TractionsThese functions are inspired by the Euclidean algorithm for boxes and the box triangle. {$R$} maps the entire triangle to the lower-left fourth (sorry, left and right get switched here).  {$M$} maps the triangle to the upper fourth,  and so on. The map {$C$} is a contraction. Using the Euclidean metric on the box triangle, distances are all halved under {$C$}. The other three are not contractions; distances are reduced, but not uniformly. They aren't contractions, so we call them, all four of them, tractions. |