Modeling A Ball of String

I may need to model a ball of string.
The tricky thing about it seems to be simulating both the continuity of the string and the layering of string upon string at hundreds of intersections, and fitting it all to a spherical shape. It all seems tricky.

Continuously wrapping a string object around a sphere in some way could be a solution, and so could starting with a sphere and subtracting from it or cutting it to create spiralling paths.

Thoughts welcome.

For a simulation based approach, you could try modifying this:

(It’s for lots of linked loops instead of one continuous thread, but the same general method should work)

Thanks Daniel. THe dreaded (but wonderful) Grasshopper, about which I know next to nothing. Might be time to dive in.