[rcfox]

You can use simple cellular automata to create somewhat natural-looking cave formations: http://rcfox.ca/random-cave-map-generation/

[dexter313]

By "set of stairs" do you mean a simple vertical line that cuts trough all of terrain?

[rcfox]

Well, I see the image as top-down view of one level in a cave. Going down stairs would mean generating another level.

It's entirely legitimate to see it as a side-view, in which case yes, you'd be cutting through the terrain.