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The Falling-Leaves Mosaic and its Equilibrium Properties

Part of: Designs and configurations Graph theory Discrete geometry Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Richard Cowan  and
Albert K. L. Tsang
Richard Cowan
Affiliation:
University of Hong Kong
Albert K. L. Tsang*
Affiliation:
University of Hong Kong
*
* Postal address: Department of Statistics, University of Hong Kong, Pokfulam Road, Hong Kong.
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Abstract

Consider a forest of maple trees in autumn, with leaves falling on the ground. Those coming late cover the others below, so eventually the fallen leaves form a statistically homogeneous spatial pattern. In particular, the uncovered leaf boundaries form a mosaic. We formulate a mathematical model to describe this mosaic, firstly in the case where the leaves are polygonal and later for leaves with curved boundaries. Mean values of certain statistics of the mosaic are derived.

Keywords

STOCHASTIC GEOMETRYMOSAICTESSELLATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Secondary: 05B45: Tessellation and tiling problems 05C80: Random graphs 52C15: Packing and covering in $2$ dimensions
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 54 - 62
Copyright
Copyright © Applied Probability Trust 1994 

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