I suggest that the "Dark Fountains" of Deltarune are exactly equivalent to singularities in a function of two independent variables, like the singularities seen in the second image, which is a graph of the absolute value of the gamma function in the complex plane, which is singular for all negative integers, producing those infinitely high "chimneys" in the graph. I propose that the DR "Dark Fountains" are simply that: mathematical singularities, as they would exist in a "flat" world.
~Chara