Complex squaring map: Difference between revisions

Revision as of 13:11, 21 March 2014

Revision as of 04:07, 13 February 2015

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# Repeatedly square that number.

This repetition (iteration) produces a sequence of complex numbers that can be described alone by their complex angle alone. Any choice of starting angle that satisfies (1) above will produce an extremely complicated sequence of angles, that belies the simplicity of the steps. In fact, itIt can be shown that the sequence will be [[Chaos theory|chaotic]], i.e. it is sensitive to the detailed choice of starting angle.

== Chaos and the complex squaring map ==