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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
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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

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References

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