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- Title
PLANAR TESSELLATIONS THAT HAVE THE HALF-GILBERT STRUCTURE.
- Authors
BURRIDGE, JAMES; COWAN, RICHARD
- Abstract
In the full rectangular version of Gilbert's planar tessellation (see Gilbert (1967), Mackisack and Miles (1996), and Burridge et al. (2013)), lines extend either horizontally (with east- and west-growing rays) or vertically (north- and south-growing rays) from seed points which form a stationary Poisson point process, each ray stopping when it meets another ray that has blocked its path. In the half-Gilbert rectangular version, east- and south-growing rays, whilst having the potential to block each other, do not interact with west and north rays, and vice versa. East- and south-growing rays have a reciprocality of blocking, as do west and north. In this paper we significantly expand and simplify the half-Gilbert analytic results that we gave in Burridge et al. (2013). We also show how the idea of reciprocality of blocking between rays can be used in a much wider context, with rays not necessarily orthogonal and with seeds that produce more than two rays.
- Subjects
TESSELLATIONS (Mathematics); PLANAR motion; BLOCKING sets; RAYS (Graph theory); RECIPROCALS (Mathematics)
- Publication
Advances in Applied Probability, 2016, Vol 48, Issue 2, p574
- ISSN
0001-8678
- Publication type
Article
- DOI
10.1017/apr.2016.15