Usually, iterations of something are experienced one at a time, and within time. Surface-tiling curves (and maybe all space-filling curves?) have the interesting property that the iteration segments, when overlaid, intersect perpendicularly, and never at corners where the direction of the curve changes. This lends itself nicely to presenting the curve in the style of a knot diagram, implying an over / under pattern for the lines.

This over / under pattern is preserved at the edges; notice how the darkest line goes under first at the top left and exits over at the bottom right. Of course, overlapping 1-dimensional lines enters into the realm of artistic license, but I’m only claiming to be making art here.

Below are several macro photos which I’m putting here because someone else might enjoy looking at them as much as I do. Looking at the piece this closely adds to the sensation of getting lost in something complex.