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A mosaic of triangular cells formed with sequential splitting rules

Part of:Distribution theory - ProbabilityMarkov processesTheory of computingGeometric probability and stochastic geometryDiscrete mathematics in relation to computer science

Published online by Cambridge University Press:  14 July 2016

Richard Cowan
Richard Cowan*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: richardc@maths.usyd.edu.au
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Abstract

The iterative division of a triangle by chords which join a randomly-selected vertex of a triangle to the opposite side is investigated. Results on the limiting random graph which eventuates are given. Aspects studied are: the order of vertices; the fragmentation of chords; age distributions for elements of the graph; various topological characterisations of the triangles. Different sampling protocols are explored. Extensive use is made of the theory of branching processes.

Keywords

Random topologyrandom geometrydistribution theorybranching processesdivision of space

MSC classification

Primary:60D05: Geometric probability and stochastic geometry60E05: Distributions60J80: Branching processes (Galton-Watson, birth-and-death, etc.)68Q80: Cellular automata68R10: Graph theory (including graph drawing)

Information

Type
Part 1. Branching processes
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004, pp. 3 - 15
Copyright
Copyright © Applied Probability Trust 2004 

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References

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