I'm playing around with the Geowave's space-filling curve library again today and create some 3D curves to look at. Geowave is my favorite free-and-open-source software library for scalable geospatial data storage and analytics. The space-filling curves are at the heart of Geowave. Hilbert, Z-order (a.k.a. Morton), and XZ-order (a variation of Z-order) are the three types of space-filling curves available in the library. They are shown below in 3D.
All of the space-filling curves above are fractal geometries similar to the fern leaves shown the top banner.