A space-filling Hilbert curve that draws itself progressively along its arc length and, on a slow loop, steps its order 2→5 up and down. The distance-to-curve is computed in O(1) per pixel: each fragment maps its own cell to a Hilbert index via the analytic xy→d bit algorithm, then reconstructs the two neighbouring cell centres (d±1) with d→xy and measures distance to that local segment — so no 4^order point loop is needed. The stroke is coloured by arc-length as a smooth hue gradient and rides inside a soft halo. The pointer scrubs the draw head, scrolling raises/lowers the order, and a press recolours the path.