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Portrait of the Hilbert Curve (2010)
The Hilbert curve is a remarkable construct in many ways, but the thing that makes it useful in computer science is the fact that it has good clustering properties. If we take a curve like the one above and straighten it out, points that are close together in the two-dimensional layout will also tend to be close together in the linear sequence.
The Hilbert curve is a remarkable construct in many ways, but the thing that makes it useful in computer science is the fact that it has good clustering properties. I've long felt that the usual visualisation of the Hilbert curve - like the one shown at the top of this post - doesn't really do its clustering properties justice. This section is based on Hamilton's version of the classic algorithm first devised by A. R. Butz in the 1970s (though, see comments in my code for corrections to some minor errors in the paper that may trip up implementers).
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