How to create a procedural mesh of tunnels

I'd like to create tubular tunnels with cross sections, how would I go about doing so?

 

A general solution, that you might like for its simplicity, would use signed distance fields/functions and marching cubes / dual contouring. It comes at the cost of non-ideal meshes and performance, but might be fine.

The solution you probably expected, an explicit formula:
Think about the most symmetric solution, and how to generate a single petal.
Then mirror/deform and merge them.