Division rules for polygonal cells.
A number of fascinating mathematical problems concerning the division of two-dimensional space are formulated from questions about the planes of cell division in embryonic epithelia. Their solution aids in the quantitative description of cellular arrangement in epithelia. Cells, considered as polygons, site their division line according to stochastic rules, eventually forming a tessellation of the plane. The equilibrium distributions for the resulting mix of polygonal types are explored for a range of stochastic rules. We find surprising links with some classical distributions from the theory of probability.
CSIRO Division of Mathematics and Statistics, Lindfield, NSW, Australia.
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R
Cowan
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Morris
D002455:Cell Division; D004848:Epithelium / Q000196:embryology*; D008433:Mathematics; D009154:Mutation