Escher’s Print Gallery: the painting that only a computer could complete

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Maurits Cornelis Escher was a genius with few equals in the history of modern art, for several reasons. Among one of the great inspirers of contemporary visuals and optical effects, his one is an art that immediately strikes the viewer, even when he lacks any artistic preparation or prior knowledge. In this sense he is more “pop art” than Andy Warhol or Roy Lichtenstein, as he can be enjoyed without having to study their intentions or philosophies. In the case of Escher, philosophy coincides with the visual outcome: representing the infinite, the optical joke, the metamorphosis, the combination of opposites, the impossible, through the use of essential structures, for which colors are hardly needed.

His most famous works are also those where the visual and conceptual effect behind the intuition is clear and direct: RelativityHand with Reflecting SphereEncounter, Drawing Hands, Waterfall, paintings that envelop the viewer because they represent perspectives, coincidences or impossible concepts, realized by amazing tricks. There is a picture, though, that although it doesn’t have the same immediate impact than his other works, subtends bigger complexity and ambition and includes advanced mathematical concepts, which not even Escher himself had full knowledge about, at the time of realization. Is his Print Gallery, 1956.

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M. c. Escher, Print Gallery, 1956

The idea behind this painting is to represent the infinite projection of the image. The protagonist is the guy on the left, which observes a representation in an art gallery. The maritime scene he’s looking contains the context in which he and the gallery itself exist. To make the concept even more complex, Escher has applied a geometric transformation that twists the picture, making it explode on the right side and coming back to the gallery where the protagonist is. The young man watches the scene containing the young man himself. At the center of this impossible transformation, Escher has left a blank space with his signature. According to the legend, he was not actually able to fill that space, and he wasn’t even sure if it was possible.

The historical myth wants Escher not particularly brilliant, nor in artistic disciplines (he often said that he “wasn’t that good at drawing after all”) nor in scientific and mathematical ones. Yet the artistic activity undertaken after school has put him increasingly into contact with contemporary mathematicians, and during his lifetime he often used geometric principles that he didn’t even know. It is said that the picture above gave him several headaches. Once finished, the debate shifted to those who appeared to be the true recipients of this representation: mathematicians.

The most complete retrospective studies on Escher’s Print Gallery was published in 2003 by two mathematicians at the University of Leiden, Netherlands. You can find it here: 12 pages of analysis, decompositions, grids and mathematical formulas, which goes into detail about the process that gave birth to the opera and the geometric structure behind it. Once the mathematics described the laws which govern that work, the next step was the plot twist: thanks to a dedicated software developed by one of the students of the University, the science has finally been able to fill the white space. With a recursive repeatition the same picture, twisted on itself and containing itself, ad infinitum. The so-called “Droste effect”, in which an image contains  a copy of itself. Exactly how Escher would have wanted it.

Years later, the Granada’s Science Park published on Youtube the video below, where Escher’s impossible geometry is explained to non-scientists as well. It’s still projected at the Escher Museum in the Hague, and it always gives a feeling of dizziness whenever you see it. Not counting how it makes you question yourself about how the genie can boldly go even where its own limitations prevent him from understanding.

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