Print Gallery (Dutch: Prentententoonstelling) is a lithograph printed in 1956 by the Dutch artist M. C. Escher. It depicts a man in a gallery viewing a print of a seaport, and among the buildings in the seaport is the very gallery in which he is standing, making use of the Droste effect.[1] The lithograph has attracted discussion in both mathematical and artistic contexts.
Origins
Bruno Ernst cites M. C. Escher as stating that he began Print Gallery "from the idea that it must be possible to make an annular bulge, a cyclic expansion ... without beginning or end."[2] Escher attempted to do this with straight lines, but intuitively switched to using curved lines which make the grid expand greatly as it rotates.[2][3]
Seeming paradox
In the book Gödel, Escher, Bach, Douglas Hofstadter explains it as a strange loop showing three kinds of "in-ness": the gallery is physically in the town ("inclusion"); the town is artistically in the picture ("depiction"); the picture is mentally in the person ("representation").[4]
Possible Droste effect
Escher's signature is on a circular void in the center of the work. In 2003, two Dutch mathematicians, Bart de Smit and Hendrik Lenstra, reported a way of filling in the void by treating the work as drawn on an elliptic curve over the field of complex numbers. They deem an idealized version of Print Gallery to contain a copy of itself (the Droste effect), rotated clockwise by about 157.63 degrees and shrunk by a factor of about 22.58.[3] Their website further explores the mathematical structure of the picture.[5]
References
- ↑ Merow, Katharine (2013). "Escher and the Droste Effect". Mathematical Association of America. Archived from the original on 2 August 2013.
- 1 2 Ernst, Bruno. De toverspiegel van M. C. Escher, Meulenhoff, Amsterdam, 1976; English translation by John E. Brigham: The Magic Mirror of M. C. Escher, Ballantine Books, New York, 1976
- 1 2 de Smit, B.; Lenstra, H. W. (2003). "The Mathematical Structure of Escher's Print Gallery". Notices of the American Mathematical Society. 50 (4): 446–451.
- ↑ Cooper, Jonathan (5 September 2007). "Art and Mathematics". Retrieved 5 September 2015.
- ↑ Lenstra, Hendrik; De Smit, Bart. "Applying mathematics to Escher's Print Gallery". Leiden University. Retrieved 10 November 2015.
- ↑ Gaggi, Silvio (1989). Modern/Postmodern: A Study in Twentieth-Century Arts and Ideas. University of Pennsulvania Press. pp. 44–45. ISBN 0-8122-8154-3.
- ↑ Freedman, Barbara (1991). Staging the gaze: postmodernism, psychoanalysis, and Shakespearean comedy. Cornell University Press. pp. 124–126. ISBN 0-8014-9737-X.
- ↑ Bretzius, Stephen (1997). Shakespeare in theory: the postmodern academy and the early modern theater. University of Michigan Press. p. 57. ISBN 0-472-10853-0.
- ↑ Ryan, Marie-Laure (2000). Narrative as virtual reality: immersion and interactivity in literature and electronic media. Johns Hopkins University Press. p. 165. ISBN 0-8018-6487-9.
External links
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Works | 1910s |
- Escher's Father
- Bookplate Bastiaan Kist
- Chrysanthemum
- Head of a child
- Skull
- Railway Bridge, Oosterbeek
- Mascot
- Portrait of a Man (I)
- Self-Portrait (I)
- Baby
- Young Thrush
- Bookplate M. C. Escher
- Self-Portrait (II)
- Jug
- The Rag Pickers
- Fiet van Stolk
- Waves
- Self-Portrait (III)
- White Cat (I)
- The Borger Oak
- Portrait
- Seated Man with cat on his lap
- Tree
- Self-Portrait (IV)
- Parrot
- White Cat (II)
- Sea-shell
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1920s |
- Self Portrait in a Chair
- Rabbits
- Female Nude in a Landscape
- Wild West
- The Fall of Men
- Escher's Father with Magnifying Glass
- Portrait of a Man (II)
- Man Standing
- Seated Old Woman
- Flower
- Seated Female Nude (I)
- Seated Female Nude (II)
- Seated Female Nude (III)
- Roosje Ingen Housz
- Poster
- Plane-filling Motif with Human Figures
- Paradise
- Seated Female Nude (IV)
- Seated Female Nude (V)
- Hand with Fir Cone
- St Francis
- Eight Heads
- Eagle, vignette
- Dolphins
- San Gimignano
- Self-Portrait (V)
- Portrait of Jetta
- Vitorchiano nel Cimino
- The First Day of the Creation
- The Sixth Day of Creation
- The Fall of Man
- Procession in Crypt
- Rome
- Castle in the Air
- Tower of Babel
- Fara San Martino, Abruzzi
- Corte, Corsica
- The Drowned Cathedral
- Infant Arthur Escher
- Self-Portrait (VI)
- Barbarano, Cimino
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1930s |
- Street in Scanno, Abruzzi
- Castrovalva
- The Bridge
- Fiumara, Calabria
- Tropea, Calabria
- Cloister near Rocca Imperiale, Calabria
- Atrani, Coast of Amalfi
- Covered Alley in Atrani
- Ravello and the Coast of Amalfi
- Coast of Amalfi
- Farmhouse, Ravello
- San Cosimo, Ravello
- Turello, Southern Italy
- Porta Maria dell'Ospidale, Ravello
- Lion of the Fountain in the Piazza at Ravello
- San Michele dei Frisone, Rome
- Mumified Priests in Gangi, Sicily
- Temple of Segeste, Sicily
- Cave Dwellings (near Sperlinga) Sicily
- Palm
- Caltavuturo in the Madonie Mountains Sicily
- Cloister of Monreale Sicily
- Lava Flow of 1928 from Etna Sicily
- Pineta of Calvi, Corsica
- Phosphorescent Sea
- Fireworks
- Old Olive Tree, Corsica
- Nonza, Corsica
- Still Life with Mirror
- Nocturnal Rome: Colonade of St Peter's
- Nocturnal Rome: Santa Maria del Popolo
- Nocturnal Rome: Trajan's Column
- Nocturnal Rome: Basilica of Constantine
- Nocturnal Rome: Castel Sant' Angelo
- Nocturnal Rome: Colosseum
- Aeroplane above Snowy Landscape
- Still Life with Spherical Mirror
- Hand with Reflecting Sphere
- Regular Division of the Plane
- Inside St Peter's
- Portrait of G.A. Escher
- Sengela, Malta
- Hell, copy after Hieronymus Bosch
- Snow
- Prickly Flower
- House in the Lava near Nunziata, Sicily
- Still Life and Street
- Metamorphosis I
- Development I
- Day and Night
- Cycle
- Sky and Water I
- Sky and Water II
- Entrance to the Oude Kerk, Delft
- Development II (I)
- Development II (II)
- Oostpoort, Delft
- Nieuwe Kerk, Delft
- Town Hall, Delft
- Voldersgracht, Delft
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1940s |
- Metamorphosis II
- Bookplate Dr. P.H.M. Travaglino
- Horse (No. 8)
- Sea Horse (No. 11)
- Lizard (No. 15)
- Eagle (No. 17)
- Two Birds (No. 18)
- Fish (No. 20)
- Clowns (No. 21)
- Bird / Fish (No. 22)
- Lizard (No. 25)
- Three Birds (No. 28)
- Fish
- Plane-filling Motif with Reptiles
- Bird / Fish (No. 34)
- Bird / Fish (No. 34B)
- Dragonfly (No. 38)
- Crab (No. 40)
- Two Fish (No. 41)
- Shells and Starfish (No. 42)
- Bird (No. 44)
- Angel-Devil (No. 45)
- Verbum
- Two Fish (No. 46)
- Frog (No. 51)
- Fish (No. 55)
- Lizard (No. 56)
- Two Fish (No. 57)
- Two Fish (No. 58)
- Two Fish (No. 59)
- Two Lizards (No. 60)
- Reptiles
- Ant
- Blowball (I)
- Blowball (II)
- Encounter
- Two Creatures (No. 61)
- Devil (No. 62)
- Pessimist-Optimist (No. 63)
- Balcony
- Doric Columns
- Three Spheres I
- Diploma Tijdelijke Academie, Eindhoven
- Winged Lion (No. 66)
- Magic Mirror
- Three Spheres II
- Horseman
- Mumified Frog
- Eye
- New Year's greeting-card
- Gallery
- Horseman (No. 67)
- Another World
- Up and Down
- Drawing Hands
- Dewdrop
- Sun and Moon
- Study for Stars
- Stars
- Fish / Duck / Lizard (No. 69)
- Butterfly (No. 70)
- Fish / Boat (No. 72)
- New Year's greeting card
- Plane-filling Motif with Birds
- Regular Division of the Plane with Birds
- Sea-shells
- Fish and Frogs
- Double Planetoid
- Flying Fish (No. 73)
- Horse / Bird (No. 76)
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1950s |
- Order and Chaos
- Rippled Surface
- Devils (vignette)
- Unicorn (No. 78)
- Flying Fish / Bird (No. 80)
- Predestination
- Plane Filling I
- Curl-up
- House of Stairs
- Bird / Fish (No. 82)
- Thirty-Six Different Motifs (No. 83)
- Bird / Fish (No. 8)
- Two Intersecting Planes
- Puddle
- Dragon
- Gravitation
- Lizard / Fish / Bat (No. 85)
- Two Birds (No. 87)
- Sea Horse (No. 88)
- Concentric Rinds
- Relativity
- Spirals
- Beetle (No. 91)
- Bookplate A.R.A. Wertheim
- Tetrahedral Planetoide
- Fish (No. 93)
- Convex and Concave
- Liberation
- Rind
- Depth
- Three Worlds
- Fish (No. 94)
- Swan (No. 96)
- Swans
- Bond of Union
- Print Gallery
- Division
- Smaller and Smaller
- Lizards (No. 101)
- Cube with Magic Ribbons
- Plane Filling II
- Whirlpools
- Belvedere
- Sphere Surface with Fish
- Sphere Spirals
- Flatworms
- Circle Limit II
- Circle Limit III
- Fishes and Scales
- Lizard (No. 104)
- Pegasus (No. 105)
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1960s | |
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