Four bugs on a rectangle

S. J. Chapman, J. Lottes, L. N. Trefethen

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


The idealized mathematical 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 10427907250, 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. This journal is © 2011 The Royal Society.
Original languageEnglish (US)
Pages (from-to)881-896
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2127
StatePublished - Nov 10 2010
Externally publishedYes


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