Magic would be a little out of place on a physics blog, so we’ll have to make do with this graphical representation of a Hilbert curve.

The fourth iteration of the Hilbert curve, from Jan Smrek and Alexander Y Grosberg J. Phys. A: Math. Theor. 48 195001

The Hilbert curve was discovered in 1891 by David Hilbert. It’s a ‘continuous space filling curve’ – imagine taking a grid and drawing a line through each box only once. Curves like this have interesting properties, and almost 125 years after its discovery this simple construct has many uses. Hilbert-type curves are applied regularly in computer science and biology, with applications like image processing, networking or database technology.

Our image of the week comes from Smrek *et al*, who have analysed and enumerated Hilbert-like curves as a first step towards characterising polymers and DNA folding.

I wonder what Hilbert would make of the techniques inspired by his discovery?

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Image: On enumeration of Hilbert-like curves by Jan Smrek and Alexander Y Grosberg 2015 *J. Phys. A: Math. Theor.* **48** 195001, copyright IOP Publishing Ltd 2015.

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Categories: JPhys+

Tags: Image of the week, Mathematical physics