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Distortion of certain Voronoi tesselations when one particle moves

  • Luis-M. Cruz Orive (a1)

Abstract

Some properties of the Voronoi polygon associated with a moving particle in a regular tessellation are studied. In particular, the area of the variable polygon has played a relevant role in previous studies on plant competition, animal predation, adjustment of the sex ratio in bisexual populations and the gregarious behaviour of animal species.

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Postal address: Department of Anatomy, University of Bern, Bühlstrasse 26, CH-3000 Bern 9, Switzerland.

References

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Cannings, C. and Cruz Orive, L.-M. (1975) On the adjustment of the sex ratio and the gregarious behaviour of animal populations. J. Theoret. Biol. 55, 115136.
Fischer, R. A. and Miles, R. E. (1973) The role of spatial pattern in the competition between crop plants and weeds. A theoretical analysis. Math. Biosci. 18, 335350.
Halmos, P. R. (1974) Measure Theory. Springer–Verlag, New York.
Hamilton, W. D. (1971) Geometry for the selfish herd. J. Theoret. Biol. 31, 295311.
Robbins, H. E. (1944) On the measure of a random set. Ann. Math. Statist. 15, 7074.
Rogers, C. A. (1964) Packing and Covering. Cambridge University Press.

Keywords

Distortion of certain Voronoi tesselations when one particle moves

  • Luis-M. Cruz Orive (a1)

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