愛藝

Waterfall is a lithograph （38 cm × 30 cm） by the Dutch artist M. C. Escher， first printed in October 1961. It shows a perpetual motion machine where water from the base of a waterfall appears to run downhill along the water path before reaching the top of the waterfall.

The watercourse supplying the waterfall （its aqueduct or leat） has the structure of two Penrose triangles. A Penrose triangle is an impossible object designed by Oscar Reutersv?rd in 1934， and found independently by Roger Penrose in 1958.

The image depicts a watermill with an elevated aqueduct and waterwheel as the main feature. The aqueduct begins at the waterwheel and flows behind it. The walls of the aqueduct step downward， suggesting that it slopes downhill. The aqueduct turns sharply three times， first to the left， then to the right， and finally to the left again. The viewer looks down at the scene diagonally， which means that from the viewer’s perspective the aqueduct appears to be slanted upward. The viewer is also looking across the scene diagonally from the lower right， which means that from the viewer’s perspective the two left-hand turns are directly in line with each other， while the waterwheel， the forward turn and the end of the aqueduct are all in line. The second left-hand turn is supported by pillars from the first， while the other two corners are supported by a tower of pillars that begins at the waterwheel. The water falls off the edge of the aqueduct and over the waterwheel in an impossible infinite cycle; in his notes on the picture， Escher points out that some water must be periodically added to this perpetual motion machine to compensate for evaporation.

The two support towers continue above the aqueduct and are topped by two compound polyhedra， revealing Escher’s interest in mathematics as an artist. The one on the left is a compound of three cubes. The one on the right is a stellation of a rhombic dodecahedron （or a compound of three non-regular octahedra） and is known as Escher’s solid.

Below the mill is a garden of bizarre， giant plants. This is actually a magnified view of a cluster of moss and lichen that Escher drew in ink as a study in 1942.

The background seems to be a climbing expanse of terraced farmland.

《瀑布》是荷蘭畫家M.C.埃舍爾創(chuàng)作的一幅平版印刷畫（38厘米×30厘米），首印于1961年10月。此畫呈現(xiàn)了一套永動裝置，瀑布底部的流水看似沿著水道往下流，之后卻流到了瀑布頂部。

為瀑布供水的水道（瀑布的渡槽或說露天水渠）由兩個彭羅斯三角構(gòu)成。彭羅斯三角是一種不可能的結(jié)構(gòu)體，1934年由奧斯卡·羅伊特斯瓦德設(shè)計而成，1958年羅杰·彭羅斯獨立發(fā)現(xiàn)了這個結(jié)構(gòu)體。

該圖描繪了一個水磨，主要構(gòu)件是一條高架渡槽和一架水車。渡槽起自水車，水向水車后方流去。渡槽槽壁向下延伸，表明整體下斜的走勢。渡槽有三次急轉(zhuǎn)彎，先向左，再向右，最后又向左。觀畫者從對角位置俯瞰畫面，意味著在觀者看來渡槽是傾斜向上的。觀者還可以從右下對角位置觀看整個畫面，意味著在觀者眼中，兩個左轉(zhuǎn)完全在一條直線上，而水車、右轉(zhuǎn)和渡槽末端槽口也在一條線上。第二左轉(zhuǎn)處的渡槽由第一左轉(zhuǎn)處的柱子支撐著，而其他兩個拐角則由水車旁向上搭建的塔柱支撐。水從渡槽槽口落下，越過水車，形成一個不可能的無限循環(huán)。在對這幅畫的注解中，埃舍爾指出，這套永動裝置須定時加水，以補(bǔ)償蒸發(fā)掉的水分。

兩座支撐塔在渡槽上方向天空延伸，塔頂是兩個復(fù)合多面體，揭示出畫家埃舍爾對數(shù)學(xué)的濃厚興趣。左塔頂是由三個立方體合成的一個復(fù)合體。右塔頂則是一個星狀菱形十二面體（或者說是由三個不規(guī)則八面體合成的一個復(fù)合體），這個多面體被稱為埃舍爾固體。

磨坊下方是一個花園，種著奇形怪狀的巨型植物。其實這是一組放大版的苔蘚和地衣，埃舍爾1942年的一幅墨水畫習(xí)作畫過它們。

背景似乎是一大片向上延伸的廣闊梯田。