Fractals and Chaos: What's the Connection?

[Apteronotus]

Hi,

I've read a little bit about fractals, being self repeating shapes. Is there a connections between fractals and chaotic systems?

Thanks

 

[HallsofIvy]

The usual "interesting question" about dynamic systems in general is "where does it go in the limit?" or "what are the attracting sets?". If a system is chaotic then the attracting (limit) sets will be fractal.

 

[John Creighto]

Hi,

I've read a little bit about fractals, being self repeating shapes. Is there a connections between fractals and chaotic systems?

Thanks

Yes. I think that some state space trajectories in chaotic systems follow the path of fractals.

 

[Apteronotus]

That is interesting.
So for all chaotic systems, the limit set is a fractal. Is this always true?
Does the reverse hold as well? (ie. Are all fractals the limit sets of some chaotic systems?)

Lastly, how trivial is it to find one given the other?
For example if we are given the fractal, can we find a chaotic system whose limit set is equal to the fractal?