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

| PDF 214Kb |

## 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 |

Repository Staff Only: item control page