Image of the week: a magical colour cube

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 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?


 

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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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