Four bugs on a rectangle
Stephen Jonathan Chapman, James W. Lottes, Lloyd N. Trefethen · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2010
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 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.