At first glance, it seems that impossible figures can only exist on a plane. In fact, incredible figures can be embodied in three-dimensional space, but for “that same effect” you need to look at them with certain point.

Distorted perspective is a common occurrence in antique painting. Somewhere this was due to the artists’ inability to construct an image, somewhere it was a sign of indifference to realism, which was preferred to symbolism. Material world was partly rehabilitated in the Renaissance. The Renaissance masters began to explore perspective and discovered games with space.

One of the images of the impossible figure refers to XVI century- in Pieter Bruegel the Elder’s painting “The Magpie on the Gallows,” that same gallows looks suspicious.

Great fame came to the impossible figures of the twentieth century. Swedish artist Oskar Rootesvard painted a triangle composed of cubes, “Opus 1,” in 1934, and a few years later, “Opus 2B,” in which the number of cubes was reduced. The artist himself notes that the most valuable thing in the development of figures, which he undertook back in school years, what should be considered is not the creation of the drawings themselves, but the ability to understand that what is drawn is paradoxical and contrary to the laws of Euclidean geometry.

My first impossible figure appeared by chance, when in 1934, in my last year at the gymnasium, I was scribbling through a Latin grammar textbook, drawing geometric figures in it.

Oscar Rootesward « Impossible figures»

In the 50s of the twentieth century, an article by the British mathematician Roger Penrose was published, devoted to the peculiarities of the perception of spatial forms depicted on a plane. The article was published in the British Journal of Psychology, which says a lot about the essence of impossible figures. The main thing about them is not even the paradoxical geometry, but how our mind perceives such phenomena. It usually takes a few seconds to figure out what exactly is “wrong” with the figure.

Thanks to Roger Penrose, these figures were looked at from a scientific point of view, as objects with special topological characteristics. The Australian sculpture, discussed above, is precisely the impossible Penrose triangle, in which all the components are real, but the picture does not add up to the integrity that can exist in the three-dimensional world. The Penrose Triangle is misleading by providing a false perspective.

Mysterious figures have become a source of inspiration for physicists, mathematicians, and artists. Inspired by Penrose's article, the graphic artist Maurits Escher created several lithographs that brought him fame as an illusionist, and subsequently continued to experiment with spatial distortions on the plane.

Impossible fork

The impossible trident, blivet or even, as it is also called, “the devil’s fork,” is a figure with three round prongs at one end and rectangular ones at the other. It turns out that the object is quite normal in the right and left parts, but in the complex it turns out to be pure madness.

This effect is achieved due to the fact that it is difficult to clearly say where the foreground is and where the background is.

Irrational cube

The impossible cube (also known as the “Escher cube”) appeared in the lithograph “Belvedere” by Maurits Escher. It seems that by its very existence this cube violates all basic geometric laws. The solution, as always with impossible figures, is quite simple: to the human eye It is common to perceive two-dimensional images as three-dimensional objects.

Meanwhile, in three dimensions, an impossible cube would look like this and from a certain point would appear the same as the picture above.

Impossible figures are of great interest to psychologists, cognitive scientists and evolutionary biologists, helping to understand more about our vision and spatial thinking. Today, computer technology, virtual reality and projections are expanding possibilities, so that controversial objects can be looked at with new interest.

In addition to the classic examples that we have given, there are many other options for impossible figures, and artists and mathematicians are coming up with new and paradoxical options. Sculptors and architects use solutions that may seem incredible, although their appearance depends on the direction the viewer is looking (as Escher promised - relativity!).

You don’t have to be a professional architect to try your hand at creating volumetric impossibilities. There are origami of impossible figures - this can be repeated at home by downloading the blank.

Useful Resources

• Impossible world - resource in Russian and English with famous paintings, hundreds of examples of impossible figures and programs for creating the incredible on your own.
• M.C. Escher - official website of M.K. Escher, founded by the MC Escher Company (English and Dutch).
• - artist’s works, articles, biography (Russian language).

Candidate of Technical Sciences D. RAKOV (Institute of Mechanical Science named after A. A. Blagonravov RAS).

Exists big class images about which you can say: “What are we seeing? Something strange.” These include drawings with a distorted perspective, objects that are impossible in our three-dimensional world, and unimaginable combinations of very real objects. Appearing at the beginning of the 11th century, such “strange” drawings and photographs have today become a whole movement of art called imp art.

William Hogard. "Impossible Perspective", where at least fourteen errors in perspective are deliberately made.

Madonna and Child. 1025

Pieter Bruegel. "Magpie on the Gallows" 1568

Oscar Rootesward. "Opus 1" (No. 293aa). 1934

Oscar Rootesward. "Opus 2B". 1940

Maurits Cornelius Escher. "Ascent and descent."

Roger Penrose. "Impossible Triangle" 1954

Construction" impossible triangle".

Sculpture "Impossible Triangle", view from different sides. It is built from curved elements and looks impossible from just one point.

Ill. 1. Morphological table for the classification of impossible objects.

A person begins examining the picture from the lower left corner (1), then moves his gaze first to the middle (2), and then to point 3.

Depending on the direction we look, we see different objects.

The impossible alphabet is a combination of possible and impossible figures, among which there is even a frame element. Drawing by the author.

Science and life // Illustrations

"Moscow" (metro line diagram) and "Two Lines of Fate". Drawings by the author; computer processing. 2003 The figures demonstrate new possibilities for creating diagrams and graphs.

Science and life // Illustrations

Cube in a cube ("Three Snails"). The rotated image has a greater degree of "impossibility" than the original one.

"Damn fork." Many impossible images have been created based on this figure.

What do we see - a pyramid or an opening?

A little history

Paintings with distorted perspective can be found already at the beginning of the first millennium. In a miniature from the book of Henry II, created before 1025 and kept in the Bavarian state library in Munich, Madonna and Child is painted. The painting depicts a vault consisting of three columns, and the middle column, according to the laws of perspective, should be located in front of the Madonna, but is behind her, which gives the painting a surreal effect. Unfortunately, we will never know whether this technique was a conscious act of the artist or his mistake.

Images of impossible figures, not as a conscious direction in painting, but as techniques that enhance the effect of the perception of the image, are found among a number of painters of the Middle Ages. Pieter Bruegel's painting "The Magpie on the Gallows," created in 1568, shows a gallows of impossible design that adds to the effect of the entire painting. In a well-known engraving of English artist XVIII century William Hogarth's "False Perspective" shows to what absurdity an artist's ignorance of the laws of perspective can lead.

At the beginning of the 20th century, the artist Marcel Duchamp painted an advertising painting "Apolinere enameled" (1916-1917), stored in the Philadelphia Museum of Art. In the design of the bed on the canvas you can see impossible three- and quadrangles.

The founder of the direction of impossible art - imp-art (imp-art, impossible art) is rightly called the Swedish artist Oscar Rutesvard (Oscar Reutersvard). The first impossible figure "Opus 1" (N 293aa) was drawn by the master in 1934. The triangle is made up of nine cubes. The artist continued his experiments with unusual objects and in 1940 created the figure “Opus 2B”, which is a reduced impossible triangle consisting of only three cubes. All cubes are real, but their location in three-dimensional space is impossible.

The same artist also created the prototype of the “impossible staircase” (1950). The most famous classical figure, the Impossible Triangle, was created by the English mathematician Roger Penrose in 1954. He used linear perspective rather than parallel perspective like Rootesward, which gave the painting depth and expressiveness and therefore a greater degree of impossibility.

Most famous artist Imp art became M. C. Escher. Among his most famous works are the paintings “Waterfall” (1961) and “Ascending and Descending”. The artist used the “endless staircase” effect, discovered by Rootesward and later expanded by Penrose. The canvas depicts two rows of men: when moving clockwise, the men constantly rise, and when moving counterclockwise, they descend.

A bit of geometry

There are many ways to create optical illusions(from Latin word"iliusio" - error, delusion - inadequate perception of an object and its properties). One of the most spectacular is the direction of imp art, based on images of impossible figures. Impossible objects are drawings on a plane (two-dimensional images), executed in such a way that the viewer gets the impression that such a structure cannot exist in our real three-dimensional world. Classic, as already mentioned, and one of the simplest such figures is the impossible triangle. Each part of the figure (the corners of the triangle) exists separately in our world, but their combination in three-dimensional space is impossible. Perceiving the entire figure as a composition of irregular connections between its real parts leads to the deceptive effect of an impossible structure. The gaze glides along the edges of an impossible figure and is unable to perceive it as a logical whole. In reality, the view tries to reconstruct the real three-dimensional structure (see figure), but encounters a discrepancy.

From a geometric point of view, the impossibility of a triangle lies in the fact that three beams connected in pairs to one another, but along three different axes of the Cartesian coordinate system, form a closed figure!

The process of perceiving impossible objects is divided into two stages: recognizing the figure as a three-dimensional object and realizing the “irregularity” of the object and the impossibility of its existence in the three-dimensional world.

The existence of impossible figures

Many people believe that impossible figures are truly impossible and cannot be created in real world. But we must remember that any drawing on a sheet of paper is a projection of a three-dimensional figure. Therefore, any figure drawn on a piece of paper must exist in three-dimensional space. Impossible objects in paintings are projections of three-dimensional objects, which means that objects can be realized in the form sculptural compositions(three-dimensional objects). There are many ways to create them. One of them is the use of curved lines as the sides of an impossible triangle. The created sculpture looks impossible only from a single point. From this point, the curved sides look straight, and the goal will be achieved - a real "impossible" object will be created.

About the benefits of imp art

Oscar Rootesvaard talks in the book “Omojliga figurer” (there is a Russian translation) about the use of imp art drawings for psychotherapy. He writes that the paintings, with their paradoxes, evoke surprise, focus attention and the desire to decipher. In Sweden, they are used in dental practice: by looking at pictures in the waiting room, patients are distracted from unpleasant thoughts in front of the dentist’s office. Remembering how long one has to wait for an appointment in various Russian bureaucratic and other institutions, one can assume that impossible pictures on the walls of reception areas can brighten up the waiting time, calming visitors and thereby reducing social aggression. Another option would be to install in reception areas slot machines or, for example, mannequins with corresponding faces as dart targets, but, unfortunately, this kind of innovation was never encouraged in Russia.

Using the phenomenon of perception

Is there any way to enhance the effect of impossibility? Are some objects more "impossible" than others? And here the peculiarities of human perception come to the rescue. Psychologists have found that the eye begins to examine an object (picture) from the lower left corner, then the gaze slides to the right to the center and drops to the lower right corner of the picture. This trajectory may be due to the fact that our ancestors, when meeting an enemy, first looked at the most dangerous right hand, and then the gaze moved to the left, to the face and figure. Thus, artistic perception will significantly depend on how the composition of the picture is constructed. This feature was clearly manifested in the Middle Ages in the manufacture of tapestries: their design was mirror image original, and the impression produced by tapestries and originals differs.

This property can be successfully used when creating creations with impossible objects, increasing or decreasing the “degree of impossibility”. The prospect of receiving interesting compositions using computer technology or from several pictures rotated (maybe using various types symmetries) one relative to the other, creating in viewers a different impression of the object and a deeper understanding of the essence of the design, or from one that rotates (constantly or jerkily) using a simple mechanism at certain angles.

This direction can be called polygonal (polygonal). The illustrations show images rotated relative to each other. The composition was created as follows: a drawing on paper, made in ink and pencil, was scanned, converted into digital form and processed in graphic editor. A regularity can be noted - the rotated picture has a greater “degree of impossibility” than the original one. This is easily explained: the artist, in the process of work, subconsciously strives to create the “correct” image.

Combinations, combinations

There is a group of impossible objects, the sculptural implementation of which is impossible. Perhaps the most famous of them is the “impossible trident”, or “devil’s fork” (P3-1). If you look closely at the object, you will notice that three teeth gradually turn into two on a common basis, leading to a conflict of perception. We compare the number of teeth above and below and come to the conclusion that the object is impossible. Based on the “fork,” a great many impossible objects have been created, including those where a part that is cylindrical at one end becomes square at the other.

Besides this illusion, there are many other types optical illusions vision (illusions of size, movement, color, etc.). The illusion of depth perception is one of the oldest and most famous optical illusions. The Necker cube (1832) belongs to this group, and in 1895 Armand Thiery published an article about special form impossible figures. In this article, for the first time, an object was drawn that later received the name Thierry and was used countless times by op art artists. The object consists of five identical rhombuses with sides of 60 and 120 degrees. In the figure you can see two cubes connected along one surface. If you look from the bottom up, you can clearly see the lower cube with two walls at the top, and if you look from the top down, you can clearly see the upper cube with the walls below.

The most simple figure of the Thierry-like ones, this is apparently a “pyramid-opening” illusion, which is a regular rhombus with a line in the middle. It is impossible to say exactly what we see - a pyramid rising above the surface, or an opening (depression) on it. This effect was used in the graphic "Labyrinth (Pyramid Plan)" of 2003. The painting received a diploma at the international mathematical conference and exhibition in Budapest in 2003 "Ars(Dis)Symmetrica" ​​03. The work uses a combination of the illusion of depth perception and impossible figures.

In conclusion, we can say that the imp art direction is like component optical art is actively developing, and in the near future we will undoubtedly expect new discoveries in this area.

LITERATURE

Rutesward O. Impossible figures. - M.: Stroyizdat, 1990.

Captions for illustrations

Ill. 1. The table constructed by the author of the article does not pretend to be complete and strict in order, but makes it possible to evaluate the whole variety of impossible figures. The table contains more than 300 thousand combinations of various elements. Graphics from the author of the article and materials from Vlad Alekseev’s website were used as illustrations.

Impossible figures are figures depicted in perspective in such a way as to appear at first glance to be an ordinary figure. However, upon closer examination, the viewer realizes that such a figure cannot exist in three-dimensional space. Escher depicted impossible figures in his famous paintings Belvedere (1958), Ascent and Descend (1960) and Waterfall (1961). One example of an impossible figure is a painting by the contemporary Hungarian artist István Orosz.

Istvan Oros "Crossroads" (1999). Reproduction of metal engraving. The painting depicts bridges that cannot exist in three-dimensional space. For example, there are reflections in the water that cannot be the original bridges.

the Mobius strip

A Möbius strip is a three-dimensional object that has only one side. This type of tape can easily be made from a strip of paper by twisting one end of the strip and then gluing both ends together. Escher depicted the Möbius strip in Riders (1946), Möbius Strip II (Red Ants) (1963) and Knots (1965).

“Knots” - Maurits Cornelis Escher 1965

Later, minimum energy surfaces became an inspiration for many mathematical artists. Brent Collins, uses Möbius strips and minimum energy surfaces, as well as other types of abstractions in sculpture.

Distorted and unusual perspectives

Unusual perspective systems containing two or three vanishing points are also a favorite theme of many artists. These also include a related field - anamorphic art. Escher used distorted perspective in several of his works, Above and Below (1947), House of Stairs (1951), and The Picture Gallery (1956). Dick Termes uses six-point perspective to draw scenes on spheres and polyhedra, as shown in the example below.

Dick Termes "A Cage for Man" (1978). This is a painted sphere that was created using six-point perspective. It depicts a geometric structure in the form of a grid, through which the landscape is visible. Three branches penetrate into the cage, and reptiles crawl along it. While some explore the world, others find themselves caged.

The word anamorphic is formed from two Greek words "ana" (again) and morthe (form). Anamorphic images are images that are so severely distorted that it can be impossible to make them out without a special mirror. This mirror is sometimes called an anamorphoscope. If you look through an anamorphoscope, the image “forms again” into a recognizable picture. European artists early renaissance were fascinated by linear anamorphic paintings, where an elongated picture became normal again when viewed from an angle. A famous example is Hans Holbein's painting "The Ambassadors" (1533), which depicts an elongated skull. The painting can be tilted at the top of the stairs so that people walking up the stairs will be startled by the image of the skull. Anamorphic paintings, which require cylindrical mirrors to view, were popular in Europe and the East in the 17th and 18th centuries. Often such images carried messages of political protest or were of erotic content. Escher did not use classic anamorphic mirrors in his work, however, he did use spherical mirrors in some of his paintings. His most famous work in this style is “Hand with a Reflecting Sphere” (1935). The example below shows a classic anamorphic image by Istvan Orosz.

Istvan Oros "The Well" (1998). The painting "Well" was printed from a metal engraving. The work was created for the centenary of the birth of M.K. Escher. Escher wrote about excursions into mathematical art as being like walking through a beautiful garden where nothing is repeated. The gate on the left side of the picture separates Escher's mathematical garden, located in the brain, from physical world. The broken mirror on the right side of the painting shows a view of the small town of Atrani on the Amalfi Coast in Italy. Escher loved the place and lived there for some time. He depicted this city in the second and third paintings from the Metamorphoses series. If you place a cylindrical mirror in place of the well, as shown on the right, Escher's face will appear in it, as if by magic.

Many people believe that impossible figures are truly impossible and cannot be created in the real world. However, we know from a school geometry course that a drawing depicted on a sheet of paper is a projection of a three-dimensional figure onto a plane. Therefore, any figure drawn on a piece of paper must exist in three-dimensional space.

Moreover, three-dimensional objects, when projected onto a plane, produce a given flat figure of an infinite set. The same applies to impossible figures. Of course, none of the impossible figures can be created by acting in a straight line. For example, if you take three identical wooden bars, you will not be able to combine them to form an impossible triangle. However, when projecting a three-dimensional figure onto a plane, some lines may become invisible, overlap each other, join each other, etc. Based on this, we can take three different bars and make the triangle shown in the photo below (Fig. 1). This photograph was created by the famous popularizer of the works of M.K. Escher, author

large quantity books by Bruno Ernst. On

As mentioned above, the number of figures corresponding to a given projection is infinite, so the above example is not the only way to construct an impossible triangle in reality. Belgian artist Mathieu Hamaekers created the sculpture shown in Fig. 2. The photo on the left shows a frontal view of the figure, making it look like an impossible triangle, the center photo shows the same figure rotated 45°, and the photo on the right shows the figure rotated 90°.

Rice. 2. Photograph of the impossible triangle figure by Mathieu Hemakerz.

As you can see, in this figure there is no straight lines, all elements of the figure are curved in a certain way. However, as in the previous case, the effect of impossibility is noticeable only at one viewing angle, when all curved lines are projected in straight lines, and if you do not pay attention to some shadows, the figure looks impossible.

Another way to create an impossible triangle was proposed by the Russian artist and designer Vyacheslav Koleichuk and published in the journal “Technical Aesthetics” No. 9 (1974).

All the edges of this design are straight lines, and the edges are curved, although this curvature is not visible in the frontal view of the figure. He created such a model of a triangle from wood. Rice. 3.

Model of the impossible triangle by Vyacheslav Koleichuk.

This model was later recreated by Gershon Elber, a member of the Computer Science Department at the Technion Institute in Israel. Its version (see Fig. 4) was first designed on a computer and then recreated in reality using a three-dimensional printer. If we slightly shift the viewing angle of the impossible triangle, we will see a figure similar to the second photograph in Fig. 4. Rice. 4.

It is worth noting that if we were now looking at the figures themselves, and not at their photographs, we would immediately see that none of the presented figures is impossible, and what is the secret of each of them. We simply would not be able to see these figures because we have stereoscopic vision. That is, our eyes, located at a certain distance from each other, see the same object from two close, but still different, points of view, and our brain, having received two images from our eyes, combines them into a single picture. It was said earlier that an impossible object looks impossible only from a single point of view, and since we view the object from two points of view, we immediately see the tricks with the help of which this or that object was created.

Does this mean that in reality it is still impossible to see an impossible object? No, you can.

If you close one eye and look at the figure, it will look impossible. Therefore, in museums, when demonstrating impossible figures, visitors are forced to look at them through a small hole in the wall with one eye. There is another way by which you can see an impossible figure, with both eyes at once. It consists of the following: it is necessary to create a huge figure with a height of multi-storey building , place it in a wide open space and look at it from a very long distance

. In this case, even looking at the figure with both eyes, you will perceive it as impossible due to the fact that both your eyes will receive images that are practically no different from each other.

Such an impossible figure was created in the Australian city of Perth. While an impossible triangle is relatively easy to construct in the real world, creating an impossible trident in three-dimensional space is not so easy. The peculiarity of this figure is the presence of a contradiction between the foreground and background of the figure, when the individual elements of the figure smoothly blend into the background on which the figure is located.

The Institute of Ocular Optics in Aachen (Germany) was able to solve this problem by creating a special installation. The design consists of two parts.

In front there are three round columns and a builder. This part is only illuminated at the bottom. Behind the columns there is a semi-permeable mirror with a reflective layer located in front, that is, the viewer does not see what is behind the mirror, but sees only the reflection of the columns in it. Rice. 6.

Installation diagram reproducing the impossible trident.

An impossible figure is one of the types of optical illusions, a figure that at first glance seems to be a projection of an ordinary three-dimensional object,

upon careful examination, contradictory connections of the elements of the figure become visible. An illusion is created of the impossibility of the existence of such a figure in three-dimensional space.

Impossible figures

The most famous impossible figures are the impossible triangle, the endless staircase and the impossible trident.

Impossible Perrose Triangle

The Reutersvard Illusion (Reutersvard, 1934)
_________

Note also that the change in figure-ground organization made it possible to perceive a centrally located “star.”

Escher's impossible cube

In fact, all impossible figures can exist in the real world. Thus, all objects drawn on paper are projections of three-dimensional objects, therefore, it is possible to create a three-dimensional object that, when projected onto a plane, will look impossible. When looking at such an object from a certain point, it will also look impossible, but when viewed from any other point, the effect of impossibility will be lost. A 13-meter sculpture of an impossible triangle made of aluminum was erected in 1999 in Perth (Australia). Here the impossible triangle was depicted in its most general form - V the form of three

beams connected to each other at right angles.
Devil's fork

Among all the impossible figures, the impossible trident (“devil’s fork”) occupies a special place. If we close the right side of the trident with our hand, we will see completely real picture

- three round teeth. If we close the lower part of the trident, we will also see the real picture - two rectangular teeth. But, if we consider the entire figure as a whole, it turns out that three round teeth gradually turn into two rectangular ones. Thus, it can be seen that the front and of this picture conflict. That is, what was originally in the foreground goes back, and the background (middle tooth) comes forward. In addition to the change in foreground and background, there is another effect in this drawing - the flat edges of the right side of the trident become round on the left.

The effect of impossibility is achieved due to the fact that our brain analyzes the contour of the figure and tries to count the number of teeth. The brain compares the number of teeth in the figure on the left and right sides of the picture, which gives rise to the feeling that the figure is impossible. If the number of teeth in the figure were significantly larger (for example, 7 or 8), then this paradox would be less pronounced.

Some books claim that the impossible trident belongs to a class of impossible figures that cannot be recreated in the real world. Actually this is not true. ALL impossible figures can be seen in the real world, but they will only look impossible from one single point of view.

______________

Impossible elephant


How many legs does an elephant have?

Stanford psychologist Roger Shepard used the idea of ​​a trident for his picture of the impossible elephant.

______________

Penrose staircase(endless staircase, impossible staircase)

The Endless Staircase is one of the most famous classical impossibilities.

It is a design of a staircase in which, if moving along it in one direction (counterclockwise in the picture to the article), a person will endlessly ascend, and if moving in the opposite direction, he will constantly descend.

In other words, we are presented with a staircase that seems to lead up or down, but the person walking along it does not rise or fall. Having completed his visual route, he will find himself at the beginning of the path. If you actually had to walk up those stairs, you would walk up and down them aimlessly an infinite number of times. You can call it an endless Sisyphean task!

Since the Penroses published this figure, it has 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.

"Rise and Descend"

The "Endless Forest" was successfully used by the artist Maurits K. Escher, this time in his enchanting lithograph "Ascent and Descend", created in 1960.
In this drawing, reflecting all the possibilities of the Penrose figure, the very recognizable Endless Staircase is neatly inscribed in the roof of the monastery. Hooded monks continuously move up the stairs in a clockwise and counterclockwise direction. They go towards each other along an impossible path. They never manage to go up or down.

Accordingly, The Endless Staircase has become more often associated with Escher, who redrew it, than with the Penroses, who invented it.

How many shelves are there?

Where is the door open?

Outward or inward?

Impossible figures occasionally appeared on the canvases of past masters, for example, such is the gallows in the painting of Pieter Bruegel (the Elder)
"The Magpie on the Gallows" (1568)

__________

Impossible Arch

Jos de Mey - Flemish artist, studied at Royal Academy Fine Arts in Ghent, Belgium, and then taught students in interior design and color for 39 years. Beginning in 1968, his focus became drawing. He is best known for his careful and realistic execution of impossible structures.

The most famous are the impossible figures in the works of the artist Maurice Escher. When examining such drawings, each individual detail seems quite plausible, but when you try to trace the line, it turns out that this line is no longer, for example, the outer corner of the wall, but the inner one.

"Relativity"

This lithograph Dutch artist Escher was first printed in 1953.

The lithograph depicts a paradoxical world in which the laws of reality do not apply. Three realities are united in one world, three forces of gravity are directed perpendicular to one another.

An architectural structure has been created, the realities are united by stairs. For people living in this world, but in different planes of reality, the same staircase will be directed either up or down.

"Waterfall"

This lithograph by the Dutch artist Escher was first printed in October 1961.

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

The structure is made up of three crossbars stacked on top of each other at right angles. The waterfall in the lithograph works like a perpetual motion machine. It also seems that both towers are the same; in fact, the one on the right is one floor below the left tower.

Well, more modern works :o)
Endless photography

Amazing construction site

Chess board

Upside down pictures

What do you see: a huge crow with prey or a fisherman in a boat, fish and an island with trees?

Rasputin and Stalin

Youth and old age

_________________

Nobleman and Queen

___________________

Angry and Merry