Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-04T21:12:40.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Random growth in a tessellation

Published online by Cambridge University Press:  24 October 2008

Daniel Richardson
Daniel Richardson
Affiliation:
Department of Mathematics, Polytechnic of the South Bank, Borough Road, London S.E.1
Get access Rights & Permissions [Opens in a new window]

Extract

Let S be n dimensional Euclidean space and let T be a division of S into cells. Assume that each cell must be either white or black at any time t. At time 0 the cell at the origin, α0, is black and all other cells are white. Let G be some stochastic growth process which tends to change white cells with black neighbours into black cells. Let C(t) be the black shape at time t. For a family, F, of such growth processes we prove the following theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 3 , November 1973 , pp. 515 - 528
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Coxeter, H. S. M.Regular polytopes (London, Methuen, 1948).Google Scholar
(2)Eden, M. A two-dimensional growth process. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. IV. Biology and problems of health, ed. Neyman, J. (1961).Google Scholar
(3)Hammersley, J. M.First passage percolation, J. Roy. Statist. Soc. 28, 1966.Google Scholar
(4)Hammersley, J. M. and Welsh, D. J. First passage percolation, subadditive processes, stochastic networks, and generalized renewal theory, in Bernoulli (1723), Bayes (1763), Laplace (1813) (Springer-Verlag, 1965).Google Scholar
(5)Morogan, R. W. and Welsh, D. J.A two-dimensional Poisson growth process. J. Roy. Statist. Soc. 27, 1965.Google Scholar
(6)Williams, T. and Bjerknes, R.A stochastic model for abnormal clone spread through epithelial basal layer. Nature 236, 3 03 1972.CrossRefGoogle ScholarPubMed