Pictorial Renormalization Group - Demo 12

Scaling at ac

An alternative version of the scaling behavior is to fix a=ac and look at the rescaled f 2n (i.e. vary only nf and nsc together):

n 2n Applet
3 8
4 16
5 32
6 64

Again to high accuracy the shape of the plotted curve does not change under this process. Even for arbitrarily high functional composition the fixed points are all unstable, and this is the borderline of chaos.

We could also look at any f 2n over the full unit interval, e.g. for n=6:

which has 128 fixed points (intersections with the diagonal), all unstable!

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Last modified Sunday, December 12, 1999
Michael Cross