M. C. Escher

1 M. C. Escher 1 1.1 Early life. . . 1 1.2 Later life. . . 1 1.3 Works . . . 2 1.4 Legacy . . . 4 1.5 Selected works. . . 4 1.6 See also . . . 5 1.7 References. . . 6 1.8 Further reading . . . 6 1.9 External links . . . 6

2 Another World (M. C. Escher) 7 2.1 Sources . . . 7

2.2 External links . . . 7

3 Ascending and Descending 8 3.1 Sources . . . 8

4 Atrani, Coast of Amalfi 9 4.1 See also . . . 9

4.2 Sources . . . 9

5 Belvedere (M. C. Escher) 10 5.1 See also . . . 10

5.2 Sources . . . 10

6 The Bridge (M. C. Escher) 11 6.1 Sources . . . 11

7 Castrovalva (M. C. Escher) 12 7.1 In popular culture . . . 12

7.2 Sources . . . 12

8 Circle Limit III 13 8.1 Inspiration . . . 13

8.4 Printing details. . . 14

8.5 Exhibits . . . 14

8.6 References. . . 14

8.7 External links . . . 15

9 Convex and Concave 16 9.1 See also . . . 16

9.2 Sources . . . 16

10 Cube with Magic Ribbons 17 10.1 References . . . 17 11 Curl-up 18 11.1 Translation. . . 18 11.2 See also . . . 18 11.3 Sources . . . 19 12 Dolphins (M. C. Escher) 20 12.1 Sources . . . 20 13 Drawing Hands 21 13.1 Sources . . . 21 14 Gravitation (M. C. Escher) 22 14.1 See also . . . 22 14.2 Sources . . . 22

15 Hand with Reflecting Sphere 23 15.1 Popular culture . . . 23

15.2 See also . . . 23

15.3 Sources . . . 23

16 House of Stairs 24 16.1 References . . . 24

17 Magic Mirror (M.C. Escher) 25 17.1 See also . . . 25 17.2 Sources . . . 25 18 Metamorphosis I 26 18.1 See also . . . 26 18.2 Sources . . . 26 19 Metamorphosis II 27

20 Metamorphosis III 28

20.1 See also . . . 28

20.2 External links . . . 28

20.3 Sources . . . 28

21 Print Gallery (M. C. Escher) 29 21.1 References . . . 29

21.2 External links . . . 29

22 Puddle (M. C. Escher) 30 22.1 See also . . . 30

22.2 Sources . . . 30

23 Regular Division of the Plane 31 23.1 Sources . . . 31 23.2 Further reading . . . 31 24 Relativity (M. C. Escher) 32 25 Reptiles (M. C. Escher) 33 25.1 See also . . . 33 25.2 References . . . 33 25.3 External links . . . 33

26 Sky and Water I 34 26.1 See also . . . 34

26.2 Sources . . . 34

27 Sky and Water II 35 27.1 See also . . . 35 27.2 Sources . . . 35 28 Snakes (M. C. Escher) 36 28.1 See also . . . 36 28.2 References . . . 36 28.3 External links . . . 36 29 Stars (M. C. Escher) 37 29.1 Description . . . 37 29.2 Influences . . . 37 29.3 Analysis . . . 38 29.4 Related works . . . 38

30 Still Life and Street 39

30.1 See also . . . 39

30.2 References . . . 39

30.3 Sources . . . 39

31 Still Life with Mirror 40 31.1 References . . . 40

32 Still Life with Spherical Mirror 41 32.1 See also . . . 41

32.2 Sources . . . 41

33 Three Spheres II 42 33.1 See also . . . 42

33.2 Sources . . . 42

34 Three Worlds (M. C. Escher) 43 34.1 See also . . . 43

34.2 Sources . . . 43

34.3 External links . . . 43

35 Tower of Babel (M. C. Escher) 44 35.1 See also . . . 44 35.2 References . . . 44 35.3 Notes . . . 44 36 Waterfall (M. C. Escher) 45 36.1 Description . . . 45 36.2 References . . . 45 36.3 External links . . . 45

36.4 Text and image sources, contributors, and licenses . . . 46

36.4.1 Text . . . 46

36.4.2 Images . . . 49

M. C. Escher

Escher (1971)

Maurits Cornelis Escher (/ˈɛʃər/, Dutch: [ˈmʌurɪts kɔrˈneːlɪs ˈɛʃər]( );[1]_{17 June 1898 – 27 March 1972),} usually referred to as M. C. Escher, was aDutch graphic artist. He is known for his oftenmathematicallyinspired

woodcuts, lithographs, and mezzotints. These feature

impossible constructions, explorations ofinfinity, archi-tecture, andtessellations.

1.1 Early life

Maurits Cornelis[2]_{was born in Leeuwarden,Friesland,} in a house that forms part of thePrincessehof Ceramics Museumtoday. He was the youngest son ofcivil engineer George Arnold Escherand his second wife, Sara

Gleich-man. In 1903, the family moved toArnhem, where he attended primary school and secondary school until 1918. He was a sickly child, and was placed in a special school at the age of seven and failed the second grade.[3]_Although he excelled at drawing, his grades were generally poor. He also took carpentryand piano lessons until he was thirteen years old. In 1919, Escher attended theHaarlem School of Architecture and Decorative ArtsinHaarlem. He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched todecorative arts.[3] _{He studied underSamuel} Jessurun de Mesquita, with whom he remained friends for years. In 1922, Escher left the school after having gained experience in drawing and makingwoodcuts.

1.2 Later life

In 1922, an important year of his life, Escher trav-eled through Italy (Florence, San Gimignano, Volterra,

Siena, Ravello) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada. The intricate decorative designs atAlhambra, which were based ongeometrical symmetriesfeaturing interlocking repetitive patterns sculpted into the stone walls and ceilings, were a powerful influence on Escher’s works.[4] _{He returned to Italy regularly in the following} years.

In Italy, Escher met Jetta Umiker, whom he married in 1924. The couple settled in Rome where their first son, Giorgio (George) Arnaldo Escher, named after his grand-father, was born. Escher and Jetta later had two more sons: Arthur and Jan.[5]

In 1935, the political climate in Italy (underMussolini) became unacceptable to Escher. He had no interest in politics, finding it impossible to involve himself with any ideals other than the expressions of his own concepts through his own particular medium, but he was averse to fanaticism and hypocrisy. When his eldest son, George, was forced at the age of nine to wear aBallilauniform in school, the family left Italy and moved toChâteau-d'Œx, Switzerland, where they remained for two years.[6]

land. In 1937, the family moved again, toUccle, a suburb ofBrussels, Belgium.World War IIforced them to move in January 1941, this time toBaarn, Netherlands, where Escher lived until 1970. Most of Escher’s better-known works date from this period. The sometimes cloudy, cold and wet weather of the Netherlands allowed him to focus intently on his work. For a time after undergoing surgery, 1962 was the only period in which Escher did not work on new pieces.

Escher moved to theRosa Spier HuisinLarenin 1970, an artists’ retirement home in which he had his own studio. He died at the home on 27 March 1972, aged 73.

1.3 Works

Drawing Hands, 1948

In his early years, Escher sketched landscapes and nature. He also sketched insects, which appeared frequently in his later work. His first artistic work, completed in 1922, featured eight human heads divided in different planes. Later around 1924, he lost interest in “regular division” of planes, and turned to sketching landscapes in Italy with irregular perspectives that are impossible in natural form. Escher’s first print of an impossible reality wasStill Life and Street, 1937. His artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. Well known examples of his work include Drawing Hands, a work in which two hands are shown, each drawing the other;Sky and Water, in which light plays on shadow tomorphthe water ground behind fish figures into bird figures on a sky back-ground; andAscending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage ofquirks of perception

andperspective.

sidered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Additionally, he ex-plored interlocking figures using black and white to en-hance different dimensions. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals. Escher was left-handed.[7]

Relativity, 1953

Although Escher did not have mathematical training— his understanding of mathematics was largely visual and intuitive—Escher’s work had a strong mathematical com-ponent, and more than a few of the worlds which he drew were built aroundimpossible objectssuch as theNecker cubeand thePenrose triangle. Many of Escher’s works employed repeated tilings calledtessellations. Escher’s artwork is especially well liked by mathematicians and scientists, who enjoy his use ofpolyhedraandgeometric

distortions. For example, inGravity, multicolored turtles poke their heads out of astellated dodecahedron. The mathematical influence in his work emerged around 1936, when he journeyed to theMediterraneanwith the Adria Shipping Company. He became interested in order andsymmetry. Escher described his journey through the Mediterranean as “the richest source of inspiration I have ever tapped.”

After his journey to theAlhambra, Escher tried to im-prove upon the art works of theMoorsusing geometric grids as the basis for his sketches, which he then overlaid with additional designs, mainly animals such as birds and lions.

His first study of mathematics, which later led to its in-corporation into his art works, began withGeorge Pólya's academic paper on planesymmetry groupssent to him by his brotherBerend. This paper inspired him to learn the concept of the 17wallpaper groups(plane symmetry groups). Using this mathematical concept, Escher

cre-a mcre-athemcre-aticcre-al cre-approcre-ach to expressions of symmetry in his art works. Starting in 1937, he created woodcuts us-ing the concept of the 17 plane symmetry groups.

Circle Limit III, 1959

In 1941, Escher summarized his findings in a sketchbook, which he labeled Regelmatige vlakverdeling in asym-metrische congruente veelhoeken (“Regular division of the plane with asymmetric congruent polygons”).[8] _His in-tention in writing this was to aid himself in integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper, in which he studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties.

Around 1956, Escher explored the concept of represent-ing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Es-cher’s interest in hyperbolic tessellations, which are regu-lar tilings of thehyperbolic plane. Escher’s wood engrav-ings Circle Limit I–IV demonstrate this concept. In 1959, Coxeter published his finding that these works were ex-traordinarily accurate: “Escher got it absolutely right to the millimeter.”

Escher was awarded the Knighthood of theOrder of Or-ange Nassauin 1955. Subsequently he regularly designed art for dignitaries around the world.

In 1958, he published a book entitledRegular Division of the Plane, with reproductions of a series of woodcuts based on tessellations of the plane, in which he described the systematic buildup of mathematical designs in his art-works. He emphasized, "Mathematicians have opened the gate leading to an extensive domain.”

Overall, his early love ofRomanand Italian landscapes and of nature led to his interest in the concept of regular

works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works. For example, in a print called "Reptiles", he combined two and three-dimensional images. In one of his papers, Escher emphasized the importance of di-mensionality and described himself as “irritated” by flat shapes: “I make them come out of the plane.”

Waterfall, 1961

Sculpture of thesmall stellated dodecahedronthat appears in Es-cher’sGravitation. It can be found in front of the “Mesa+" build-ing on the Campus of theUniversity of Twente.

Escher also studiedtopology. He learned additional con-cepts in mathematics from the British mathematician

Roger Penrose. From this knowledge he created Water-fall and Up and Down, featuring irregular perspectives

ginning part of a series of designs that told a story through the use of pictures. These works demonstrated a culmi-nation of Escher’s skills to incorporate mathematics into art. In Metamorphosis I, he transformedconvex polygons

into regular patterns in a plane to form a human motif. This effect symbolizes his change of interest from land-scape and nature to regular division of a plane.

His pieceMetamorphosis IIIis wide enough to cover all the walls in a room, and then loop back onto itself. After 1953, Escher became a lecturer at many organiza-tions. A planned series of lectures in North America in 1962 was cancelled due to an illness, but the illustrations and text for the lectures, written out in full by Escher, were later published as part of the book Escher on Es-cher. In July 1969 he finished his last work, a woodcut calledSnakes, in which snakes wind through a pattern of linked rings which fade to infinity toward both the center and the edge of a circle.

1.4 Legacy

TheEscher MuseuminThe Hague

See also:M. C. Escher in popular culture

The special way of thinking and the rich graphic work of M.C. Escher has had a continuous influence in science and art, as well as being referenced in popular culture. Ownership of the Escher intellectual property and of his unique art works have been separated from each other. In 1969, Escher’s business advisor, Jan W. Vermeulen, author of a biography in Dutch on the artist, established the M.C. Escher Stichting (M.C. Escher Foundation), and transferred into this entity virtually all of Escher’s unique work as well as hundreds of his original prints. These works were lent by the Foundation to the Hague Museum. Upon Escher’s death, his three sons dissolved the Founda-tion, and they became partners in the ownership of the art

all of the documentation and the smaller portion of the art works.

The copyrights remained the possession of the three sons – who later sold them to Cordon Art, a Dutch company. Control of the copyrights was subsequently transferred to The M.C. Escher Company B.V. of Baarn, Netherlands, which licenses use of the copyrights on all of Escher’s art and on his spoken and written text.

A related entity, the M.C. Escher Foundation of Baarn, promotes Escher’s work by organizing exhibitions, pub-lishing books and producing films about his life and work. The primary institutional collections of original works by M.C. Escher are the Escher Museum, a subsidiary of the Haags Gemeentemuseum in The Hague; theNational Gallery of Art(Washington, DC); theNational Gallery of Canada(Ottawa); theIsrael Museum(Jerusalem); Huis ten Bosch(Nagasaki, Japan); and theBoston Public Li-brary.

Gödel, Escher, BachbyDouglas Hofstadter,[9]_published in 1979, discusses the ideas of self-reference andstrange loops, drawing on a wide range of artistic and scientific work, including the art of M. C. Escher and the music of

J. S. Bach, to illustrate ideas behindGödel’s incomplete-ness theorems.

1.5 Selected works

• St. Bavo’s, Haarlem, ink (1920)

• Flor de Pascua (The Easter Flower),woodcut/book illustrations (1921)

• Eight Heads, woodcut (1922)

• Dolphinsalso known as Dolphins in Phosphorescent Sea, woodcut (1923)

• Tower of Babel, woodcut (1928)

• Street in Scanno, Abruzzi,lithograph(1930) • Castrovalva, lithograph (1930)

• The Bridge, lithograph (1930) • Palizzi, Calabria, woodcut (1930) • Pentedattilo, Calabria, lithograph (1930) • Atrani, Coast of Amalfi, lithograph (1931) • Ravello and the Coast of Amalfi, lithograph (1931) • Covered Alley in Atrani, Coast of Amalfi, wood

• Still Life with Spherical Mirror, lithograph (1934) • Hand with Reflecting Sphere also known as

Self-Portrait in Spherical Mirror, lithograph (1935) • Inside St. Peter’s, wood engraving (1935) • Portrait of G.A. Escher, lithograph (1935)

• “Hell”, lithograph, (copied from a painting by

Hieronymus Bosch) (1935)

• Regular Division of the Plane, series of drawings that continued until the 1960s (1936)

• Still Life and Street (his first impossible reality), woodcut (1937)

• Metamorphosis I, woodcut (1937) • Day and Night, woodcut (1938) • Cycle, lithograph (1938)

• Sky and Water I, woodcut (1938) • Sky and Water II, lithograph (1938) • Metamorphosis II, woodcut (1939–1940)

• Verbum (Earth, Sky and Water), lithograph (1942) • Reptiles, lithograph (1943)

• Ant, lithograph (1943) • Encounter, lithograph (1944)

• Doric Columns, wood engraving (1945) • Three Spheres I, wood engraving (1945) • Magic Mirror, lithograph (1946) • Three Spheres II, lithograph (1946)

• Another World Mezzotint also known as Other World Gallery,mezzotint(1946)

• Eye, mezzotint (1946)

• Another Worldalso known as Other World, wood en-graving and woodcut (1947)

• Crystal, mezzotint (1947)

• Up and Down also known as High and Low, litho-graph (1947)

• Drawing Hands, lithograph (1948) • Dewdrop, mezzotint (1948) • Stars, wood engraving (1948)

• Double Planetoid, wood engraving (1949)

• Rippled Surface, woodcut and linoleum cut (1950) • Curl-up, lithograph (1951)

• House of Stairs, lithograph (1951) • House of Stairs II, lithograph (1951) • Puddle, woodcut (1952)

• Gravitation, (1952)

• Dragon, woodcut lithograph and watercolor (1952) • Cubic Space Division, lithograph (1952)

• Relativity, lithograph (1953)

• Tetrahedral Planetoid, woodcut (1954)

• Compass Rose (Order and Chaos II), lithograph (1955)

• Convex and Concave, lithograph (1955) • Three Worlds, lithograph (1955) • Print Gallery, lithograph (1956) • Mosaic II, lithograph (1957)

• Cube with Magic Ribbons, lithograph (1957) • Belvedere, lithograph (1958)

• Sphere Spirals, woodcut (1958) • Circle Limit III, woodcut (1959)

• Ascending and Descending, lithograph (1960) • Waterfall, lithograph (1961)

• Möbius Strip II (Red Ants) woodcut (1963) • Knot, pencil and crayon (1966)

• Metamorphosis III, woodcut (1967–1968) • Snakes, woodcut (1969)

1.6 See also

• Asteroid4444 Escherwas named in Escher’s honor in 1985.

[1] Duden Aussprachewörterbuch (6 ed.). Mannheim: Bibli-ographisches Institut & F.A. Brockhaus AG. 2005.ISBN 3-411-04066-1.

[2] “We named him Maurits Cornelis after S.'s [Sara’s] beloved uncle Van Hall, and called him 'Mauk' for short ....”, Diary of Escher’s father, quoted in M. C. Escher: His

Life and Complete Graphic Work, Abradale Press, 1981,

p. 9.

[3] Barbara E, PhD. Bryden. Sundial: Theoretical

Relation-ships Between Psychological Type, Talent, And Disease.

Gainesville, Fla: Center for Applications of Psycholog-ical Type.ISBN 0-935652-46-9.

[4] Roza, Greg (2005). An Optical Artist: Exploring Patterns

and Symmetry. Rosen Classroom. p. 20. ISBN 978-1-4042-5117-5.

[5] “ESCHER”. Geom.uiuc.edu. Retrieved 7 December 2013.

[6] Ernst, Bruno, The Magic Mirror of M.C. Escher, Taschen, 1978; p. 15

[7] “The Official M.C. Escher Website – Biography”. Mcescher.com. Retrieved 7 December 2013.

[8] Barry Cipra (1998). Paul Zorn, ed. What’s Happening in

the Mathematical Sciences, Volume 4. American

Mathe-matical Society. p. 103.ISBN 0-8218-0766-8.

[9] Hofstadter, Douglas R. (1999) [1979], Gödel, Escher,

Bach: An Eternal Golden Braid, Basic Books,ISBN 0-465-02656-7

1.8 Further reading

• Abrams (1995). The M. C. Escher Sticker Book. Harry N. Abrams.ISBN 0-8109-2638-5.

• Ernst, Bruno; Escher, M. C. (1995). The Magic Mirror of M. C. Escher (Taschen Series). Taschen America LLC. ISBN 1-886155-00-3 Escher’s art with commentary by Ernst on Escher’s life and art, including several pages on his use of polyhedra. • Escher, M. C. (1971) The Graphic Work of M. C.

Escher, Ballantine. Includes Escher’s own commen-tary.

• Locher, J. L. (2000). The Magic of M. C. Escher.

Harry N. Abrams, Inc. ISBN 0-8109-6720-0. • Locher, J. L., ed. (1981) M. C. Escher: His Life and

Complete Graphic Work, Amsterdam

• O'Connor, J. J. (17 June 2005)Escher. University of St Andrews, Scotland.

Pomegranate Communications ISBN 0-906212-28-6.

• Schattschneider, Doris(2004). M. C. Escher : Vi-sions of Symmetry, New York, N.Y. : Harry N. Abrams, 2004.ISBN 0-8109-4308-5.

• Schattschneider, Doris & Emmer, Michele, eds (2003). M. C. Escher’s Legacy: a Centennial Cele-bration; collection of articles coming from the M. C. Escher Centennial Conference, Rome, 1998 / Berlin; London: Springer-Verlag. ISBN 3-540-42458-X(hbk).

• “Escher, M. C.” in: The World Book Encyclopedia; 10th ed. 2001.

Media

• M. C. Escher, The Fantastic World of M. C. Escher, Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.

1.9 External links

• “Math and the Art of M.C. Escher”. USA: SLU. • Artful Mathematics: The Heritage of M. C. Escher.

USA: AMS.

• Escherization problem and its solution. CA: Univer-sity of Waterloo.

• “Escher for Real”. IL: Technion. — physical repli-cas of some of Escher’s “impossible” designs • “M.C. Escher: Life and Work”. USA: NGA. • “US Copyright Protection for UK Artists”. UK.

Copyright issue regarding Escher from the Artquest Artlaw archive.

• Schattschneider, Doris (June–July 2010). “The Mathematical Side of M. C. Escher”(PDF).Notices of the American Mathematical Society(USA) 57 (6): 706–18. Retrieved 9 July 2010.

Another World (M. C. Escher)

printby theDutchartistM. C. Escherfirst printed in Jan-uary 1947.

It depicts a cubic architectural structure made from brick. The structure is aparadoxwith an open archway on each of the five visible sides of the cube. The structure wraps around the vertical axis to enclose the viewer’s perspec-tive. At the bottom of the image is an archway which we seem to be looking up from the base, and through it we can see space. At the top of that arch is another arch which is level with our perspective, and through it we are looking out over a lunar horizon. At the top of that arch is another arch which covers the top of the image. We are looking down at this arch from above and through it onto the lunar surface.

Standing in each archway along the vertical axis is a metal sculpture of a bird with a humanoid face. In each side archway is a horn or cornucopia hanging on chains. It is interesting to note that the views from above and be-low are consistent, placing the statue so that it faces the horn, however the horizontal view reverses the relative positions of the statue and the horn, and rotates the horn 180 degrees.

The previous month (December 1946), Escher created a

mezzotint called Another World (Other World Gallery). The image in that print is the same as this one except that the arches continue on as an infinite corridor.

The bird/human sculpture is a real sculpture which was given to Escher by his father-in-law. This sculpture first appears in Escher’s 1934lithograph Still Life with Spher-ical Mirror.

2.1 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Harry N. Abrams, Inc. ISBN 0-8109-6720-0.

2.2 External links

Ascending and Descending

DutchartistM. C. Escherfirst printed in March 1960. The original print measures 14 in × 111_⁄

4in (35.6 cm ×

28.6 cm). The lithograph depicts a large building roofed by a never-ending staircase. Two lines of identically dressed men appear on the staircase, one line ascending while the other descends. Two figures sit apart from the people on the endless staircase: one in a secluded court-yard, the other on a lower set of stairs. While most two-dimensional artists use relative proportions to create an illusion of depth, Escher here and elsewhere uses con-flicting proportions to create the visual paradox.

Ascending and Descending was influenced by, and is an artistic implementation of, the Penrose stairs, an

impossible object;Lionel Penrosehad first published his concept in the February 1958 issue of theBritish Journal of Psychology. Escher developed the theme further in his printWaterfall, which appeared in 1961.

The two concentric processions on the stairs use enough people to emphasise the lack of vertical rise and fall. In addition, the shortness of the tunics worn by the people makes it clear that some are stepping up and some are stepping down.

The structure is embedded in human activity. By show-ing an unaccountable ritual of what Escher calls an 'un-known' sect, Escher has added an air of mystery to the people who ascend and descend the stairs. Therefore, the stairs themselves tend to become incorporated into that mysterious appearance.

There are 'free' people and Escher said of these: 'recalci-trant individuals refuse, for the time being, to take part in the exercise of treading the stairs. They have no use for it at all, but no doubt, sooner or later they will be brought to see the error of their non-conformity.'

Escher suggests that not only the labours, but the very lives of these monk-like people are carried out in an in-escapable, coercive and bizarre environment. Another possible source for the people’s looks is the Dutch id-iom “a monk’s job”, which refers to a long and repetitive working activity with absolutely no practical purposes or results, and, by extension, to something completely use-less.

Two earlier Escher pictures that feature stairs areHouse of StairsandRelativity.

3.1 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Atrani, Coast of Amalfi

Atrani in 2003.

Atrani,Coast of Amalfiis alithographprint by theDutch

artistM. C. Escher, first printed in August 1931. Atrani

is a small town and commune on the Amalfi Coast in theprovince of Salernoin theCampaniaregion of south-westernItaly. Atrani is the second smallest town in Italy and was built right at the edge of the sea. This image of Atrani recurs several times in Escher’s work, most notably in his series of Metamorphosis prints:Metamorphosis I,II

andIII.

4.1 See also

4.2 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

Belvedere (M. C. Escher)

Escher, first printed in May 1958. It shows a plausible-looking building that is actually animpossible object. In this print, Escher uses two-dimensional images to de-pict objects free of the confines of the three-dimensional world. The image is of a rectangular three-story build-ing. The upper two floors are open at the sides with the top floor and roof supported by pillars. From the viewer’s perspective, all the pillars on the middle floor are the same size at both the front and back, but the pillars at the back are set higher. The viewer also sees by the corners of the top floor that it is at a different angle than the rest of the structure. All these elements make it possible for all the pillars on the middle floor to stand at right angles, yet the pillars at the front support the back side of the top floor while the pillars at the back support the front side. This

paradoxalso allows a ladder to extend from the inside of the middle floor to the outside of the top floor.

There is a man seated at the foot of the building holding animpossible cube. He appears to be constructing it from a diagram of aNecker cubeat his feet with the intersect-ing lines circled. The window next to him is closed with an iron grille that is geometrically valid but practically impossible to assemble.

The woman who is about to climb the steps of the build-ing is modeled after a figure from the right panel of

Hieronymus Bosch's 1500 triptychThe Garden of Earthly Delights. This panel is individually titled Hell. A portion of Hell had earlier been recreated by Escher as a litho-graph in 1935.

The ridge in the background is part ofMorrone Moun-tains in Abruzzo, that Escher had visited several times when living in Italy during the 1920s and 30s.

5.1

See also

5.2 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

The Bridge (M. C. Escher)

Escher, first printed in March 1930.

It depicts a bridge connecting two sheer cliffs. On the top of the left hand cliff is a city. The chasm between the two cliffs is narrow but plummets out of view. In the distance is another outcrop with a city built on top. Both the rock and the architecture on this third outcrop are darker in colouration than in the foreground. The buildings appear to be modelled partly after southern Italian architecture. The rock is in blocky formations that appeared often dur-ing Escher’s Italian period and it is possible that the vil-lage seen is Assisi.

6.1 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

Castrovalva (M. C. Escher)

C. Escher, first printed in February 1930. Like many of Escher’s early works, it depicts a place that he visited on a tour ofItaly.

It depicts theAbruzzovillage ofCastrovalva, which lies at the top of a sheer slope. The perspective is toward the northwest, from the narrow trail on the left which, at the point from which this view is seen, makes a hairpin turn to the right, descending to the valley. In the foreground at the side of the trail, there are several flowering plants, grasses, ferns, a beetle and a snail. In the expansive valley below there are cultivated fields and two more towns, the nearest of which isAnversa degli Abruzzi, withCasalein the distance.

7.1 In popular culture

• In 1982 the name “Castrovalva” was used ina story

in theBBCtelevision seriesDoctor Who. The story-line also relied heavily onrecursion, a favorite theme in Escher’s later and more famous works, and used ideas taken fromBelvedere,Ascending and Descend-ing, andRelativityto trap the protagonists in the city of Castrovalva.

• The comicKingdom of the Wickedis set in an imag-inary world named Castrovalva.

7.2 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

Circle Limit III

Circle Limit III, 1959

Circle Limit III is a woodcutmade in 1959 by Dutch artistM. C. Escher, in which “strings of fish shoot up like rockets from infinitely far away” and then “fall back again whence they came”.[1]

It is one of a series of four woodcuts by Escher depict-ing ideas from hyperbolic geometry. Dutch physicist and mathematician Bruno Ernst called it “the best of the four”.[2]

8.1 Inspiration

Escher became interested intesselations of the plane af-ter a 1936 visit to theAlhambrainGranada, Spain,[3][4] and from the time of his 1937 artworkMetamorphosis I

he had begun incorporating tessellated human and animal figures into his artworks.[4]_{In a 1958 letter from Escher} toH. S. M. Coxeter, Escher wrote that he was inspired to make his Circle Limit series by a figure in Coxeter’s article “Crystal Symmetry and its Generalizations”.[2][3] Coxeter’s figure depicts atessellationof the hyperbolic planebyright triangleswith angles of 30°, 45°, and 90° (a shape that is possible in hyperbolic geometry but not in Euclidean geometry); this tessellation may be interpreted

The (6,4,2) triangular hyperbolic tiling that inspired Escher

as depicting the lines of reflection and fundamental do-mains of the(6,4,2) triangle group.[5]

8.2 Geometry

Escher seems to have believed that the white curves of his woodcut, which bisect the fish, represent hyperbolic lines in thePoincaré disk model of the hyperbolic plane, in which the whole hyperbolic plane is modeled as a disk in the Euclidean plane, and hyperbolic lines are modeled as circular arcs perpendicular to the disk boundary. Indeed, Escher wrote that the fish move “perpendicularly to the boundary”.[1]_{However, as Coxeter demonstrated, there is} no hyperbolicarrangement of lineswhose faces are alter-nately squares and equilateral triangles, as the figure de-picts. Rather, the white curves arehypercyclesthat meet the boundary circle at angles of cos−1₍₍₂1/4_{− 2}−1/4_)/2),

approximately 80°.[2]

The symmetry axes of the triangles and squares that lie between the white lines are true hyperbolic lines. The squares and triangles of the woodcut have the same in-cidence pattern as the faces of thetritetragonal tilingof

Thetritetragonal tiling, ahyperbolic tilingof squares and equi-lateral triangles, overlaid on Escher’s image

the hyperbolic plane, but their geometry is not the same: in the tritetragonal tiling, the sides of the squares and tri-angles are hyperbolically straight line segments, while in Escher’s woodcut they are arcs of hypercycles, so that the smooth curves of Escher correspond to polygonal chains with corners in the tritetragonal tiling. The points at the centers of the quadrilaterals, where four fish meet at their fins, form the vertices of anorder-8 triangular tiling, while the points where three fish fins meet and the points where three white lines cross together form the vertices of itsdual, theoctagonal tiling.[2]_Similar tessel-lations by lines of fish may be constructed for other hy-perbolic tilings formed by polygons other than triangles and squares, or with more than three white curves at each crossing.[6]

Euclidean coordinates of circles containing the three most prominent white curves in the woodcut may be obtained by calculations in the field of rational numbers extended by the square roots of two and three.[7]

8.3 Symmetry

Viewed as a pattern, ignoring the colors of the fish, in the hyperbolic plane, the woodcut has three-fold and four-foldrotational symmetryat the centers of its triangles and squares, respectively, and order-three dihedral symme-try(the symmetry of an equilateral triangle) at the points where the white curves cross. InJohn Conway'sorbifold notation, this set of symmetries is denoted 433. Each fish provides a fundamental region for this symmetry group. Contrary to appearances, the fish do not havebilateral symmetry: the white curves of the drawing are not axes of reflection symmetry.[8][9]

The fish in Circle Limit III are depicted in four colors, allowing each string of fish to have a single color and each two adjacent fish to have different colors. Together with the black ink used to outline the fish, the overall woodcut has five colors. It is printed from five wood blocks, each of which provides one of the colors within a quarter of the disk, for a total of 20 impressions. The diameter of the outer circle, as printed, is 41.5cm.[10]

8.5 Exhibits

As well as being included in the collection of theEscher MuseuminThe Hague, there is a copy of Circle Limit III in the collection of theNational Gallery of Canada.[11]

8.6 References

[1] Escher, as quoted byCoxeter (1979).

[2] Coxeter, H. S. M.(1979), “The non-Euclidean symmetry of Escher’s picture 'Circle Limit III'", Leonardo 12: 19– 25,JSTOR 1574078.

[3] Emmer, Michele (2006), “Escher, Coxeter and symmetry”, International Journal of Geometric Methods in Modern Physics 3 (5-6): 869–879,

doi:10.1142/S0219887806001594,MR 2264394. [4] Schattschneider, Doris(2010),“The mathematical side of

M. C. Escher”, Notices of the AMS 57 (6): 706–718. [5] An elementary analysis of Coxeter’s figure, as Escher

might have understood it, is given by Casselman, Bill (June 2010),How did Escher do it?, AMS Feature Col-umn. Coxeter expanded on the mathematics of trian-gle group tessellations, including this one inCoxeter, H. S. M.(1997), “The trigonometry of hyperbolic tessella-tions”, Canadian Mathematical Bulletin 40 (2): 158–168,

doi:10.4153/CMB-1997-019-0,MR 1451269.

[6] Dunham, Douglas, “More “Circle Limit III” patterns”,

The Bridges Conference: Mathematical Connections in Art, Music, and Science, London, 2006.

[7] Coxeter, H. S. M.(2003), “The trigonometry of Escher’s woodcut Circle Limit III", M.C.Escher’s Legacy: A

Centen-nial Celebration, Springer, pp. 297–304,doi: 10.1007/3-540-28849-X_29.

[8] Conway, J. H.(1992), “The orbifold notation for surface groups”, Groups, Combinatorics & Geometry (Durham,

1990), London Math. Soc. Lecture Note Ser. 165,

Cambridge: Cambridge Univ. Press, pp. 438–447,

doi:10.1017/CBO9780511629259.038, MR 1200280. Conway wrote that “The work Circle Limit III is equally intriguing” (in comparison to Circle Limit IV, which has a different symmetry group), and uses is it as an example of this symmetry group.

Mathematik 31 (5): 144–148,doi:10.1007/BF02659805. Paper presented to the 8th International Conference on Geometry, Nahsholim (Israel), March 7–14, 1999. [10] Escher, M. C. (2001),M. C. Escher: The Graphic Work,

Taschen, p. 10.

[11] Circle Limit III, National Gallery of Canada, retrieved 2013-07-09.

8.7 External links

• Douglas Dunham Department of Computer Science University of Minnesota, Duluth

• Examples Based on Circle Limits III and IV, 2006:More “Circle Limit III” Patterns, 2007:A “Circle Limit III” Calculation

Convex and Concave

artistM. C. Escher, first printed in March 1955. It depicts an ornate architectural structure with many stairs, pillars and other shapes. The relative aspects of the objects in the image are distorted in such a way that many of the structure’s features can be seen as both con-vex shapes and concave impressions. This is a very good example of Escher’s mastery in creating illusion of “Im-possible Architectures”. Thewindows, roads, stairs and other shapes can be perceived as opening out in seem-ingly impossible ways and positions. Even the image on the flag is ofreversible cubes. One can view these features as concave by viewing the image upside-down.

Note that all additional elements and decoration on the left are consistent with a viewpoint from above, while those on the right with a viewpoint from below: hiding half the image makes it very easy to switch between con-vex and concave.

9.1 See also

9.2 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

Cube with Magic Ribbons

Dutchartist M. C. Escher first printed in 1957. It de-picts two interlocking bands wrapped around the frame of a cube. The cube framework by itself is perfectly pos-sible but the interlocking of the “magical” bands within it is impossible. This print is significant for being the first Escher drawing to use a trueimpossible object.

10.1 References

• Ernst, Bruno (2006), “Optical Illusions”, Impossible Worlds: 2 in 1 Adventures with Impossible Objects, Cologne: Taschen,ISBN 3-8228-5410-7

Curl-up

This article is about the lithograph print. For the exercise, seeCrunch (exercise).

Curl-up or Wentelteefje (original Dutch title) is a

lithographprint byM. C. Escher, first printed in Novem-ber 1951.

This is the only work by Escher consisting largely of text. The text, which is written in Dutch, describes an imagi-nary species called Pedalternorotandomovens centrocula-tus articulosus, also known as “wentelteefje” or “rolpens”. He says this creature came into existence because of the absence in nature of wheel shaped, living creatures with the ability to roll themselves forward.

The creature is elongated and armored with several

keratinized joints. It has six legs, each with what ap-pears to be a human foot. It has a disc-shaped head with a parrot-like beak and eyes on stalks on either side. It can either crawl over a variety of terrain with its six legs or press its beak to the ground and roll into a wheel shape. It can then roll, gaining acceleration by pushing with its legs. On slopes it can tuck its legs in and roll freely. This rolling can end in one of two ways; by abruptly unrolling in motion, which leaves the creature belly-up, or by brak-ing to a stop with its legs and slowly unrollbrak-ing backwards. The word wentelteefje is Dutch forFrench toast, “wen-tel” meaning “to turn over”. Rolpens is a dish made with chopped meat wrapped in a roll and then fried or baked. “Een pens” means “belly”, often used in the phrase beer-belly.

There is a diagonal gap through the text containing an il-lustration showing the step by step process of the creature rolling into a wheel. This creature appears in two more prints completed later the same month, House of Stairs

and House of Stairs II.

11.1 Translation

The translation of the surrounding text is as follows: The Pedalternorotandomovens Centrocula-tus Articulosus (curl-up) came into existence

(spontaneous generation), because of the ab-sence, in nature, of wheel shaped, living crea-tures with the ability to roll themselves forward. The accompanying 'beastie' depiction, referred to as 'revolving bitch' or 'roll paunch' in lay-men’s terms, subsequently anticipates the need with sensitivity. Biological details are still few: is it a mammal, a reptile, or an insect? It has a long, drawn-out, horned, sectioned body and three sets of legs; the ends of which look like the human foot. In the middle of the fat, round head, that is provided with a strong, bent par-rots beak; they have bulb-shaped eyes, which, placed on posts, protrude far out from both sides of the head. In the stretched out position, the an-imal can, slow and cautiously, with the use of his six legs, move forward over a variety of ter-rains (it can potentially climb or descend steep stairs, plow through bushes, or scramble over boulders). However, when it must cover a great distance, and has a relatively flat path to his dis-posal, he pushes his head to the ground and rolls himself up with lightning speed, at which time he pushes himself off with his legs- for as much as they can still touch the ground. In the rolled up state it exhibits the form of a discus, of which the eye posts are the central axle. By pushing off al-ternately with one of his three pairs of legs, he can achieve great speeds. It is also sometimes desirable during the rolling (i.e. The descent of an incline, or coasting to a finish) to hold up the legs and 'freewheel' forward. Whenever it wants, it can return again to the walking position in two ways: first abruptly, by suddenly extend-ing his body, but then it’s lyextend-ing on his back with his legs in the air, and second through gradual deceleration (braking with his feet) and slowly unrolling backwards in standing position.

11.2 See also

• Locher, J. L. (2000). The Magic of M. C. Escher.

Dolphins (M. C. Escher)

Sea is a woodcut print by the Dutch artist M. C. Es-cher. This work was first printed in February, 1923. Es-cher had been fascinated by the glowing outlines of ocean waves breaking at night and this image depicts the out-lines made by a school of dolphins swimming and breach-ing ahead of the bow of a ship. The glow was created by

bioluminescent dinoflagellates.

12.1 Sources

• Lewis, J.L. (2002). The Magic of M. C. Escher.

Drawing Hands

Drawing Hands is alithographby theDutchartistM. C. Escherfirst printed in January 1948. It depicts a sheet of paper out of which, from wrists that remain flat on the page, two hands rise, facing each other and in the

paradoxical act of drawing one another into existence. Although Escher used paradoxes in his works often, this is one of the most obvious examples.

It is referenced in the book Gödel, Escher, Bach, by

Douglas Hofstadter, who calls it an example of astrange loop. It is also used inStructure and Interpretation of Computer ProgramsbyHarold AbelsonandGerald Jay Sussmanas an allegory for theevalandapplyfunctions of programming language interpreters incomputer science, which feed each other.

13.1 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Gravitation (M. C. Escher)

work by theDutchartistM. C. Eschercompleted in June 1952. It was first printed as a black-and-whitelithograph

and then coloured by hand inwatercolour.

It depicts anonconvex regular polyhedronknown as the

small stellated dodecahedron. Each facet of the figure has atrapezoidaldoorway. Out of these doorways protrude the heads and legs of twelve turtles without shells, who are using the object as a common shell. The turtles are in six coloured pairs (red, orange, yellow, magenta, green and indigo) with each turtle directly opposite its counterpart.

14.1 See also

14.2 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Hand with Reflecting Sphere

in Spherical Mirror is alithographprint byDutchartist

M. C. Escher, first printed in January 1935. The piece depicts a hand holding a reflective sphere. In the reflec-tion, most of the room around Escher can be seen, and the hand holding the sphere is revealed to be Escher’s. Self-portraits in reflective, spherical surfaces are com-mon in Escher’s work, and this image is the most promi-nent and famous example. In much of his self-portraiture of this type, Escher is in the act of drawing the sphere, whereas in this image he is seated and gazing into it. On the walls there are several framed pictures, one of which appears to be of anIndonesian shadow puppet.

15.1 Popular culture

Frank O'Connor, the manager of theHalo video game series, made an illustration that references this work. It appears inthe Halo Graphic Novel.

In Disney’sTRON: Legacy, Jeff Bridges’ Character, CLU, is seen holding a reflective apple in which he sees his own reflection. This may be in homage to Escher, as there are twooctahedraon a nearby shelf, and much of the digital world is made up oftessellations, a subject largely focused on by Escher.

15.2 See also

• Still Life with Spherical Mirror

• Three Spheres II

• Lithography

15.3 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

House of Stairs

For other works titled “House of Stairs”, see House of Stairs (disambiguation).

House of Stairs is alithographprint by theDutchartist

M. C. Escherfirst printed in November 1951. This print measures 18⅝" × 9⅜". It depicts the interior of a tall structure crisscrossed with stairs and doorways.

A total of 46 "wentelteefje" (imaginary creatures created by Escher) are crawling on the stairs. The wentelteefje has a long, armored body with six legs, humanoid feet, a parrot-like beak and eyes on stalks. Some are seen to roll in through doors, wound in a wheel shape and then unroll to crawl up the stairs, while others crawl down stairs and wind up to roll out. The wentelteefje first appeared ear-lier the same month in the lithographCurl-up. Later that month, House of Stairs was extended to a vertical length of 55½" in a print titled House of Stairs II by repeating and mirroring some of the architecture and creatures.

16.1 References

• Locher, J. L. (2000). The Magic of M. C. Escher.

Magic Mirror (M.C. Escher)

This article is about the lithograph by M. C. Escher. For other uses of Magic mirror, seeMagic mirror.

Magic Mirror is a lithograph print by theDutchartistM. C. Escherfirst printed in January, 1946.

It depicts a mirror standing vertically on wooden supports on a tiled surface. The perspective is looking down at an angle at the right hand side of the mirror. There is a sphere at each side of the mirror. The main focus of the image is a procession of smallgriffin(winged lion) sculptures that emerge from the surface of the mirror and trail away from it in single file. Both the angular reflec-tion of the tiles and the offset between the reflecreflec-tion of the sphere in front of the mirror and the sphere behind it prove it is a mirror. Yet the reflection of the griffin pro-cession continues to emerge from behind the mirror. The griffin processions of both sides loop around to the front and enter atessellatedpattern on the tile surface.

17.1 See also

• Regular Division of the Plane

• Printmaking

• Paradox

17.2 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Metamorphosis I

Metamorphosis I is awoodcutprint by theDutchartist

M. C. Escherwhich was first printed in May, 1937. This piece measures 19.5 by 90.8 centimetres (7.7 in × 35.7 in) and is printed on two sheets.

The concept of this work is to morph one image into atessellatedpattern, then gradually to alter the outlines of that pattern to become an altogether different image. From left to right, the image begins with a depiction of the coastal Italian town ofAtrani(seeAtrani, Coast of Amalfi). The outlines of the architecture then morph to a pattern of three-dimensional blocks. These blocks then slowly become a tessellated pattern of cartoon-like figures in oriental attire.

18.1 See also

• Metamorphosis III

• Regular Division of the Plane

• Printmaking

18.2 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Metamorphosis II

M. C. Escher. It was created between November, 1939 and March, 1940. This print measures 19.2 by 389.5 centimetres (7.6 in × 153.3 in) and was printed from 20 blocks on 3 combined sheets.

Like Metamorphosis I, the concept of this piece is to morph one image into a tessellated pattern and then slowly alter that pattern eventually to become a new im-age.

The process begins left to right with the word metamor-phose (the Dutch form of the wordmetamorphosis) in a black rectangle, followed by several smaller metamor-phose rectangles forming a grid pattern. This grid then becomes a black and white checkered pattern, which then becomes tessellations of reptiles, a honeycomb, insects, fish, birds and a pattern of three-dimensional blocks with red tops.

These blocks then become the architecture of the Italian coastal town of Atrani (seeAtrani, Coast of Amalfi). In this image Atrani is linked by a bridge to a tower in the water, which is actually a rook piece from a chess set. There are other chess pieces in the water and the water becomes a chess board. The chess board leads to a check-ered wall, which then returns to the word metamorphose.

19.1 See also

• Metamorphosis III

• Regular Division of the Plane

• Tessellation

• Printmaking

19.2 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Metamorphosis III

M. C. Eschercreated during 1967 and 1968. Measuring 19 cm × 680 cm (7½ × 268 inches - 22'4”), this is Escher’s largest print. It was printed on thirty-three blocks on six combined sheets and mounted on canvas. This print was partly coloured by hand.

It begins identically to Metamorphosis II, with the word metamorphose (the Dutch form of the word

metamorphosis) forming a grid pattern and then becom-ing a black-and-white checkered pattern. Then the first set of new imagery begins. The angles of the checkered pattern change to elongated diamond shapes. These then become an image of flowers with bees. This image then returns to the diamond pattern and back into the check-ered pattern.

It then resumes with the Metamorphosis II imagery un-til the bird pattern. The birds then become sailing boats. From the sailing boats the image changes to a second fish pattern. Then from the fish to horses. The horses then be-come a second bird pattern. The second bird pattern then becomes black-and-white triangles, which then become envelopes with wings. These winged envelopes then re-turn to the black-and-white triangles and then to the orig-inal bird pattern. It then resumes with the Metamorphosis II print until its conclusion.

20.1 See also

• Metamorphosis II

• Atrani, Coast of Amalfi

• Regular Division of the Plane

• Tessellation

• Printmaking

20.2 External links

• Images of Metamorphosis III and other well known works at mcescher.com

20.3 Sources

• Locher, J. L. (2000). The Magic of M. C. Escher.

Print Gallery (M. C. Escher)

lithographprinted in 1956 by theDutchartistM. C. Es-cher. It depicts a man in a gallery viewing a print of a sea-port, and among the buildings in the seaport is the very gallery in which he is standing. In the bookGödel, Es-cher, Bach, Douglas Hofstadterexplains it as astrange loopshowing three kinds of “in-ness": the gallery is phys-ically in the town (“inclusion”); the town is artistphys-ically in the picture (“depiction”); the picture is mentally in the person (“representation”).

Escher’s signature is on a circular void in the center of the work. In 2003, two Dutch mathematicians, Bart de Smit andHendrik Lenstra, reported a way of filling in the void by treating the work as drawn on anelliptic curve over the field ofcomplex numbers. They deem an idealized version of Print Gallery to contain a copy of itself, ro-tated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58.[1]

Print Gallery has been discussed in relation to post-modernism by a number of writers, including Silvio Gaggi,[2] _{Barbara Freedman,}[3] _{Stephen Bretzius,}[4] _and Marie-Laure Ryan.[5]

21.1 References

[1] de Smit, B. (2003). “The Mathematical Structure of Es-cher’s Print Gallery”.Notices of the American Mathemat-ical Society50 (4): 446–451.

[2] Gaggi, Silvio (1989). Modern/Postmodern: A Study in

Twentieth-Century Arts and Ideas. University of

Pennsul-vania Press. pp. 44–45.ISBN 0-8122-8154-3.

[3] Freedman, Barbara (1991). Staging the gaze:

postmod-ernism, psychoanalysis, and Shakespearean comedy.

Cor-nell University Press. pp. 124–126.ISBN 0-8014-9737-X.

[4] Bretzius, Stephen (1997). Shakespeare in theory: the

post-modern academy and the early post-modern theater. University

of Michigan Press. p. 57.ISBN 0-472-10853-0. [5] Ryan, Marie-Laure (2000). Narrative as virtual reality:

immersion and interactivity in literature and electronic me-dia. Johns Hopkins University Press. p. 165. ISBN 0-8018-6487-9.

21.2 External links

• HarryCarry5 (Jul 26, 2009). Escher’s Print Gallery Explained. YouTube.

• Artful Mathematics: The Heritage of M. C. Escher, by Bart de Smit and Hendrik Lenstra

Puddle (M. C. Escher)

Since 1936, Escher’s work had become primarily focused onparadoxes,tessellationand other abstract visual con-cepts. This print, however, is a realistic depiction of a simple image that portrays two perspectives at once. It depicts an unpaved road with a large pool of water in the middle of it at twilight. Turning the print upside-down and focusing strictly on the reflection in the water, it be-comes a depiction of a forest with a full moon overhead. The road is soft and muddy and in it there are two dis-tinctly different sets of tire tracks, two sets of footprints going in opposite directions and two bicycle tracks. Es-cher has thus captured three elements: the water, sky and earth.

22.1 See also

• Printmaking

22.2 Sources

• Locher, J.L. (2000). The Magic of M. C. Escher.

Regular Division of the Plane

Regular Division of the Plane III, woodcut, 1957 - 1958.

Regular Division of the Plane is a series of drawings by theDutchartistM. C. Escherwhich began in 1936. These images are based on the principle oftessellation, irregular shapes or combinations of shapes that interlock completely to cover a surface or plane.

The inspiration for these works began in 1936 with a visit to theAlhambra, a fourteenth-centuryMoorish cas-tle nearGranada,Spain. Escher had visited the Alhambra once before in 1922 but in this visit he had spent several days studying and sketching the ornate tile designs there. In 1958 Escher published his book The Regular Divi-sion of the Plane. This book included severalwoodcut

prints to demonstrate the concept, but the series of draw-ings continued until the late 1960s, ending at drawing #137. While not Escher’s most artistically important works, some of these patterns are among Escher’s most famous, having been used for a number of commercial products, including neckties.

23.1 Sources

23.2 Further reading

• Locher, J.L. (2000). The Magic of M. C. Escher.

Harry N. Abrams, Inc. ISBN 0-8109-6720-0. • Schattsneider, Doris (2004) M.C. Escher: Visions

of SymmetryHarry N. Abrams, Inc. ISBN 0-8109-4308-5.

Relativity (M. C. Escher)

Escher, first printed in December 1953.

It depicts a world in which the normal laws ofgravitydo not apply. The architectural structure seems to be the centre of an idyllic community, with most of its inhab-itants casually going about their ordinary business, such as dining. There are windows and doorways leading to park-like outdoor settings. All of the figures are dressed in identical attire and have featureless bulb-shaped heads. Identical characters such as these can be found in many other Escher works.

In the world of Relativity, there are three sources of grav-ity, each beingorthogonalto the two others. Each in-habitant lives in one of thegravity wells, where normal physical laws apply. There are sixteen characters, spread between each gravity source, six in one and five each in the other two. The apparent confusion of the lithograph print comes from the fact that the three gravity sources are depicted in the same space.

The structure has seven stairways, and each stairway can be used by people who belong to two different gravity sources. This creates interesting phenomena, such as in the top stairway, where two inhabitants use the same stair-way in the same direction and on the same side, but each using a different face of each step; thus, one descends the stairway as the other climbs it, even while moving in the same direction nearly side-by-side. In the other stair-ways, inhabitants are depicted as climbing the stairways upside-down, but based on their own gravity source, they are climbing normally.

Each of the three parks belongs to one of the gravity wells. All but one of the doors seem to lead to basements below the parks. Though physically possible, such basements are certainly unusual and add to the surreal effect of the picture.

This is one of Escher’s most popular works and has been used in a variety of ways, as it can be appreciated both artistically and scientifically. Interrogations about

perspectiveand the representation of three-dimensional

images in a two-dimensional picture are at the core of Es-cher’s work, and Relativity represents one of his greatest achievements in this domain.

Reptiles (M. C. Escher)

It depicts a desk on which is a drawing of atessellated

pattern of reptiles. The reptiles at one edge of the draw-ing come to life and crawl around the desk and over the objects on it to eventually re-enter the drawing at its op-posite edge. The desk is littered with ordinary objects, as well as a metaldodecahedronthat the reptiles climb over. Although only the size of small lizards, these reptiles ap-pear to have tusks and the one standing on the dodecahe-dron blows smoke from its nostrils.

Like many of Escher’s works, this image was intended to depict aparadoxicaland slightly humorous concept with no real philosophical meaning. There were, however, many popular misconceptions about the image’s mean-ing. Once a woman telephoned Escher and told him that she thought the image was a “striking illustration of

reincarnation". The most common myth revolves around a small book on the desk with the letters JOB printed on it. Many people believed it to be the biblicalBook of Job, when in fact it was a book ofJOBbrand cigarette papers. A colorized version of the lithograph was used by rock band Mott the Hoople as the sleeve artwork for its

eponymous first album, released in 1969.

25.1 See also

• Regular Division of the Plane

25.2 References

• Locher, J. L. (2000). The Magic of M. C. Escher.

Harry N. Abrams, Inc. ISBN 0-8109-6720-0.

25.3 External links

Sky and Water I

Sky and Water I is awoodcutprint by theDutchartist

M. C. Escherfirst printed in June 1938.

The basis of this print is a regular division of the

plane consisting of birds and fish. Both prints have thehorizontalseries of theseelements—fitting into each other like the pieces of ajigsaw puzzle—in the middle, transitional portion of the prints. In this central layer the pictorial elements are equal: birds and fish are alternately foreground or background, depending on whether the eye concentrates on light or dark elements. The birds take on an increasingthree-dimensionality in the upward direc-tion, and the fish, in the downward direction. But as the fish progress upward and the birds downward they grad-ually lose their shapes to become a uniform background of sky and water, respectively.

According to Escher: “In the horizontal center strip there are birds and fish equivalent to each other. We associate flying with sky, and so for each of the black birds the sky in which it is flying is formed by the four white fish which encircle it. Similarly swimming makes us think of water, and therefore the four black birds that surround a fish become the water in which it swims.”

This print has been used inphysics,geology,chemistry, and inpsychologyfor the study ofvisual perception. In the pictures a number of visual elements unite into a simple visual representation, but separately each forms a point of departure for the elucidation of atheoryin one of these disciplines.

26.1 See also

• Sky and Water II

• Tessellation

26.2 Sources

• M. C. Escher—The Graphic Work; Benedikt-Taschen Publishers.

• M. C. Escher—29 Master Prints; Harry N. Abrams, Inc., Publishers.

• Locher, J. L. (2000). The Magic of M. C. Escher.

Sky and Water II

Sky and Water II is alithographprint by theDutchartist

M. C. Escherfirst printed in 1938. It is similar to the

woodcut Sky and Water I, which was first printed only months earlier.

27.1 See also

• Printmaking

27.2 Sources

• M. C. Escher—The Graphic Work; Benedikt-Taschen Publishers.

• M. C. Escher—29 Master Prints; Harry N. Abrams, Inc., Publishers.

Snakes (M. C. Escher)

It depicts a disc made up of interlocking circles that grow progressively smaller towards the center and towards the edge. There are three snakes laced through the edge of the disc.

Snakes hasrotational symmetryof order3, comprising a single wedge-shaped image repeated three times in a cir-cle. This means that it was printed from three blocks that were rotated on a pin to make three impressions each. Close inspection reveals the central mark left by the pin. The image is printed in three colours: green, brown and black. In several earlier works Escher explored the limits of infinitesimal size and infinite number, for example the

Circle Limitseries, by actually carrying through the ren-dering of smaller and smaller figures to the smallest possi-ble sizes. By contrast, in Snakes, the infinite diminution of size – and infinite increase in number – is only sug-gested in the finished work. Nevertheless, the print shows very clearly how this rendering would have been carried out to the limits of human visibility.

This was Escher’s last print.

28.1 See also

28.2 References

• Locher, J. L. (2000). The Magic of M. C. Escher.

Harry N. Abrams, Inc. ISBN 0-8109-6720-0.

28.3

External links

• A 3-dimensional animation based on Escher’s print