The image at right shows the Hilbert curve as an example. Indeed, the Hilbert curve fills a square. And its 3D counterpart fills a cube.
However, a space-filling curve (or…to just stick with two dimensions: a plane-filling curve) can be more generally described as a curve that fills a region of the plane that is topologically equivalent to a square (or…a disk). Note that a filled-in square, a disk, and a cone are topologically the same. “A cone?” you may ask. Yes, it has one surface (interior), and one boundary.
Now consider the following space-filling curves:
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