Let $H:[0,1]\to[0,1]\times [0,1]$ the Hilbert space filling curve map. I'm interested in visualizing and studying the curve that would result from pulling it up along the $z$-axis, i.e. the graph of the map $t\mapsto (H(t), t)$.
Do you have a reference to any study involving this curve? Do you know about its properties?
And more importantly, would anyone be able to code a 3D visualisation of it?