Q:

What knots tend to form?

Most people note that cables tend to form knots and links if left to their own devices. Its sometimes fun to take a look at a headphone cable and identify the knot it formed after being in your pocket for a while. If the cable very long, the knot will be very big and sometimes a direct sum of many other knots.
It seems obvious that there must be some kind of work done about this, ie a distribution on what knots appear in physical strings depending on "string parameters" and "jumble intensity". This must be a lot of fun, my question is asking for such a reference.
I guess for example there is only one string parameter that is relevant to the distribution, something like a ratio between length and "bendiness" (elasticity?), and that the distribution becomes stationary with high enough "jumble intensity", ie that after a point shaking more does not alter what kind of knots you expect.
But it sure would be interesting to see somebody carry this out with real strings!

A:

All of them$^{(*)}$. There is some analysis of this in Raymer and Smith Spontaneous knotting of an agitated string:

120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed.

$^{(*)}$ To some extent: see the notion of Physical knots, which means knots that can physically arise in real life objects (from ropes to DNA). The linked article discusses mathematical notions and physical properties of strings that allow one to bound the complexity of physical knots.

