In 1956, the Dutch graphic artist M.C. Escher made an unusual lithograph with the title ‘Print Gallery’. It shows a young man viewing a print in an exhibition gallery. Amongst the buildings depicted on the print, he sees paradoxically the very same gallery that he is standing in.

A lot is known about the way in which Escher made his lithograph. It is not nearly as well known that it contains a hidden ‘Droste effect’, or infinite repetition; but this is brought to light by a mathematical analysis of the studies used by Escher. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others, what happens inside the mysterious spot in the middle of the lithograph that Escher left blank.

Professor Hendrik Lenstra from Universiteit Leiden and his team have applied mathematics to Escher’s Print Gallery and filled in the blank. You can see the results in animation at: http://escherdroste.math.leidenuniv.nl/index.php.