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World order from chaotic beginnings. (English)
Math. Gaz. 88, No. 511, 39-45 (2004).
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.
Classification: I80 G50
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