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Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher
also Wallpaper Designs Hungarian Needlework Elliot A. Tanis Hope College
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A repeating pattern or a tessellation or a tiling of the plane is a covering of the plane by one or more figures with a repeating pattern of the figures that has no gaps and no overlapping of the figures. Examples: Equilateral triangles Squares Regular Hexagons Regular Polygons
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Some examples of periodic or repeating patterns, sometimes called “wallpaper designs,” will be shown. There are 17 “plane symmetry groups” or types of patterns.
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Examples of places where repeating patterns are found:
Wallpaper Designs Chinese Lattice Designs Hungarian Needlework Islamic Art The Alhambra M. C. Escher’s Tessellations
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Wallpaper Designs
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Chinese Lattice Designs
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Chinese Lattice Design
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Chinese Garden
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p1 p211 p1m1 pg c1m1 p2mm p2gg p4gm p2mg p4m c2mm p4 p3 p3m1 p6 p31m p6mm
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p2gg p2mm p2mg p4mm p4gm p6mm p1 p4 p3m1 cm p6 p31m p2 c2mm p3 pm pg
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Wall Panel, Iran, 13th/14th cent(p4mm)
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Wall Panel, Iran, 13th/14th cent (p6mm)
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Design at the Alhambra
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Design at the Alhambra
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Hall of Repose - The Alhambra
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Hall of Repose - The Alhambra
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Resting Hall - The Alhambra
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Collage of Alhambra Tilings
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Church/Mosque in Cordoba
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Church/Mosque in Cordoba
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Pillars by M. C. Escher
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Cordoba
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Seville
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Seville
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M. C. Escher,
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Keukenhof Gardens
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Keukenhof Gardens
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Escher’s Drawings of Alhambra Repeating Patterns
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Escher Sketches of designs in the Alhambra and La Mezquita (Cordoba)
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Mathematical Reference:
“The Plane Symmetry Groups: Their Recognition and Notation” by Doris Schattschneider, The Mathematical Monthly, June-July, 1978 Artistic Source: Maurits C. Escher ( ) was a master at constructing tessellations
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Visions of Symmetry Doris Schattschneider W.H. Freeman 1990
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1981, 1982, 1984, 1992
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A unit cell or “tile” is the smallest region in the plane having the property that the set of all of its images will fill in the plane. These images may be obtained by: Translations Rotations Reflections Glide Reflections
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Unit Cell -- de Porcelain Fles
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Translation
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Translation
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Pegasus - p1 105 D Baarn, 1959 System I
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Pegasus - p1
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Ernest R. Ranucci Joseph L. Teeters
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Suggestion From Ranucci and Teeters
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Outline Of One Pegasus
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Why Is Red Used?
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A School in The Hague
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Slightly Modified Pattern Types
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p1 Birds Baarn 1959
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p1 Birds
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p1 Birds Baarn 1967
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p1 Birds Baarn 1967
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3-Fold Rotation
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Reptiles, Ukkel, 1939
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Suggestion From Rannuci and Teeters
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One Of Escher’s Sketches
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Escher’s Drawing – Unit Cell
p3
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Pattern Type
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p3 Toads
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Sketch for Reptiles
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Reptiles, 1943 (Lithograph)
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Metamorphosis II November 1939 - March 1940
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Metamorphosis II November 1939 - March 1940
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Woodcut Metamorphosis III
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Metamorphose, PO, Window 5
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Metamorphose, Windows 6-9
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Metamorphose, Windows 11-14
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Air Mail Letters Baarn 1956
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Air Mail Letters in PO
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Post Office in The Hague Metamorphosis is 50 Meters Long
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2-Fold Rotation
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Doves, Ukkel, Winter p2
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p211 Doves
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4-Fold Rotation
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Reptiles, Baarn, 1959 p4
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p4 Reptiles
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Reptiles, Baarn, 1963 p4
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6-Fold Rotation
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Reptiles, Baarn, 1942 p6
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Rotations
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Reflection
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p11m Cows
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Glide Reflection
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Glide Reflection
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p1g1 Toads
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p1g1 Toads
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Flukes Baarn 1959
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p31m
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p31m “flukes”
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p3m1 Baarn 1952
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p2mm Baarn 1950
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c1m1 Baarn 1953
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p2gg Baarn 1963
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Baarn 1964
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p4gm
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Determine the Pattern Type and Then Replicate This Design
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p4mm
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Belvedere May 1958 Lithograph
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Man with Cuboid, 1958, Wood Engraving
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Relativity, 1953 Woodcut Lithograph
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Relativity, 1953 Lithograph Woodcut
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Mobius Strip II (Red Ants), 1963
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Ascending And Descending 1960 Lithograph
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Drawing Hands, 1948, Lithograph
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Creation
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Keukenhof Garden
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