I remember this from my dynamical systems class at uni. How useful are these for generating pseudo-random numbers? From what I recall they never retrace the s

I remember this from my dynamical systems class at uni. How useful are these for generating pseudo-random numbers? From what I recall they never retrace the same path so if you picked one of those narrow lines and take a cross section which you map to some space that you care about, say a unit interval, and then sample whenever it comes past that cross section you should have a pretty good source of randomness, no? Might not be the most efficient sampling scheme but should have the nice property of being aperiodic? I guess given simulation with finite precision it will have to repeat eventually but how long will those cycles be in practice? Also, if you're willing to trade off some space then you could track all points sampled and if detect a cycle then you rerun the previous cycle at higher precision and stay at the increased precision until you detect the next cycle, rinse and repeat.