爱艺

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 Reutersvärd 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》是荷蘭画家M.C.埃舍尔创作的一幅平版印刷画（38厘米×30厘米），首印于1961年10月。此画呈现了一套永动装置，瀑布底部的流水看似沿着水道往下流，之后却流到了瀑布顶部。

为瀑布供水的水道（瀑布的渡槽或说露天水渠）由两个彭罗斯三角构成。彭罗斯三角是一种不可能的结构体，1934年由奥斯卡·罗伊特斯瓦德设计而成，1958年罗杰·彭罗斯独立发现了这个结构体。

该图描绘了一个水磨，主要构件是一条高架渡槽和一架水车。渡槽起自水车，水向水车后方流去。渡槽槽壁向下延伸，表明整体下斜的走势。渡槽有三次急转弯，先向左，再向右，最后又向左。观画者从对角位置俯瞰画面，意味着在观者看来渡槽是倾斜向上的。观者还可以从右下对角位置观看整个画面，意味着在观者眼中，两个左转完全在一条直线上，而水车、右转和渡槽末端槽口也在一条线上。第二左转处的渡槽由第一左转处的柱子支撑着，而其他两个拐角则由水车旁向上搭建的塔柱支撑。水从渡槽槽口落下，越过水车，形成一个不可能的无限循环。在对这幅画的注解中，埃舍尔指出，这套永动装置须定时加水，以补偿蒸发掉的水分。

两座支撑塔在渡槽上方向天空延伸，塔顶是两个复合多面体，揭示出画家埃舍尔对数学的浓厚兴趣。左塔顶是由三个立方体合成的一个复合体。右塔顶则是一个星状菱形十二面体（或者说是由三个不规则八面体合成的一个复合体），这个多面体被称为埃舍尔固体。

磨坊下方是一个花园，种着奇形怪状的巨型植物。其实这是一组放大版的苔藓和地衣，埃舍尔1942年的一幅墨水画习作画过它们。

背景似乎是一大片向上延伸的广阔梯田。