Intersecting L-system branches

Hi Everyone,

I'm after producing multiple curved L-systems, with their branches intertwined  (I envision it looking like vines). Which later on, I will convert to pipes. Do you have any ideas on how I'll be able to implement it?

I was able to produce my current L-system (Hoopsnake) using a code from one of the links given to me through my other discussion. 

Current Status:

Definition: