# Is there any relationship between the Riemann z function and strange attractors?

I have this question in mind since the first time I saw a graphical representation of the zeta function (like in the sample below). Just by looking to them I wondered if there is any relationship between the Riemann zeta function as showed in the sample and strange attractors? Disclaimer: my question is just based in the visual look of both structures.

For instance the Lorenz's strange attractor looks like this (sorry I do not know how to reduce the size of the images):

And a graphic of the zeta function for ($\frac{1}{2}+it$) looks like this:

I have been trying to find any reference regarding Riemann zeta function and attractors but if I am not wrong there is nothing and probably this is just a visual similarity but without any real background behind. Thank you!

UPDATE 2015/05/26

So far I have found some papers and some hints, but nothing clear about this yet! Here is the list:

1. "Magic Angle Precession and the Riemann Zeta Function" (Binder): The Riemann zeta function and the magic angle precession strange attractor are related by their functional equations.

• Concerning iterations and fractals you may enjoy this (probably not an answer to your question but neat!) – Raymond Manzoni May 17 '15 at 18:10
• @Raymond Manzoni, thank you for the reference! it is really interesting, I had a look to it, I guess I will need a weekend to read it slowly. :) – iadvd May 18 '15 at 0:02
• Two more things you may enjoy : the universality of zeta and the related paper by Woon "Riemann zeta function is a fractal". Fine reading, – Raymond Manzoni May 22 '15 at 21:48