M.C. Escher A Morphing Bio

Diseño por José Roberto Villalobos Jiménez

M.C. Escher A Morphing Bio

Chapter Index Introduction...............................................................3 First Years of Life..................................................................4 The Young Maurits..............................................................4

Beginnings..................................................................9 Beginning with Architecture................................................9 Beginning in Graphic Arts.................................................12

New Surroundings................................................... 17 Italy Landscapes................................................................. 17 Swiss Uninspiring...............................................................18

Mathematics and Art............................................... 23 17 Planes.............................................................................24 The Mathematician............................................................28 Reaching Perfection...........................................................32 An Artist to Remember......................................................35 Last Impression...................................................................38

Symmetry and other Works..................................... 41

Escherâ€™s Work Index Introduction

Linoleum Cut

New Surroundings

Begginings

Self-Portrait

5

Jug

5

Waves

7

Fiet van Stolk

7 Castrovalva

Lithography

Woodcut

Plane-filling Motif with Human Figures

13 Hand with Ref lecting Sphere

W hite Cat

11

Tree

11

Eight heads

13

Sea- Shell Rabbits

15 Jetta 15

Self-Portrait

15

Hand With Fir

Self-Portrait

Metamor15 phose I

Mathematics and Art

19

Up & and Down

29

Bonds of Union

33

21 Ascending and Descend- 37 ing 18

Sky and Water

25

18

Day and Night

27

Other World

31

Circle Limit 20 III

33

Snakes

39

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I Introduction Escher, a world renown graphic artist, hard to box in one specif ic genre, he found fame in art as well as in math, the last one mainly because of his so-called impossible structures in a tridimensional world, but extraordinarily intriguing how to f igure out those fantastical worlds.

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First Years of Life . . . . . . . . . . . . . . . A great artist was born on June 17, 1898 in Leeuwarden in the Netherlands (Holland), his name Maurits Cornelius Escher, always referred to by his parents as Mauk, but known by the rest of the world as M.C. Escher. He was youngest son of civil engineer George Arnold Escher and his second wife Sara Gleichman. Five years later Escher and his family move from Leeuwarden to Arnhem where he would spend most of his young life.

The Young Maurits . . . . . . . . . . . . . He lived with his four older brothers, Arnold, Johan, Berend, and Edmond. Maurits attended both elementary and secondary school in Arnhem between 1912 and 1918, where he failed to shine in many of his subjects, but exhibited an early interest in both music and carpentry.

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Introduction

Self-Portrait, 1917 Linoleum cut

Jug, 1917 Linoleum cut in two tones of brown

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People expressed the opinion that he possessed a mathematical brain but he never excelled in the subject at any stage during his schooling and treated the subject with some considerable unease. He wrote:

At high school in Arnhem, I was extremely poor at arithmetic and algebra because I had, and still have, great diff iculty with the abstractions of numbers and letters. When, later, in stereometry [solid geometry], an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject. But our path through life can take strange turns.

Early reports detailed his methodological approach to life which was taken to be an unconscious reaction to his engineering family upbringing. As a child, Maurits always had an intensely creative side and an â€˜acute sense of wonderâ€™. He often claimed to see shapes that he could relate to in the clouds. Maurits, and his good friend Bas Kist both developed a deep interest in printing techniques as a consequence of receiving good reports from their respective art departments who had encouraged their student to experiment.

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Introduction

Waves, 1918 Linoleum cut and watercolor in grey and red

Fiet van Stolk, 1918 Linoleum cut

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b Beginnings Beginning with Architecture Family aspirations that Escher would be an architect were disappointed when he failed his f inal exams in history, constitutional organisations, political economies and book keeping, as a result he never off icially graduated. His family moved to Oosterbeek where a loophole in the law allowed Maurits to enrol at the Higher Technical School in Delft (1918-1919) and thus allowed him to repeat some of the subjects he had failed.

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Unable and unwilling to catch up following poor health, Maurits decided to concentrate on his drawing and his woodcut techniques. He was inf luenced and trained by R N Roland Holst: “He strongly advised me to do some woodcuts, and I immediately followed his advice ... It is wonderful work but far more diff icult than working with linoleum”

In September 1920 Maurits moved to Haarlem in a f inal attempt to try follow his father’s wish that he study architecture and he enrolled at the School for Architecture and Decorative Arts. A chance meeting with Samuel Jesserum de Mesquita, a graphic arts teacher, proved a landmark event in Escher’s life and he became convinced that a graphic arts programme would be better suited to his skills. De Mesquita taught the eager Escher all he knew of woodcut printing techniques, gave him space to experiment, and encouraged him to experiment widely in order to develop his skills. Escher was regularly heard to complain about his lack of natural drawing ability and as a result most of his pieces took a long time to complete, and required numerous attempts before he was completely happy. In his youth he concentrated on landscapes, many of which were drawn from unusual perspectives. He also made numerous sketches of plants and even insects, all of which regularly appear in his later work.

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Beginnings

White Cat, 1919 Woodcut

Tree, 1919 Woodcut

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Beginning in Graphic Arts . . . . . . . Travelling took up a large part of Escherâ€™s life from this point on. He made a trip with two friends to Florence in April 1922 and spent the whole time sketching and drinking. Escher then spent a further month travelling alone around Italy gathering material to use in his experimental woodcuts. During his early drawing career Escher touched only brief ly on the subject of â€˜f illing the planeâ€™, signs of which had been visible from an early age. Many years later a lady:

... remembered the care with which this little boy [Escher] had selected the shape, quantity and size of his slices of cheese, so that, f itted one against the other, they would cover as exactly as possible the entire slice of bread. This particular trait never left him ...

His f irst work featuring regular division of the plane was named Eight Heads, and was completed in 1922. Escher visited Spain in June 1922, making the voyage on a sea freighter, and there his interest in regular division was brief ly revitalised. He

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Beginnings

Plane-filling Motif with Human Figures , 1920 Lithograph in blue, green and red

Eight Heads, 1922 Woodcut

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travelled widely and visited many palaces and was inspired by a great number of both buildings and landscapes. One building which was to have an immense inf luence on his life was the Alhambra Palace in Grenada. Escher was overwhelmed by the beauty of the 14th century Moorish palace and in particular, by the decorative majolica tiling which decorated many of the surfaces of the building. Unlike the Moors, Escher was both keen and permitted to use recognisable objects in his ad-hoc versions of the tiling. He made a number of attempts at using this style of artwork over the next couple of years but was unhappy about both the length of time this passion was taking (due to its trial and error nature) and the poor quality of his f inal work, and he left aside regular division for a number of years. We wrote that, in about 1924:

... for the f irst time I printed on a cloth a single animal motif cut out of wood which repeats itself according to a certain system, thereby adhering to the principle that no blank spaces may occur. I needed at least three colours; with each in turn I rolled my stamping block in order to contrast one motif with its adjoining congruent repetitions. I exhibited this cloth together with my other work, but I did not have any success with it.

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Beginnings

Sea-shell, 1919 Woodcut

Rabbits, 1920 Woodcut

Self-Portrait, 1919 Woodcut

Hand with Fir, 1921 Woodcut

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n New Surroundings Italy Landscapes Following his return from Spain, Escher went to live in Italy. Again he travelled widely and in 1923, whilst staying in the town of Ravello, he met his future wife Jetta Umiker. They married on 12 June 1924 and made their home in Frascati, just outside Rome. They are the parents of three children, George (born 23 June 1926 in Frascati), then Arthur (born 8 December 1928) and Jan (born 6 March 1938).

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Escher and his new family took frequent holidays around Italy during the next decade. Years of sketching Italian landscapes, most of them with impossible perspectives, followed before the family were forced to leave Italy as a result of the Fascist political uprising which developed in Italy during the summer months of 1935. They moved to the mountain village of Chateau-dâ€™Oex in Switzerland but Jetta missed Italy and the high Swiss prices forced Escher to sell more prints.

Swiss Uninspiring . . . . . . . . . . . . . . SelfPortrait, 1922 Woodcut

The family was unhappy at f irst in their new surroundings and, lacking inspiration for his work, Maurits and Jetta set out on a Mediterranean excursion. Escher managed to negotiate a deal with the Adria Shipping Company which gave free passage and meals for himself and also a one way ticket for Jetta. He made payment with prints which he completed using sketches made on the journey. The trip began on the 26 April 1936, and during the next two months the pair made volumes of sketches from which to work from in the future. Escherâ€™s fascination with order and symmetry took over his life after this Mediterranean journey in 1936 after he made his second visit to the Alhambra. Escher remarked that it was:

Portrait of Jetta,1925 Woodcut

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...the richest source of inspiration I have ever tapped.

New Surroundings

Castrovalva, February 1930 Lithography, 530 x 421 mm (20 7/8 x 16 5/8’’)

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Escher and his wife spent days on end working at the Alhambra Palace, where they sketched as much as they could. These sketches were to become a fundamental source for much of Escher’s future work. After this trip Escher became obsessed with the concept of regular division of the plane. He wrote: It remains an extremely absorbing activity, a real mania to which I have become addicted, and from which I sometimes f ind it hard to tear myself away.

Escher felt that he could improve upon the work of the Moorish artists and used his sketches as a geometric grid from which to design his own characters to f ill the plane. He experimented with many different motifs such as birds, weightlifters and lions, all of which appear in many of his early designs. In October 1937 Escher showed some of his new work to his brother Berend, by then a professor of geology at Leiden University, when both were visiting their parents home in The Hague. Recognising the connection between his brother’s woodcuts and crystallography, Berend sent his brother a list of articles that he felt would be of assistance. This will change his work being this Escher’s f irst contact with mathematics.

Metamorphose I, 1937 Woodcut printed on two sheets

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New Surroundings

Hand with Ref lecting Sphere, January 1935 Lithography, 318 x 213 mm (12 1/2 x 8 3/4’’)

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m Mathematics and Art Escher read Pólya’s 1924 paper on plane symmetry groups. Although he did not understand the abstract concept of groups discussed in Pólya’s paper he did understand the 17 plane symmetry groups described there. He subsequently taught himself the principles by which each of the 17 groups operated. Between 1937 and 1941 Escher worked on possible periodic tiling producing 43 coloured drawings with a wide variety of symmetry types. He adopted a highly mathematical approach with a systematic study using notation which he invented himself. Escher also studied an article written by F Haag in 1923 and he eventually challenged some of the views expressed in the literature following further research into the topic.

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24

Mathematics and Art

Day and Night, 1938 Woodcut in black and grey printed from 2 blocks We can see how Escher was very inspired by his homeland e.g. the windmills.

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Near the end of 1937 the Escher family moved to Belgium which became their home until the 20 February 1941 when the invading German army forced them to f lee to Baarn in Holland. World War II was a deeply emotional time for Escher and prevented him from concentrating.

17 Planes . . . . . . . . . . . . . . . . . . . . . . Over the years that followed, Escher made numerous woodcuts utilising each of the 17 symmetry groups. With practice his skills naturally improved and as a result he could design and complete each piece far quicker than in his earlier years. His art formed an integral part of family life, and Escher would work in his study between 8 am and 4 pm every day. New concepts could take months or even years to come to fruition before the f inished work was discussed and explained to the family. One of his children wrote:

The end of the cycle, making the f irst print, gave father a mixture of joy and sadness. It was exciting and satisfying to lift the paper from the inked wood for the f irst time, to see the f inished print, crisp and immaculate, gradually appearing around the edge of the paper as it was carefully raised. But father had

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Mathematics and Art

Sky and Water I, June 1938 Woodcut,435 x 439 mm (17 1/8 x 17 1/4’’)

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always a feeling of disappointment, of not having been able to depict adequately his thoughts. After all his efforts, how far short of the originally so lucid and misleading simple idea did this result fall!

Extensive research and investigation culminated in 1941 with his f irst notebook Regular Division of the plane with Asymmetric congruent Polygons. This notebook was extended and improved over the course of the following year, when the results obtained from extensive colour based division investigations were included. These books were never meant for publication - only for background information to allow him to continue as a visionary artist.

The Mathematician . . . . . . . . . . . . . The notebooks were evidence of the fact that Escher had become a research mathematician of the highest order, regardless of his personal feeling of mathematical insecurity. He had developed his own categorization system which covered all the possible combinations of shape, colour and symmetrical properties. As such he had unknowingly studied areas of crystallography years in advance of any professional mathematician working in this f ield. He wrote:

A long time ago, I chanced upon this domain [of regular division of the plane] in one of my wanderings... However, on the other side I landed in a wilderness.... I came to the open gate of mathematics. Sometimes I think I have covered the whole area and then, I suddenly discover a new path and experience fresh delights.

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Mathematics and Art

Up & Down,July 1947 Lithography 503 x 205 mm (19 3/4 x 8 1/8’’)

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Escher was inundated with requests to go all over the world giving lectures. In a lecture in 1953 Escher said: ... I have often felt closer to people who work scientif ically (though I certainly do not do so myself ) than to my fellow artists.

By around 1956 Escherâ€™s interests changed again taking regular division of the plane to the next level by representing inf inity on a f ixed 2-dimensional plane. Earlier in his career he had used the concept of a closed loop to try to express inf inity as demonstrated in Horseman. He had put his designs on to a variety of threedimensional objects such as columns and spheres during the 1940s, again in an attempt to impart an endless perspective to his work. Later tried working with the concept of similarities, using identical motifs of diminishing size, arranged in a series of concentric circles. In 1958 Escher met Coxeter and they became life-long friends. Escher came across an article written by Coxeter, and again whilst unable to understand the text, he was able to determine the rules regarding hyperbolic tessellations using only the diagrams in the paper. Escher paid thanks to Coxeter by sending him a copy of one of his new works Circle Limit I. Escher continued to develop and enhance this f ield and produced many more prints using both circles and squares as the frames for his works.

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Mathematics and Art

Other World, January 1947 Wood engraving and woodcut 318 x 231 mm (12 1/2 x 10 1/4’’)

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Reaching Perfection . . . . . . . . . . . . . This new found style of artwork required enormous dedication because of the careful planning and trial sketches required, coupled with the necessary hand and carving skill, despite all of this, it was an enormous source of satisfaction to Escher. He wrote:

I discovered once again that the human hand is capable of executing small and yet completely controlled movements, on the condition that the eye sees suff iciently clearly what the hand is doing.

In 1995 Coxeter published a paper which proved that Escher had achieved mathematical perfection in one of his etchings. Circle Limit III was created using only simple drawing instruments and Escher’s great intuition, but Coxeter proved that:

... [Escher] got it absolutely right to the millimetre, absolutely to the millimetre .... Unfortunately he didn’t live long enough to see my mathematical vindication.

This proof serves to highlight Escher’s amazing natural ability of being able to combine both his artistic skills and the techniques that he learned from others, into mathematically perfect designs.

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Mathematics and Art

Bonds of Union, April 1956 Lithography, 253 x 339 mm (10 x 13 3/8’’)

Circle Limit III, 1959 Woodcut

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By 1958 Escher had achieved remarkable fame. He continued to give lectures and correspond with people who were eager to learn from him. He had given his f irst important exhibition of his works and had also been featured in Time magazine. Escher received numerous awards over his career including the Knighthood of the Oranje Nassau (1955) and was regularly commissioned to design art for dignitaries around the world. In 1958 he published Regular Division of the Plane and in this work he says: At f irst I had no idea at all of the possibility of systematically building up my f igures. I did not know ... this was possible for someone untrained in mathematics, and especially as a result of my putting forward my own laymanâ€™s theory, which forced me to think through the possibilities.

In another quote from Regular Division of the Plane, Escher says:

In mathematical quarters, the regular division of the plane has been considered theoretically. ... [Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature they are more interested in the way in which the gate is opened than in the garden lying behind it.

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Escher’s work covered a variety of subjects throughout his life. His early love of portraits, Roman and Italian landscapes and of nature, eventually gave way to regular division of the plane. Many of his pieces were drawn from unusual perspectives thus creating enigmatic spatial effects. He was skilled in the art of a number of different printing techniques such as woodcuts, lithographs and mezzotints. Over 150 colourful and recognisable works testify to Escher’s ingenuity and interest in regular division of the plane. He managed to capture the notion of hyperbolic space on a f ixed 2-dimensional plane as well as translating the principles of regular division onto a number of 3-dimensional objects such as spheres, columns and cubes. A number of his prints combine both 2 and 3-dimensional images with startling effect e.g. in Reptiles. He wrote:

Mathematics and Art

An Artist to Remember . . . . . . . . . .

When an element of plane division sug gests to me the form of an animal, I immediately think of a volume. The “f lat shape” irritates me - I feel as if I were shouting to my f igures, “You are too f ictitious for me; you just lie there static

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and frozen together; do something, come out of there and show me what you are capable of!” So I make them come out of the plane. But do they really do that? On the contrary, I am deliberately inconsistent, sug gesting plasticity in the plane by means of light and shadow.

He was fascinated by topology, which only began to be studied during his lifetime, as illustrated by the Möbius strip. In his later years he learned much from the British mathematician Roger Penrose and used this knowledge to design many of his “impossible” etchings such as Waterfall or Up and down. Escher used pictures to tell a story in his Metamorphosis series of designs. These designs brought together many of Escher’s skills and show the transformation from one distinct object to another, by means of a series of slight changes to a regular pattern in the plane. Metamorphosis 1 in particular, printed in 1933, yields an insight into the change of artistic style which occurred in Escher’s life at this time. An Italian coastline is transformed through a series of convex polygons into a regular pattern in the plane until f inally a distinct, coloured, human motif emerges, signifying his change of perspective from landscape work to regular division of the plane.

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Mathematics and Art

Ascending and Descending, March 1960 Lithography, 255 x 285 mm (14 x 11 1/4â€™â€™)

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Last Impression . . . . . . . . . . . . . . . . Escher fell ill initially in 1964 whilst delivering a series of lectures in North America. As a result he was forced to cut down his schedule substantially, later devoting most of his time to correspondence with friends. His last years are described as follows:

When Escherâ€™s view of the world turned inward he produced his best known puzzling prints, which, art aside, were truly intellectually playful, yet he was not. His life turned inward, he cut himself off and he had few friends. ... He died after a protracted illness...

His f inal graphic work, a woodcut, Snakes took six months to complete and was f inally unveiled in July 1969. This exceptional etching heads off to inf inity at both the centre and the edges of the picture. Following further operations Escher moved to the Rosa Spier house in Laren and later died in hospital on March 27th, 1972.

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Mathematics and Art

Snakes, 1969 Woodcut in orange, green and black printed from 3 blocks

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S Symmetr y and other Works Some of the other works from his early years and his experimentation with tessellations. There is also Relativity, July 1953, which is one of his most recognized work and Methamorphose III the biggest creation by Escher.

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It begins identically to Metamorphosis II, with the word metamorphose (the Dutch form of the word metamorphosis) forming a grid pattern and then becoming a blackand-white checkered pattern.

Then the f irst set of new imagery begins. The angles of the checkered pattern change to elongated diamond shapes. These then become an image of f lowers with bees. This image then returns to the diamond pattern and back into the chequered pattern.

It then resumes with the Metamorphosis II which is the checkered pattern changes into reptiles. Then into a beehive, then the bees coming out of it. This then become f ishes, and the negative decomposition of the bees become now birds starting now with a new tessellation from Metamorphose III.

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The birds then become sailing boats. From the sailing boats the image then changes to a second f ish pattern. Then from the f ish into horses. And then the horses become yet again a second bird pattern.

The second bird pattern then becomes black-and-white triangles which then become envelopes with wings. These winged envelopes then return to the black-and-white triangles and then to the original bird pattern.

It then resumes with the Metamorphosis II. The birds become three dimensional blocks with red tops. These blocks then become the architecture of the Italian coastal town of Atrani. Which was also featured in Metamorphose I.

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Sy mmet r y and other Works

Regular division of a plane 99, 1954 With just a pattern of one f igure in two colors it was possible for him to hide basic geometry. Also it makes a game for the eye to try to se the negative

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Sy mmet r y and other Works

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