Print Gallery 《畫廊》

愛藝

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 G?del， 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》是荷蘭畫家M.C. 埃舍爾創作的一幅平版印刷畫（31.7厘米×31.9厘米），首印于1956年。

該畫描繪了一個男子在畫廊中觀看一幅描繪海港的版畫，畫面呈現的海港建筑中就有男子所處的這家畫廊。埃舍爾創作時利用了視覺遞歸的德羅斯特效應。這幅平版印刷畫在數學和藝術領域都引發了討論。

布魯諾·恩斯特引用埃舍爾本人的話說，他創作《畫廊》是“源于這樣一個念頭，即肯定可以畫出一個環狀凸起，一種循環擴展……沒有起點也沒有終點”。埃舍爾試圖用直線來呈現，但又跟隨直覺改用曲線，這使畫中的網格在旋轉時可以極大擴展。

在《哥德爾、艾舍爾、巴赫》一書中，侯世達將此畫詮釋為一個怪圈，展示出三種“X在Y中”的情景：畫廊以實體形式存在于小鎮中（“包含”）;小鎮經藝術加工存在于圖畫中（“描繪”）;圖畫因引發思考而存在于觀畫者大腦中（“表征”）。

埃舍爾的簽名位于此畫中央的圓形空當中。2003年，兩位荷蘭數學家巴特·德斯密特和亨德里克·倫斯特拉報稱找到了一種填充空當的方法，即把此畫看作在復數域上繪制的橢圓曲線。他們認為，理想的《畫廊》應包含一個自身的復制品（根據德羅斯特效應），順時針旋轉約157.63度，縮小約22.58%。他們在自己的網站上進一步探索了此畫的數學結構。