Waterfall lithograph. Escher is a Dutch graphic artist. All metamorphoses of Escher. Maurits Cornelis Escher, Dutch graphic artist

Maurits Escher is an outstanding Dutch graphic artist known throughout the world for his work. In the center, in the museum, opened in 2002, and named after him "Escher in het Paleis", a permanent exhibition of 130 works by the master is open. Are you saying graphics are boring? Maybe... maybe that could be said about the work of graphic artists, but not about Escher. The artist is known for his unusual vision of the world and playing with the logic of space.

Escher's fantastic engravings, literally, can be perceived as graphic image theory of relativity. The works depicting impossible figures and reincarnations are literally mesmerizing, they are not like anything else.

Maurits Escher was a real master of puzzles and his optical illusions show something that doesn't really exist. In his paintings, everything changes, smoothly flows from one form to another, stairs have no beginning and end, and water flows upwards. Someone will exclaim - this cannot be! See for yourself.
The famous painting "Day and Night"

“Climbing and descending”, where people go up the stairs all the time... or down?

“Reptiles” - here the alligators turn from drawn into three-dimensional...

"Drawing hands" - on which two hands draw each other.

"Meeting"

"Hand with reflective ball"

The main pearl of the museum is the 7-meter work of Escher - "Metamorphoses". This engraving allows you to experience the connection between eternity and infinity, where time and space come together as one.

Museum located in the former winter palace Queen Emma is the great-grandmother of the current Queen Beatrix. Emma bought the palace in 1896 and lived there until her death in May 1934. In two halls of the museum, which are called the “Royal Rooms”, furniture and photographs of Queen Emma have been preserved, and on the curtains there is information about the interior of the palace of those times.

On the top floor of the museum there is an interactive exhibition “Look Like Escher”. This is real Magic world illusions. Worlds appear and disappear in the magic ball, walls move and change, and children look taller than their parents. A little further there is an unusual floor, which optically falls under every step, and in a silver ball you can see yourself through the eyes of Escher.

Curved white lines, intersecting, divide each other into sections; each is equal to the length of the fish - from the infinitesimal to the largest, and again - from the largest to the infinitesimal. Each row is monochrome. At least four colors must be used to achieve the tonal contrasts of these series. From a technological point of view, five boards are required: one for black elements and four for color ones. To fill the circle, each board in the shape of a rectangular circle should be pulled four times. thus a finished print would require 4x5=20 prints. Here is one of two types of "non-Euclidean" space described by the French mathematician Poincaré. To understand the features of this space, imagine that you are inside the picture itself. As you move from the center of the circle to its border, your height will decrease in the same way as the fish in this picture decrease. Thus, the path that you will need to go to the border of the circle will seem to you endless. In fact, being in such a space, at first glance, you will not notice anything unusual in it compared to ordinary Euclidean space. For example, to reach the boundaries of Euclidean space, you also need to go through an infinite path. However, if you look closely, you will notice some differences, for example, all similar triangles have the same size in this space, and you will not be able to draw figures there with four right angles connected by straight lines. Waterfall. Lithography. 38×30 cm K: Lithographs 1961

This work by Escher depicts a paradox - the falling water of a waterfall controls a wheel that directs the water to the top of the waterfall. The waterfall has the structure of the "impossible" Penrose triangle: the lithograph was created based on an article in the British Journal of Psychology.

The design is made up of three crossbars laid on top of each other at right angles. The waterfall on the lithograph works like a perpetual motion machine. Depending on the movement of the eye, it alternately seems that both towers are the same and that the tower located on the right is one floor lower than the left tower.

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Links

• Official site: (English)

An excerpt characterizing the Waterfall (lithograph)

- There is none; orders for battle were made.
Prince Andrei went to the door, through which voices were heard. But just as he was about to open the door, the voices in the room fell silent, the door opened of its own accord, and Kutuzov, with his aquiline nose on his plump face, appeared on the threshold.
Prince Andrei stood directly opposite Kutuzov; but from the expression of the commander-in-chief's only sighted eye, it was clear that thought and care occupied him so much that it seemed as if his vision was obscured. He looked directly at the face of his adjutant and did not recognize him.
- Well, are you finished? he turned to Kozlovsky.
“Just a second, Your Excellency.
Bagration, not tall, with an oriental type of hard and immovable face, dry, not yet an old man, went out for the commander-in-chief.
“I have the honor to appear,” Prince Andrei repeated rather loudly, handing the envelope.
“Ah, from Vienna?” Okay. After, after!
Kutuzov went out with Bagration to the porch.
“Well, good-bye, prince,” he said to Bagration. “Christ is with you. I bless you for a great achievement.
Kutuzov's face suddenly softened, and tears appeared in his eyes. He pulled Bagration to himself with his left hand, and with his right hand, on which there was a ring, he apparently crossed him with a habitual gesture and offered him a plump cheek, instead of which Bagration kissed him on the neck.

Illusory works of art have a certain charm. They are the triumph of fine art over reality. Why are illusions so interesting? Why do so many artists use them in their artwork? Perhaps because they do not show what is actually drawn. Everyone celebrates the lithograph "Waterfall" by Maurits C. Escher. The water here circulates endlessly, after the rotation of the wheel, it flows further and falls back to the starting point. If such a structure could be built, then there would be a perpetual motion machine! But upon closer examination of the picture, we see that the artist is deceiving us, and any attempt to build this structure is doomed to failure.

Isometric drawings

To convey the illusion of three-dimensional reality, two-dimensional drawings (drawings on a flat surface) are used. Usually the deception consists in depicting projections of solid figures, which the person tries to represent as three-dimensional objects in accordance with his personal experience.

Classical perspective is effective in simulating reality in the form of a "photographic" image. This presentation is incomplete for several reasons. It does not allow us to see the scene from different points of view, to get closer to it, or to view the object from all sides. Nor does it give us the effect of depth that a real object would have. The effect of depth occurs due to the fact that our eyes look at the object from two different points of view, and our brain combines them into one image. A flat drawing represents a scene from only one specific point of view. An example of such a picture can be a photograph taken with a conventional monocular camera.

When using this class of illusions, the drawing appears at first glance to be an ordinary representation. solid body in perspective. But a closer look reveals the internal contradictions of such an object. And it becomes clear that such an object cannot exist in reality.

Penrose illusion

Escher Falls is based on the Penrose illusion, sometimes called the impossible triangle illusion. This illusion is illustrated here in its simplest form.

It seems that we see three bars square section connected in a triangle. If you close any corner of this figure, you will see that all three bars are connected correctly. But when you remove your hand from the closed corner, the deception becomes obvious. Those two bars that will connect in this corner should not even be close to each other.

The Penrose illusion uses "false perspective". "False perspective" is also used in the construction of isometric images. Sometimes this perspective is called the Chinese one. This method of drawing was often used in Chinese fine arts. With this way of drawing, the depth of the drawing is ambiguous.

In isometric drawings, all parallel lines appear to be parallel, even if they are tilted with respect to the observer. An object that has an angle of inclination directed away from the observer looks exactly the same as if it were tilted towards the observer by the same angle. The double-bent rectangle (Mach figure) clearly shows this ambiguity. This figure may appear to you as an open book, as if you are looking at the pages of a book, or it may appear as a book with the cover turned towards you and you are looking at the cover of the book. This figure may also appear to be two parallelograms combined, but a very small number of people will see this figure in the form of parallelograms.

Thiery figure illustrates the same duality

Consider the Schroeder ladder illusion, a "pure" example of isometric depth ambiguity. This figure can be perceived as a staircase that could be climbed from right to left, or as a view of the stairs from below. Any attempt to change the position of the figure's lines will destroy the illusion.

This simple drawing is reminiscent of a line of cubes shown from the outside and from the inside. On the other hand, this drawing resembles a line of cubes, shown first from above, then from below. But it is very difficult to perceive this drawing as just a set of parallelograms.

Let's paint some areas black. Black parallelograms can look like we are looking at them either from below or from above. Try, if you can, to see this picture differently, as if we are looking at one parallelogram from below, and at the other from above, alternating between them. Most people cannot perceive this picture in this way. Why are we unable to perceive the picture in this way? I think this is the most complex of simple illusions.

The figure on the right uses the illusion of an impossible triangle in an isometric style. This is one of the "hatching" patterns of the AutoCAD(TM) drafting software. This sample is called "Escher".

An isometric drawing of a cube wire structure shows isometric ambiguity. This figure is sometimes called the Necker cube. If the black dot is in the center of one side of the cube, is that side the front or the back? You can also imagine that the dot is near the bottom right corner of a side, but you still can't tell if that side is a face or not. You also can't have any reason to assume that the point is on or inside the cube, it could just as well be in front of or behind the cube, since we don't have any information about the actual dimensions of the point.

If you imagine the faces of a cube as wooden planks, you can get unexpected results. Here we have used an ambiguous connection of horizontal bars, which will be discussed below. This version of the figure is called an impossible box. It is the basis for many similar illusions.

The impossible box cannot be made of wood. And yet we see here a photograph of an impossible box made of wood. This is a lie. One of the drawer slats, which appears to be running behind the other, is actually two separate slats with a gap, one closer and the other farther than the crossing slat. Such a figure is visible only from a single point of view. If we were to look at a real construction, then with our stereoscopic vision we would see a trick that makes the figure impossible. If we changed our point of view, then this trick would become even more noticeable. That is why, when demonstrating impossible figures in exhibitions and museums you have to look at them through a small hole with one eye.

Ambiguous connections

What is the basis of this illusion? Is it a variation of Mach's book?

In fact, it's a combination of Much's illusion and an ambiguous connection of lines. The two books share a common middle surface of the figure. This makes the slope of the book cover ambiguous.

position illusions

The Poggendorf illusion, or "crossed rectangle", misleads us which line A or B is the continuation of line C. An unambiguous answer can only be given by attaching a ruler to line C, and tracing which of the lines coincides with it.

Illusions of form

The illusions of form are closely related to the illusions of position, but here the very structure of the drawing forces us to change our judgment about the geometric form of the drawing. In the example below, the short slanted lines give the illusion that the two horizontal lines are curved. In fact, they are straight parallel lines.

These illusions use the ability of our brain to process visible information, including hatched surfaces. One hatch pattern can dominate so much that other elements of the pattern appear distorted.

A classic example is a set of concentric circles with a square superimposed on them. Although the sides of the square are perfectly straight, they appear to be curved. The fact that the sides of the square are straight can be verified by attaching a ruler to them. Most form illusions are based on this effect.

The following example works on the same principle. Although both circles are the same size, one of them looks smaller than the other. This is one of many size illusions.

This effect can be explained by our perception of perspective in photographs and paintings. IN real world we see that two parallel lines converge as the distance increases, so we perceive that the circle touching the lines is farther away from us and therefore must be larger.

If the circles are painted with black circles and areas bounded by lines, then the illusion will be weaker.

The width of the brim and the height of the hat are the same, although it does not seem so at first glance. Try rotating the image 90 degrees. Did the effect persist? This is an illusion of relative sizes within a painting.

Ambiguous ellipses

Tilt circles are projected onto the plane as ellipses, and these ellipses have a depth ambiguity. If the figure (above) is a tilted circle, then there is no way to know if the top arc is closer to us or further away from us than the bottom arc.

The ambiguous connection of lines is an essential element in the ambiguous ring illusion:

Ambiguous ring, © Donald E. Simanek, 1996.

If you close half of the picture, then the rest will resemble half of an ordinary ring.

When I came up with this figure, I thought that it could be the original illusion. But later I saw an advertisement with the logo of the fiber optics corporation, Canstar. Although the emblem of Canstar is mine, they can be classified as one class of illusions. Thus, I and the corporation developed independently of each other the figure of the impossible wheel. I think if you dig deeper, you can probably find earlier examples of the impossible wheel.

Endless Stair

Another of Penrose's classic illusions is the impossible staircase. She is most often depicted as an isometric drawing (even in Penrose's work). Our version of the infinite staircase is identical to the version of the Penrose staircase (except for the hatching).

It can also be shown in perspective, as is done in the lithograph by M. K. Escher.

The deception on the lithograph "Ascent and Descent" is built in a slightly different way. Escher placed the ladder on the roof of the building and depicted the building below in such a way as to convey the impression of perspective.

The artist depicted an endless staircase with a shadow. Like shading, the shadow could destroy the illusion. But the artist placed the light source in such a place that the shadow blends well with other parts of the picture. Perhaps the shadow of the stairs is an illusion in itself.

Conclusion

Some people are not at all intrigued by illusory pictures. "Just the wrong picture," they say. Some people, perhaps less than 1% of the population, do not perceive them because their brains are not capable of converting flat pictures into three-dimensional images. These people tend to have difficulty understanding technical drawings and illustrations of 3D figures in books.

Others may see that there is "something wrong" with the picture, but they won't even think to ask how the deception comes about. These people never have the need to understand how nature works, they cannot focus on the details for lack of elementary intellectual curiosity.

Perhaps understanding visual paradoxes is one of the hallmarks of that kind creativity possessed by the best mathematicians, scientists and artists. Among the works of M.C. Escher (M.C. Escher) there are a lot of paintings-illusions, as well as complex geometric paintings, which can be attributed rather to "intellectual math games than to art. However, they impress mathematicians and scientists.

It is said that people who live on some Pacific island or deep in the Amazon jungle, where they have never seen a photograph, will not be able at first to understand what the photograph represents when they are shown it. Interpreting this particular kind of image is an acquired skill. Some people master this skill better, others worse.

Artists began using geometric perspective in their work long before the invention of photography. But they could not study it without the help of science. Lenses became publicly available only in the 14th century. At that time they were used in experiments with darkened chambers. A large lens was placed in a hole in the wall of the darkened chamber so that the inverted image was displayed on the opposite wall. The addition of a mirror made it possible to cast the image from the floor to the ceiling of the camera. This device was often used by artists who were experimenting with the new "European" perspective style in art. By that time, mathematics was already complex enough to provide a theoretical basis for perspective, and these theoretical principles were published in books for artists.

Only by trying to draw illusory pictures on your own can you appreciate all the subtleties necessary to create such deceptions. Very often the nature of illusion imposes its own limitations, imposing its "logic" on the artist. As a result, the creation of the picture becomes a battle of the wit of the artist with the oddities of illogical illusion.

Now that we've covered some of the illusions, you can use them to create your own illusions, as well as classify any illusions you come across. After a while you will have large collection illusions, and you will need to somehow dismantle them. I designed a glass showcase for this.

Showcase of illusions. © Donald E. Simanek, 1996.

You can check the convergence of lines in perspective and other aspects of the geometry of this drawing. By analyzing such pictures, and trying to draw them, one can learn the essence of the deceptions used in the picture. M. C. Escher used similar tricks in his Belvedere painting (below).

Donald E. Simanek, December 1996. Translated from English

Maurits Cornelis Escher, Dutch graphic artist

Escher Maurits Cornelis(Maurits Cornelis Escher) (June 17, 1898, Leeuwarden, The Netherlands - March 27, 1972, Hilversum, The Netherlands) was a Dutch graphic artist who illustrated books, stamps and frescoes, invented tapestries. Known primarily for his conceptual lithographs, engravings on wood and metal, in which he masterfully explored the plastic aspects of the concepts of infinity and symmetry, as well as the psychological perception of complex three-dimensional objects, the most striking representative of imp art. Escher quite consciously chose a career as an engraver, and not as a painter (in oil). According to the researcher of his work, Hans Locher, Escher was attracted by the possibility of obtaining many prints, which was provided by graphic techniques, since he was already in early age interested in the possibility of repetition of images. One of the most outstanding aspects of Escher's work is the depiction of "metamorphoses", which appear in various forms in a variety of works. The artist explores in detail the gradual transition from one geometric figure to the other, through minor changes in outline. In addition, Escher repeatedly painted metamorphoses that occur with living beings (birds turn into fish, etc.) and even “animate” during metamorphoses inanimate objects turning them into living beings. Escher produced 448 lithographs, prints and woodcuts and over 2,000 drawings and sketches. His work continues to impress and amaze millions of people around the world. IN last years Escher's health fails and he practically does not work. He undergoes many surgeries and eventually dies in the hospital from bowel cancer. Escher left behind his wonderful lithographs, paintings, drawings and three sons.

Main dates

• 1898 - Moritz Cornelis Escher was born on June 17 in Liverden (Netherlands), younger son in the family of hydraulic engineer G. A. Escher and Sarah Glichman.
• 1903 - The family moves to Arnhem.
• 1912-18 - Enters the gymnasium and fails the final exams.
• 1919 - At the request of his father, Escher begins to study architecture in Haarlem, but after a few months he moves to the class graphic design led by Jeseran de Mesquite.
• 1921 - First trip to Italy. The first publication in the magazine of the work "Easter Flowers" (woodcut)
• 1922 - Graduates from art school and travels to central Italy; makes a lot of sketches. In September, he visits the Alhambra in Spain, considering it the most interesting, especially its huge mosaics of "colossal complexity and mathematical and artistic meaning."
• 1923 - Travel to Italy; meets his future wife Jetta (Jetta Umiker). Draws from life. His first exhibition in Siena.
• 1924 - First exhibition in The Hague, Netherlands June 12 is married to Yetta in Viareggio; moves to Rome.
• 1926 - Very successful exhibition in Rome in May. Later, Escher has a permanent exhibition in Holland and mainly positive reviews. On June 23, their first son Georg will be born in the Escher family. In subsequent years, Moritz Escher traveled constantly (for example, to Tunisia), including on foot to Arbuzi; makes a lot of landscape and architectural sketches.
• 1928 - December 8, son Arthur is born.
• 1929 - First lithograph "View of Goriano Sicoli", Arbuzzi
• 1931 - The first wood engraving, but in essence it was a wooden matrix for printing invitations to an exhibition in The Hague. Escher becomes a member of the association of graphic artists, a little later - a member of the Pulchi studio. He is highly respected as a "patient, calm, cold draftsman" and his work is criticized for being "too intellectual".
• 1932 - In the almanac "XXIV Emblemata dat zijns zinnebeelden" his woodcuts are printed.
• 1933 - The book "The Terrible Adventures of Scholasticism" comes out of print with woodcuts by Escher.
• 1934 - His work at the exhibition of modern prints (printing) "Century of Progress" in Chicago receives only positive reviews.
• 1935 - The repressive policies of Fascist Italy force Escher to move to Switzerland.
• 1936 - A trip to Spain, where he is again actively engaged in Moorish tile ornaments (Alhambra). Redrawing them inspires Escher to create paintings in which he uses the correct periodic division of the planes.
• 1938 - On March 6, another son, Jan, was born. And Escher concentrates on "inner paintings" and almost completely leaves the drawing of nature.
• 1939 - Death of his father at the age of 96.
• 1940 - "M.C. Escher en zijn experimenten" is published. His mother dies.
• 1941 - The Escher family returns to their homeland in Holland, in Baarn (B╠rn)
• 1948 Escher begins lecturing on his work along with demonstrations.
• 1954 - Escher's great exhibition on the occasion of the great Mathematical Congress. Following her - an exhibition in Washington.
• 1955 - April 30 receives a large royal award.
• 1958 - "Regelmatige vlakverdeling" (Correct division of planes) is published.
• 1959 - "Grafik en Tekeningen" (Graphic works) is published
• 1960 - Exhibition and lecture at the Crystallographic Congress in Cambridge, Massachusetts
• 1962 - Emergency operation, and a long stay in the hospital.
• 1964 - Leaves for Canada for another operation.
• 1965 - Hilversum Art Prize. "Symmetry Aspect" is printed (Symmetric aspects of Escher's periodic drawings).
• 1967 - Second Queen's Award.
• 1968 - A huge retrospective in honor of the 70th anniversary in The Hague. At the end of the year, Yetta returns to Switzerland.
• 1969 - In July, Escher creates his last woodcut "Snakes".
• 1970 - Operation and again a long hospitalization. Escher moves to the Rosa-Spier-Foundation Laaren in a retirement home for artists.
• 1971 - De werelden van M.C. Escher (Escher's World) is published.
• 1972 - MS Escher dies in Hilversum Lutheran Hospital.