Magic paintings by Maurice Escher, which illustrate the textbooks of crystallography. Principles of Construction of Illusions ♦♦♦ Impossible Figures

20.06.2020

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Illusory artworks have a certain charm. They are triumph of fine art over reality. Why are the illusions so interesting? Why so many artists use them in their works? Perhaps because they show not what is really painted. All are marked with lithography "Waterfall") Maurice Escher (Maurits C. Escher). Water here circulates infinitely, after rotating the wheel, it flows further and falls back at the starting point. If such a design could be built, there would be an eternal engine! But with a more attentive consideration of the picture, we see that the artist deceives us, and any attempt to build this design is doomed to failure.

Isometric drawings

For the transmission of the illusion of three-dimensional reality, two-dimensional drawings are used (drawings on a flat surface). Usually, the deception consists in the image of the projections of solid figures that a person is trying to imagine as three-dimensional objects in accordance with their personal experience.

The classic perspective is effective when imitating reality in the form of a "photographic" image. This representation is incomplete for several reasons. It does not allow us to see the scene from different points of view, approach it or consider the object from all sides. It does not give us the effect of the depth, which the real object would have. The effect of the depth arises 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. Flat pattern represents the scene only from one specified point of view. An example of such a picture can be a photograph made using a conventional monocular photo camera.

When using this class of illusions, the picture seems at first glance the usual representation of the solid in perspective. But with a closer examination, the internal contradictions of such an object become visible. And it becomes clear that such an object cannot exist in reality.

Illusion of Penrose

The waterfall of the Escher is based on the illusion of Penrose, sometimes called the illusion of the impossible triangle. Here this illusion is illusing in its simplest form.

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

In the illusion of Penrose uses "false perspective". "False Perspective" is also used when building isometric images. Sometimes such a prospect is called Chinese (approx. Translator: Reethersward called such a Japanese perspective). This method of drawing was often used in Chinese visual art. With this method of drawing the depth of the mixture of the ambiguous.

In isometric patterns, all parallel lines are submitted parallel, even if they are tilted with respect to the observers. The object having an angle of inclination directed from the observer looks just like if he was tilted to the observer for the same angle. The rectangle is bent twice (MacH figure (Mach)) brightly shows such ambiguity. This figure may seem to you with a revealed book, as if you look at the pages of the book, or it may seem a book deployed to you binding and you look at the book cover. This figure can also seem to be two combined parallelograms, but a very small number of people will see this figure precisely in the form of parallelograms.

Thiery Figure (Thiery) illustrates the same duality

Consider the illusion of the stairs of the Srooreder (Schroeder) - "pure" example of isometric ambiguity of depth. This figure can be perceived as a staircase at which it was possible to rise to the right left, or as a view of the staircase from below. Any attempt to change the position of the lines of the figure will destroy the illusion.

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

Fill some areas black. Black parallelograms may look as if we look at them or from below or from above. Try, if you can, see this picture differently, as if on one parallelograms, we look at the bottom, and on the other from above, alternating them. Most people cannot perceive this picture. Why are we not able to perceive the picture in this way? I believe that it is the most difficult of simple illusions.

The figure right uses the illusion of an impossible triangle in isometric style. This is one of the samples of "hatching" programs for the drawing of AutoCAD (TM). This sample is called "Escher".

Isometric drawing of the wire design of the cube shows isometric ambiguity. This figure is sometimes called Necker Cube. If the black point is in the center of one sides of the cube, is this face face or rear? You can also imagine that the point is located near the right lower corner of the side, but you still can not say whether this side is facial or not. You also can not have reasons to assume that the point is on the surface of the cube or inside it, it can be with the same success to the cube and behind it, since we do not have any information about the real dimensions of the point.

If you imagine the edge of the cube in the form of wooden planks, you can get unexpected results. Here we used an ambiguous connection of horizontal planks, which will be told below. This version of the figure is called an impossible box. It is the basis for many similar illusions.

The impossible box can not be made of wood. And yet we see here a photo of an impossible drawer made of wood. This is a lie. One of the plates of the box, which, as it seems, passes behind the other, is actually two separate straps with a break, one closer, and the other further than crossing the plank. Such a figure is visible only from a single point of view. If we looked at the real construction, with the help of our stereoscopic vision, we would see a trick, at the expense of which the figure becomes impossible. If we changed the point of view, then this trick would have become even more noticeable. That is why when demonstrating the impossible figures at exhibitions and in museums you are forced to look at them through a small hole with one eye.

Ambiguous compounds

What is the basis of this illusion? Is she a type of Macha's book?

In fact, this is a combination of the illusion of the Macha and the ambiguous connection of the lines. Two books share the total middle surface of the figure. This makes the slope of the book cover ambiguous.

Illusions of the situation

The illusion of Poggestorf (Poggendorf), or "Crossed Rectangle", misleads, which of the lines A or B is a continuation of the line C. The unambiguous answer can be given only by attaching a ruler to the C line, and the trace of which of the lines coincides.

Illusions of form

The illusions of the form are closely related to the illusions of the situation, but the structure itself is the structure itself makes our judgment about the geometric shape of the pattern. In the example below, short inclined lines create the illusion that the two horizontal lines are curved. In fact, it is direct parallel lines.

These illusions use the peculiarity of our brain to process visible information, including stroked surfaces. One sample of hatching can dominate so strongly that other elements of the drawing seem distorted.

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

In the same principle, the following example works. Although both circles have the same size, one of them looks less than the other. This is one of many illusions of size.

An explanation of such an effect can be our perception of the prospects in photographs and paintings. In the real world, we see that two parallel lines converge with increasing distance, so we perceive that the circle relating to the lines is further from us and, therefore, should be larger.

If the circles paint the circles and areas limited to the lines, then the illusion will be weaker.

The width of the fields and the height of the hats is the same, although it does not seem at first glance. Try to turn the image by 90 degrees. Is the effect preserved? This is the illusion of relative sizes within the picture.

Multiple ellipses

Inclined circles are projected onto the plane by ellipses, and these ellipses have ambiguity of depth. If the figure (above) is a tilted circle, then there is no way to find out whether the upper arc is closer to us or further from us than the lower arc.

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

An ambiguous ring, © Donald E. Simek, 1996.

If you close half the picture, the rest will resemble half of the usual ring.

When I came up with this shape, I thought it could be the original illusion. But later I saw advertising with the emblem of the Corporation producing fiber, Canstar. Although my Canstar emblem can be attributed to one class of illusions. Thus, I and the corporation have developed independently of each other shape of the impossible wheel. I think, if you get deeper, you can probably find earlier examples of the impossible wheel.

Infinite staircase

Another of the classic illusions of Penrose is an impossible staircase. It is most often portrayed in the form of an isometric pattern (even in the work of Penrose). Our version of the infinite staircase is identical to the Penrose Staircase version (with the exception of hatching).

It can also be depicted in perspective, as is done on lithographs M. K. Escher.

Cheating on lithography "climbing and descent" is somewhat different ways. Escher placed the staircase on the roof of the building and portrayed the building below in such a way as to transmit the impression of the prospects.

The artist portrayed an endless staircase with a shadow. Like a hatching, the shadow could destroy the illusion. But the artist placed the light source in such a place that the shadow is well combined with other parts of the picture. Perhaps the shadow from the staircase is an illusion by itself.

Conclusion

Some people do not intrigue illusory paintings. "Just the wrong picture" - they say. Some people, perhaps less than 1% of the population, do not perceive them, because their brain is not able to convert flat paintings into three-dimensional images. These people tend to have difficulties in the perception of technical drawings and illustrations of three-dimensional figures in books.

Others can see what the picture is wrong with the picture, but they will not think to ask how deception is. These people never have the need to understand how nature works, they cannot focus on the details for lack of elementary intellectual curiosity.

Perhaps an understanding of visual paradoxes is one of the signs of the type of creativity, which the best mathematics, scientists and artists possess. Among the works of M. K. Escher (M.C. Escher) there are a lot of pictures, as well as complex geometric paintings that can be attributed to "intellectual mathematical games" than to art. However, they impress the mathematicians and scientists.

It is said that people living on some Pacific island or deep in the Amazon jungle, where they never saw photos, they will not be able to first understand that it depicts a photo when they show it. The interpretation of this specific type of image is an acquired skill. Some people master this skill better, others are worse.

Artists began to use the geometrical perspective in their works much earlier than the invention of photography. But they could not explore it without help from science. The lenses became publicly available only in the XIV century. At that time they were used in experiments with darkened cameras. The large lens was placed in the hole in the wall of the darkened chamber so that the inverted image is displayed on the opposite wall. Adding a mirror made it possible to discard the image of the floor chamber ceiling. This device was often used by artists who experimented with a new "European" promising style in artistic art. By that time, mathematics was already quite complex science to give theoretical substantiation of the prospects, and these theoretical principles were published in books for artists.

Only self trying to draw illusory patterns, you can estimate all the subtleties necessary to create similar deceptions. Very often, the nature of illusion imposes its limitations, imposing its "logic" by the artist. As a result, creating a picture becomes the battle of the artist's wit with strangeness of illogical illusion.

Now that we discussed the essence of some illusions, you can use them to create your own illusions, as well as classify any illusions that you will meet. After a while you will have a big collection of illusions, and you will need to somehow demolish them. I developed a glass showcase for this.

Showcase illusions. © Donald E. Simandek, 1996.

You can check the convergence of lines in perspective and other aspects of the geometry of this picture. Analyzing such pictures, and trying to draw them, you can find out the essence of the deceptions used in the picture. M. K. Escher (M. C. Escher) used similar tricks in his picture "Belvedere" (below).

Donald E. Simanek, December 1996. Translation from English

Does science and art have common intersection points? Can one of these worlds supplement and enrich the discoveries of another? The Great Creators of the Renaissance in this formulation would not even see the contradiction. For them, the ways of knowledge of the world and self-expression were not shared so tough as for us. The works of the Netherlands Graphics Graphics of Maunice (Maurice) Escher usually produce a hypnotic effect on people, because they are blurred in our consciousness the rigid boundaries between logical and impossible, between constant and changing.

In fact, each of the paintings is a scientific and artistic study of the patterns of space and the characteristics of our perception. Specialists consider his creativity in the context of the theory of relativity and psychoanalysis. But you can simply distract for a few minutes and plunge into the world, where a clear logic that reigns inside the picture, suddenly turns out to be distorted about our world.

Laws of Symmetry

Pictures, landmarks for Escher, can be considered lithographs resembling Moorish mosaics. By the way, the artist admitted that this topic was inspired by visiting Alhambra's castle. The filling of the plane by identical figures could be considered a children's fun of a high artistic level, if not one item: from a mathematical point of view, these figures are satisfied with certain types of symmetry (in each one). By the way, it is the same as in crystalline lattices. Therefore, the works of Maurice Escher are recommended as illustrations when studying crystallography.

Metamorphosis

This interesting topic practically follows from previous drawings. Take a happy: similar motives, but gradual changes come to replace the clear ordering - from black to white, from small to large, from the bird to fish ... and from the plane to the volume!

Logic space

Why do we love tricks? Because they are safe for our psyche, for a few seconds they give to feel the presence of magic. That is, we record violations of the patterns of our world, but immediately understand that we are simply masterfully inflated, and therefore the world is in place. With the paintings of Escher, in which the artist explored the patterns of space, occurs about the same. At first glance, there are beautiful pictures, on the second and third - "We spent somewhere, we must understand where exactly" ... and you hang for a long time, trying to understand, "how so?".

Self-reproduction of information

"Drawing hands" is one of the most famous paintings by Escher. It is believed that on her idea of \u200b\u200bthe artist pushed the sketch to the "portrait of Jinevier de Benchi" Leonardo da Vinci. By the way, this drawing is not at all absolutely symmetrical, as it may seem at first glance.

Maurice Esher himself wrote about his work: "Although I absolutely disobey in the exact sciences, it sometimes seems to me that I am closer to mathematicians than to my colleagues-artists." In fact, scientists of men give a charter due to this master, because in his works one can also find illustrations for the topics "Mosaic splitting of the plane", "Nevklidova Geometry", "Projecting three-dimensional figures on the plane", "impossible figures" and many others. In addition, the Escher was ahead of mathematicians in working with fractals, the theoretical description was given only in the 1970s, and the paintings using this mathematical model the artist created much earlier.

Surrealistic watercolors created by the Spanish artist Borh Sanchez,

"Waterfall" - lithography of the Dutch artist of Escher. First was printed in October 1961.
In this work, Escher depicts a paradox - the waterfall falling water controls the wheel, which directs water to the vertex of the waterfall. The waterfall has the structure of the "impossible" triangle of Penrose: lithography was created based on the article in the British magazine of psychology.
The design is made up of three crossbars, put on each other at right angles. Waterfall on lithography works as an eternal engine. Depending on the movement of the view alternately, it seems that both towers are the same and that located on the right tower on the floor below the left tower.

Connected concepts

Related concepts (continued)

Regular park (or garden; also French or geometric park; sometimes also "garden in regular style") - a park having a geometrically correct layout, usually with pronounced symmetry and regularity of the composition. It is characterized by straight alarms that are axes of symmetry, flower beds, parmers and basins of the right shape, haircut trees and shrubs with giving landings for a variety of geometric shapes.

"Two pines and smooth distance" (Kit. Trad. 雙松平遠) - a handwritten scroll, created by about 1310 by the Chinese artist Zhao Manfu. A scenery with pines is depicted on the scroll, part is filled with calligraphy. Currently, the work is in the metropolitan-museum meeting, where the drawing was transmitted in 1973.

Playing Chinese Chess (Fr. Le Jeu D "Échets chinois) - the etchings of the British Engraving John Ingram (English. John Ingram, 1721-1771?, Active until 1763) in the drawing of French artist Francois Boucher (Fr. Francois Boucher). Pictures Allegedly Chinese national game in Xianzi (Kit. 象棋, Pinyin Xiàngqí), in fact a spoant game (all the figures in real Xianzi have a checkered form).

Dirama (DIA-Greek. Διά (DIA) - "Through", "Through" and ὅραμα (Horama) - "View", "Spectacular") - a lintel-shaped, crucible picturesque picture with an anterior object (structures, real and butafors Items). Dirama refers to mass entertainment art, in which the illusion of the presence of the viewer in natural space is achieved by the synthesis of artistic and technical means. If the artist performs a full circular review, then they talk about "panorama".

Snowball (English Snow Globe), also called "glass ball with snow" - a popular Christmas souvenir in the form of a glass bowl, in which there is a certain model (for example, a house decorated with a holiday). When shaking such a ball on the model, artificial "snow" begins to fall. Modern snowballs are very beautifully decorated; Many have a factory and even built-in mechanism (similar to those used in music boxes), which plays a Christmas tune.

Constellations (English Constellations) - a series of 23 small gaisas Joana Miro, begun in 1939 in Varanzhville-sur-Committee and completed in 1941, between Mallorca and Mont-Roche del Camp. The Morning Star, one of the most important works of the series, stores Joan Miro Foundation. The works were the gift of the artist to his wife, later she handed them to the Foundation.

Astrarium, also called Planetarium - Vintage Astronomical Watch, created in the XIV century Italian Giovanni de Dondi. The appearance of this tool marked the development of technologies in Europe related to the manufacture of mechanical time instruments. The Astrarium simulated the solar system and, in addition to the time and presentation of calendar dates and holidays, showed how the planets on the celestial sphere moved. It was its main task, in comparison with astronomical clock, the main ...

"Regular division of the plane" - a series of xylographs of the Netherlands Artist of Escher, started in 1936. The basis of these works is the principle of tessellation, in which the space is divided by the part, fully covering the plane, without crossing and not overlapping at each other.

The kinetic architecture is such a direction of architecture in which buildings are designed in such a way that their parts can move relative to each other without disturbing the overall integrity of the structure. A different kinetic architecture is called dynamic, and refer to the direction of the architecture of the future.

Circles on the fields (English Crop Circles), or agroglyphs (port. Agroglifos; fr. Agroglyphes; "Agro" + "glyphs"), - geoglyphs; Geometrical patterns in the form of rings, circles and other figures formed in the fields with the help of flooded plants. It can be both small and very large, completely distinguishable only from a bird's eye view or from an airplane. They attracted public attention, starting from the 1970s-1980s, when their in many began to detect in the south of Great Britain.

Imaginary prisons, fantastic images of prisons, or dunnament - this is a series of etching Giovanni Battists Pirasei, started in 1745 and has become the most famous work of the author. Approximately in 1749-1750 14 sheets were published, and in 1761 the engraving series was reprinted in the amount of 16 sheets. In both editions, the engravings were missing names, but in the second, in addition to recycling, serial numbers were obtained. The last edition was published in 1780.

Dance with bedspread (Fr. Danser Avec Un Voile) - Sculpture of the work of Antoine Emil Bardella. Located on a permanent exposition in GMIA. A. S. Pushkin in Moscow. Made from bronze in 1909, size - 69.5 x 26 x 51 cm.

The tower in the Bollingen is a structure created by the Swiss Psychiatrist and a psychologist Carl Gustav Jung. It is a small castle with several towers, located in the town of Bolingen on the shore of Zurich Lake near the mouth of the river River.

Mentioned in the literature (continued)

Landscape style, unlike regular, close to nature as much as possible. It was created in the East and gradually spread around the world. In China and Japan, always bowed to the natural beauty of nature, believed that, creating landscapes, it is necessary to proceed From the laws of nature. Only in this case can be achieved harmony and equilibrium. The design of the site in the landscape style requires much smaller cost of strength compared to regular style. For him, it is not necessary to specifically change the terrain to create a cascade of waterfalls. You can use the natural relief of your site and organize in its lowland a small pond of free outlines, surrounding it with a flower bed of unpretentious ornamental plants, and on the elevation to arrange an alpine slide, covered with moss and surrounded by river pebbles.

Baroque, as you know, sought to move in architecture, create an illusion of movement ("illusion" is typical for Baroque). In Gardening Park Art, Baroque opened a clear possibility from illusion to move to real implementation movement in art. Therefore, fountains, Cascades, waterfalls - a typical phenomenon of baroque gardens. Water beats up and as if overcome the laws of nature. Plug, pegged under the wind, is also an element of movement in Baroque gardens.

The Japanese always considered the nature of Divine Creation. From ancient times, they bowed to her beauty, worshiped mountain heights, rocks and stones, mighty old trees, picturesque water bodies and waterfalls. According to the Japanese, the most beautiful areas of the natural landscape are the housing of spirits and gods. In the VI-VII centuries. The first artificially created Japanese appear gardens that are miniature simulatory imitation The coast, later becoming popular Chinese-style gardens using stone fountains and bridges. In the time of Hayan, the shape of ponds with palace parks changes. It becomes more so hot: waterfalls, streams, pavils for fishing decorate parks and gardens.

The second stage of recovery work continued from 1945 to 1951. At this time, fountains were restored, the lost decorative was recreated sculpture. Finally, August 26, 1946 was introduced The alley of fountains, terrace and Italian ("bowls") fountains, water homes and waterfalls of a large cascade. And on September 14, 1947 he earned a fountain with a bronze group "Samson, bursting the mouth of the lion." From 1947 to 1950, for a large cascade were made instead of stolen decorative details: bas-reliefs, arms, mascurns, brackets, monumental statues "Tritons", "Volkhov", "Neva". At the same time, the largest fountains of the Lower Park began to function: "Adam", "Eve", Meager, Roman, Nymph, Danaida, Cascade "Golden Mountain", the fountain-cracker "umbrella". As a result of the second stage of the restoration, the seven fountains of the Monplasir Garden resumed.

In addition, in the park "Golden Gate "There are many other interesting zones: Chalet Park, Shakespeare Garden, Biblical Garden, the highest artificial waterfall in the western states of the United States, Yang's Fine Arts Museum, Magnificent Botanical Garden Strebing Arboterium and others.

The landowners of the beginning of the XIX century saw the ideal in natural beauty, and therefore the ponds on the lakes were resolutely changed, smoothly - on winding paths, exactly trimmed lawns - on the lawns, where instead of individual trees with kruna-balls or squares of Green, miniature groves. The man-made nature was complemented "almost like real "waterfalls," medieval "towers, "Shepherds" huts and ruins are structures stylized for disgrace, launitions, isolated from diverse (old and new, large and small) parts, for the sweeping effect covered with creeping greenery.

Switzerland in the literature. Albrecht von Galler (1708-1777) wrote the epic poem "Alps", the story Thomas Mann "Magic mountain "made famous Davos, and Jean-Jacques Rousseau in the novel "Julia, or New Eloiza" glorified the beauty of the Lake Geneva. Thanks to the "Packages about Sherlock Holmes" Reichenbakh Waterfall as a grave of Professor Moriarty.

The book describes the highest mountains and the deepest ocean depressions, the most dry deserts and the largest seas, the highest volcanoes and geasers, the deepest disappearance and the longest caves, the highest waterfalls, in general, The most, most, most.

The attractiveness of the trails is associated with a picturesque landscape, a harmonious combination of living and inanimate nature, a variety of vegetable and animal peace, originality of particularly attractive objects and Natural phenomena (lakes, beautiful ducts, rocks, canyons, waterfalls, caves, etc.).

The impossible figure is one of the types of optical illusions, the figure that seems at first glance the projection of the usual three-dimensional object,

With a careful consideration of which the contradictory compounds of the elements of the figure become visible. The illusion of the impossibility of the existence of such a figure in three-dimensional space is created.

♦♦♦
Impossible figures

The most famous impossible figures: the impossible triangle, an infinite staircase and an impossible trident.

Impossible triangle Perrose

Reutersvard Illusion (Reutersvard, 1934)

Pay attention also to the fact that the change in the organization "Figure-background" made possible perception located in the center of "Stars".
_________

Impossible cube Escher

In fact, all impossible figures can exist in the real world. Thus, all objects drawn on paper are projections of three-dimensional objects, therefore, you can create such a three-dimensional object, which when projection to the plane will look impossible. When looking at such an object from a specific point, it will also look impossible, but when a review from any other point, the effect of impossibility will be lost.

The 13-meter sculpture of the impossible triangle of aluminum was erected in 1999 in Perth (Australia). Here, the impossible triangle was depicted in the most general form - in the form of three beams connected to each other under the right corners.

Chestova fork
Among all the impossible figures, the impossible trident occupies a special place ("Damn Fork").

If you close the right side of the troll, we will see a completely real picture - three round teeth. If you close the lower part of the trident, we will also see the real picture - two rectangular teeth. But, if we consider the whole figure of the whole, it turns out that three round teeth are gradually turning into two rectangular.

Thus, it can be seen that the front and rear plans of this picture conflict. That is, what was originally in the foreground goes back, and the back plan (medium tooth) gets out forward. In addition to the change of the front and rear plans in this picture there is another effect - the flat faces of the right side of the trident become round in the left.

The effect of the inability is achieved due to the fact that our brain analyzes the contour of the figure and tries to calculate the number of teeth. The brain compares the number of teeth of the figure in the left and right part of the figure, because of which there is a feeling of the impossibility of the figure. If the number of teeth in the figure was significantly larger (for example, 7 or 8), then this paradox would be less pronounced.

Some books argue that the impossible trident belongs to the class of impossible figures that cannot be recreated in the real world. In fact, it is not. All impossible figures can be seen in the real world, but they will be impossible to look only from one single point of view.

______________

Impossible elephant

How many legs of the elephant?

Psychologist from Stepford Roger Shepard (Roger Shepard) used the idea of \u200b\u200ba trident for his picture of the impossible elephant.

______________

Penrose staircase (Infinite staircase, impossible staircase)

The infinite staircase "is one of the most famous classical impossibility.

It is the design of the staircase at which in the event of a movement along it in one direction (in the figure to the article counterclockwise), a person will raise an infinitely, and when moving in the opposite - constantly descend.

In other words, we appear the staircase leading, seemingly up or down, but at the same time a person walking along it does not rise and does not fall. After completing his visual route, it will be at the beginning of the way. If you really had to go through this stairs, you would be aimlessly climbed and descended the infinite number of times. You can call it an endless sympathetic work!

Since Penrouse published this figure, it appeared in print more often than any other impossible object. The "endless staircase" can be found in books about games, puzzles, illusions, in textbooks on psychology and other subjects.

"Climbing and descent"

The "Infinite Forestry" "was successfully used by the artist Mauritz K. Escher, this time in his charming lithography" climbing and descent "created in 1960.
In this picture, reflecting all the features of the Figure Figure, a completely recognizable endless staircase is neatly inscribed in the roof of the monastery. Monks in the hoods are continuously moving along the stairs in the direction clockwise and against it. They go towards each other by the impossible path. They are never able to go upstairs, nor go down.

Accordingly, the "endless staircase" became more likely to be associated with Escher, who resulted in it than with Penrose, who came up with it.

How many shelves are there?

Where is the door open?

Outside or inward?

Impossible figures occasionally appeared on the canvases of the masters of the past, for example, such a gallows on the picture of Peter Bruegel (senior)
"Forty on the gallows" (1568)

__________

Impossible Arch

Jos De Mey - Flemish artist, studied at the Royal Academy of Fine Arts in Ghent (Belgium), and then taught students design interiors and color for 39 years. Since 1968, the center has become drawing. It is most famous for the careful and realistic performance of impossible structures.

The most famous impossible figures in the works of the artist Maurice Escher. When viewed by such drawings, each individual item seems quite plausible, but when trying to trace the line, it turns out that this line is already, for example, not an outer angle of the wall, but internal.

"Relativity"

This lithography of the Dutch artist Escher was first printed in 1953.

On lithographs, a paradoxical world is depicted, in which the laws of reality do not apply. In one world, three reality are combined, three gravity are directed perpendicular to one other.

A architectural structure has been created, reality combined with stairs. For people living in this world, but in different planes of reality, the same staircase will be directed or up or down.

"Waterfall"

This lithography of the Dutch artist Escher was first printed in October 1961.

In this work, Escher depicts a paradox - the waterfall falling water controls the wheel, which directs water to the vertex of the waterfall. The waterfall has the structure of the "impossible" triangle of Penrose: lithography was created based on the article in the British magazine of psychology.

The design is made up of three crossbars, put on each other at right angles. Waterfall on lithography works as an eternal engine. It also seems that both towers are the same; In fact, the one is the right, on the floor below the left tower.

Well, more modern work: o)
Infinite photography