\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2006a.00588}
\itemau{Newth, Gerald}
\itemti{World order from chaotic beginnings.}
\itemso{Math. Gaz. 88, No. 511, 39-45 (2004).}
\itemab
This article explains the variety of patterns which arise in sequences of bilinear functions of the form (p+qx)/(r+sx). Some produce a rather chaotic sequence, whilst others are periodic or convergent. The differences can be understood by generalising to the complex plane and then projecting on to the surface of a sphere. To illustrate the ideas, Autograph is used.
\itemrv{~}
\itemcc{I80 G50}
\itemut{bilinear transformations; interative sequences; conformal mappings; projections; complex plane}
\itemli{}
\end