> I'm even further from my armchair comfort zone but I'll try: You can round the corners of the Hilbert curve too? This is supposed to be close to my area of e

> I'm even further from my armchair comfort zone but I'll try: You can round the corners of the Hilbert curve too? This is supposed to be close to my area of expertise, I will try to give a precise answer. The usual finite Hilbert curve is not space filling. the property of the Hilbert curve is that successive iterations converge to a continuous space filling curve. There are well known techniques to transform continuous function in differentiable functions (https://en.wikipedia.org/wiki/Convolution#Differentiation https://en.wikipedia.org/wiki/Convolution#Differentiation) furthermore you can "smooth" the finite Hilbert curves so that the limit remains the same. But the true Hilbert curve (that is the limit of the finite approximations) will not be differentiable even if built as a limit of differentiable functions.