Periodic forests of stunted trees

@article{Miller1970PeriodicFO,
  title={Periodic forests of stunted trees},
  author={J. C. P. Miller},
  journal={Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences},
  year={1970},
  volume={266},
  pages={111 - 63}
}
  • J. Miller
  • Published 5 March 1970
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
We may define a forest of stunted trees as follows: Consider an infinite background of nodes at the vertices of an infinite plane tessellation of equilateral triangles., and start from a straight line of nodes at unit distance apart, which we shall consider as the ground; other parallel lines of nodes are then spaced at successive levels of linearly increasing heights above the ground. Any node may be live (if a tree passes through it) or vacant otherwise. Any live node may give rise to a… 
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Periodic forest whose largest clearings are of size 3
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  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1970
Miller has observed that there are a finite number of periodic forests whose largest clearings are of size 1 or 2, and an infinite number whose largest clearings are of size 4. In this note the basic
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