The Mathematical Institute, University of Oxford, Eprints Archive

Four bugs on a rectangle

Chapman, S. J. and Lottes, J. and Trefethen, L. N. (2010) Four bugs on a rectangle. Proceedings of the Royal Society A . (Submitted)

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Abstract

The problem of four bugs in cyclic pursuit starting from a 2-by-1 rectangle is considered, and asymptotic formulas are derived to describe the motion. In contrast to the famous case of four bugs on a square, here the trajectories quickly freeze to essentially one dimension. After the first rotation about the centre point, the scale of the configuration has shrunk by a factor of 10^427907250, and this number is then exponentiated four more times with each successive cycle. Relations to Knuth’s double-arrow notation and level-index arithmetic are discussed.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1012
Deposited By:Peter Hudston
Deposited On:28 Oct 2010 14:35
Last Modified:09 Feb 2012 15:54

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