symmetry: chinese lattice designs the alhambra m. c. escher
DESCRIPTION
Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher. Wallpaper Designs Hungarian Needlework. also. Elliot A. Tanis Hope College. - PowerPoint PPT PresentationTRANSCRIPT
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Symmetry:Chinese Lattice Designs
The AlhambraM. C. Escher
• Wallpaper Designs
• Hungarian Needlework
also
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.
• Equilateral triangles
• Squares
• Regular Hexagons
Examples:
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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p1p211 p1m1
p2mg p2gg c2mm
pg c1m1 p2mm
p4 p4m p4gm
p3 p3m1 p31m p6p6mm
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p1 p4
p2 p6
p3 pm
p2mm p2gg
p4mm p2mg
p6mmp4gm
cm
c2mm
p3m1
p31m
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, 1898 - 1972
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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 (1898-1972) 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 - p1105
Baarn, 1959System I D
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Pegasus - p1
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Joseph L. Teeters
Ernest R. Ranucci
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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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1967 - 1968
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 HagueMetamorphosis is 50 Meters Long
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2-Fold Rotation
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Doves, Ukkel, Winter 1937-38
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 Typeand 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
Woodcut Lithograph
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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