Onion Curve: A Space Filling Curve with Near-Optimal Clustering (2018)
I&#x27;m disappointed, I was looking forward to seeing a new fractal. The onion curve in 2d is just a spiral, as mentioned, but the word &quot;spiral&quot; doesn&#x27;t appear at all. I think this paper is mostly without merit, unfortunately.<p>Egregiously, the table comparing the (reasonably defined, I think) clustering metric of the spiral with the Hilbert curve is only for rectangular queries which ask for <i>almost the entire space</i>, with the query side length differing from the overall space&#x27;s side length by a constant.<p>An obvious advantage of the fractal nature of the Hilbert curve is that its clustering properties will be scale invariant, but the spiral will quickly degrade to a &quot;space filling curve&quot; that just goes row by row for small queries. Perhaps later the paper gives some reason to hope for the onion curve, but I&#x27;m disinclined to look.