[6]  J Bures,et al.  Spiral waves of spreading depression in the isolated chicken retina. , 1983, Journal of neurobiology.

[7]  James R. Munkres,et al.  Topology; a first course , 1974 .

[8]  D Durrer,et al.  Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements , 1980, Circulation research.

[9]  A. T. Winfree,et al.  The prehistory of the Belousov-Zhabotinsky oscillator , 1984 .

[10]  H. Helmholtz.  LXIII. On Integrals of the hydrodynamical equations, which express vortex-motion , 1858 .

[11]  A. Winfree.  The geometry of biological time , 1991 .

[12]  P. Devreotes,et al.  Adenosine 3',5'-monophosphate waves in Dictyostelium discoideum: a demonstration by isotope dilution--fluorography. , 1981, Science.

[13]  V. I. Krinsky,et al.  Multi-armed vortices in an active chemical medium , 1982, Nature.

[14]  Arthur T. Winfree,et al.  Rotating Chemical Reactions , 1974 .

[15]  John E. Smith.  Fungal differentiation. A contemporary synthesis. , 1983 .

[16]  Donald P. Greenberg,et al.  A Comprehensive Light-Source Description for Computer Graphics , 1984, IEEE Computer Graphics and Applications.

[17]  A. Zhabotinsky,et al.  Concentration Wave Propagation in Two-dimensional Liquid-phase Self-oscillating System , 1970, Nature.

[18]  Brian J. Welsh,et al.  Three-dimensional chemical waves in the Belousov–Zhabotinskii reaction , 1983, Nature.

[19]  M. Allessie,et al.  Circus Movement in Rabbit Atrial Muscle as a Mechanism of Tachycardia , 1973, Circulation research.

[20]  O. Burešová,et al.  The mechanism and applications of Leão's spreading depression of electroencephalographic activity , 1974 .

[21]  J. Buresˇ,et al.  Circulation of cortical spreading depression around electrically stimulated areas and epileptic foci in the neocortex of rats , 1979, Brain Research.

[22]  F. Crick.  Linking numbers and nucleosomes. , 1976, Proceedings of the National Academy of Sciences of the United States of America.

[23]  R. J. Field,et al.  Oscillations and Traveling Waves in Chemical Systems , 1985 .

[24]  A. Winfree.  Two kinds of wave in an oscillating chemical solution , 1974 .

[25]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions: I. Geometrically simple waves , 1983 .

[26]  F. B. Fuller.  The writhing number of a space curve. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[27]  A. Kleber,et al.  Flow of “Injury” Current and Patterns of Excitation during Early Ventricular Arrhythmias in Acute Regional Myocardial Ischemia in Isolated Porcine and Canine Hearts: Evidence for Two Different Arrhythmogenic Mechanisms , 1980, Circulation research.

[28]  S. Strogatz,et al.  Singular filaments organize chemical waves in three dimensions: III. Knotted waves , 1983 .

[29]  A. Winfree,et al.  Sudden Cardiac Death: A Problem in Topology , 1983 .

[30]  William F. Pohl,et al.  DNA and differential geometry , 1980 .