alt Hacker News> It really depends on what you mean by "interesting".
Yes. I haven't gotten far enough in my journey to be able to formulate that.
The first insight is that the details of branching make a difference: humans don't pick the routes with the same likelihood at a crossroad.
Loops seem fine for the wrong paths looping onto other wrong paths: having to backtrack is somewhat unsatisfying, plus loops make the solving less mechanical - it's necessary to keep an eye where you'd been and where you haven't. It's possible to get confused and take the same wrong path twice, once from each direction. But certainly it matters where the loops are and how exactly they're formed - "simply convert some walls to pathways at random" is not the right way to construct them.
And I guess I think there should be one solution, though perhaps it can have few short loops somewhere in the middle (so it isn't really "one solution" anymore).
I wish there was research on how easy/difficult differently constructed mazes of a specific size are for humans to solve.
So you only want dead ends to have loops? You might try computing the depth of each node, marking the solution, and then assigning each branch off of the solution a unique color.
At that point knocking out walls only within the same color won't interfere with the solution.
Alternatively you could take care to track depth and knock out walls between different colors only when the total resulting path length would be greater than the existing solution.
Just go try stuff! All of the examples on Bostock's page that I linked earlier link to JS implementations that you could fork.