
02367583
j
2006a.00588
Newth, Gerald
World order from chaotic beginnings.
Math. Gaz. 88, No. 511, 3945 (2004).
2004
Cambridge University Press, Cambridge; Mathematical Association (MA), Leicester
EN
I80
G50
bilinear transformations
interative sequences
conformal mappings
projections
complex plane
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.