Hello @eightohnine,
This inspired me to write some related code to generating a path.
This may be something in here of interest in your research:
The last one is generating mazes and inspired me to solve a maze by looking ahead to see what was in the way and making a decision based on that. A lot of interesting and related stuff may come up in a maze related search.
In one example of code I simply looked ahead to see if there was a pixel color change. In others I kept track of nodes on a grid (where I have been) in an array and checked array to see if something was ahead.
Thinking about it already I am, green eggs and ham!
Pick a random direction from your current direction and look ahead and draw your *curves! It should be simple enough to check nodes in the path; the nodes being stored in an array. Since these are tiles the nodes can represent each tile.
*According to one source a line is a curve without any curvature. :)
I do not have any algorithms or approaches to suggest for this as I generally code from scratch to engage my brain and then may look at other approaches.
Have fun!
:)