Print Gallery 《画廊》

爱艺

Print Gallery is a lithograph （31.7 cm × 31.9 cm） printed in 1956 by the Dutch artist M. C. Escher.

It depicts a man in a gallery viewing a print of a seaport， and among the buildings in the seaport is the very gallery in which he is standing， making use of the Droste effect1 with visual recursion2. The lithograph has attracted discussion in both mathematical and artistic contexts.

Bruno Ernst3 cites M. C. Escher as stating that he began Print Gallery “from the idea that it must be possible to make an annular bulge， a cyclic expansion... without beginning or end.” Escher attempted to do this with straight lines， but intuitively switched to using curved lines which make the grid expand greatly as it rotates.

In the book Gödel， Escher， Bach4， Douglas Hofstadter explains it as a strange loop showing three kinds of “in-ness”： the gallery is physically in the town （“inclusion”）; the town is artistically in the picture （“depiction”）; the picture is mentally in the person （“representation”）5.

Escher’s signature is on a circular void in the center of the work. In 2003， two Dutch mathematicians， Bart de Smit and Hendrik Lenstra， reported a way of filling in the void by treating the work as drawn on an elliptic curve over the field of complex numbers6. They deem an idealized version of Print Gallery to contain a copy of itself （the Droste effect）， rotated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58. Their website further explores the mathematical structure of the picture.

《畫廊》是荷兰画家M.C. 埃舍尔创作的一幅平版印刷画（31.7厘米×31.9厘米），首印于1956年。

该画描绘了一个男子在画廊中观看一幅描绘海港的版画，画面呈现的海港建筑中就有男子所处的这家画廊。埃舍尔创作时利用了视觉递归的德罗斯特效应。这幅平版印刷画在数学和艺术领域都引发了讨论。

布鲁诺·恩斯特引用埃舍尔本人的话说，他创作《画廊》是“源于这样一个念头，即肯定可以画出一个环状凸起，一种循环扩展……没有起点也没有终点”。埃舍尔试图用直线来呈现，但又跟随直觉改用曲线，这使画中的网格在旋转时可以极大扩展。

在《哥德尔、艾舍尔、巴赫》一书中，侯世达将此画诠释为一个怪圈，展示出三种“X在Y中”的情景：画廊以实体形式存在于小镇中（“包含”）;小镇经艺术加工存在于图画中（“描绘”）;图画因引发思考而存在于观画者大脑中（“表征”）。

埃舍尔的签名位于此画中央的圆形空当中。2003年，两位荷兰数学家巴特·德斯密特和亨德里克·伦斯特拉报称找到了一种填充空当的方法，即把此画看作在复数域上绘制的椭圆曲线。他们认为，理想的《画廊》应包含一个自身的复制品（根据德罗斯特效应），顺时针旋转约157.63度，缩小约22.58%。他们在自己的网站上进一步探索了此画的数学结构。