Transcript Symmetry: Chinese Lattice Designs The Alhambra M. C. Escher

Symmetry:
Chinese Lattice Designs
The Alhambra
M. C. Escher
also
• Wallpaper Designs
• Hungarian Needlework
Elliot A. Tanis
Hope College
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
Regular
• Squares
Polygons
• Regular Hexagons
Some examples of periodic or
repeating patterns, sometimes
called “wallpaper designs,” will be
shown. There are 17 “plane
symmetry groups” or types of
patterns.
Examples of places where
repeating patterns are found:
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Wallpaper Designs
Chinese Lattice Designs
Hungarian Needlework
Islamic Art
The Alhambra
M. C. Escher’s Tessellations
Wallpaper Designs
Chinese Lattice Designs
Chinese
Lattice
Design
Chinese Garden
p1
p211
p1m1
p2mg
p2gg
c2mm
p3
p3m1
p31m
pg
p4
p6
c1m1
p2mm
p4m
p4gm
p6mm
p2mm
p4mm
p2gg
p2mg
p4gm
p6mm
p1
p4
p3m1
cm
p2
p6
p31m
c2mm
p3
pm
pg
Wall Panel, Iran, 13th/14th cent(p4mm)
Wall Panel, Iran, 13th/14th cent (p6mm)
Design at the Alhambra
Design at the Alhambra
Hall of Repose - The Alhambra
Hall of Repose - The Alhambra
Resting Hall - The Alhambra
Collage of
Alhambra
Tilings
Church/Mosque in Cordoba
Church/Mosque in Cordoba
Pillars by M. C. Escher
Cordoba
Seville
Seville
M. C. Escher, 1898 - 1972
Keukenhof Gardens
Keukenhof Gardens
Escher’s Drawings of
Alhambra Repeating Patterns
Escher Sketches of designs in the
Alhambra and La Mezquita (Cordoba)
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
Visions of
Symmetry
Doris
Schattschneider
W.H. Freeman
1990
1981, 1982,
1984, 1992
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:
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Translations
Rotations
Reflections
Glide Reflections
Unit Cell -- de Porcelain Fles
Translation
Translation
Pegasus - p1
105
System I D
Baarn, 1959
Pegasus - p1
Ernest R. Ranucci
Joseph L. Teeters
Suggestion
From
Ranucci
and
Teeters
Outline
Of
One
Pegasus
Why
Is
Red
Used?
A School in The Hague
Slightly
Modified
Pattern
Types
p1
Birds
Baarn
1959
p1 Birds
p1
Birds
Baarn
1967
p1
Birds
Baarn
1967
3-Fold Rotation
Reptiles, Ukkel, 1939
Suggestion
From
Rannuci
and
Teeters
One
Of
Escher’s
Sketches
Escher’s Drawing – Unit Cell
p3
Pattern Type
p3 Toads
Sketch for Reptiles
Reptiles, 1943 (Lithograph)
Metamorphosis II
November 1939 - March 1940
Metamorphosis II
November 1939 - March 1940
Metamorphosis III
1967 - 1968
Woodcut
Metamorphose, PO, Window 5
Metamorphose, Windows 6-9
Metamorphose, Windows 11-14
Air Mail
Letters
Baarn
1956
Air Mail Letters in PO
Post Office in The Hague
Metamorphosis is 50 Meters Long
2-Fold Rotation
Doves, Ukkel, Winter 1937-38
p2
p211 Doves
4-Fold Rotation
Reptiles, Baarn, 1959
p4
p4 Reptiles
Reptiles, Baarn, 1963
p4
6-Fold Rotation
Reptiles, Baarn, 1942
p6
Rotations
Reflection
p11m Cows
Glide Reflection
Glide Reflection
p1g1 Toads
p1g1 Toads
Flukes
Baarn
1959
p31m
p31m “flukes”
p3m1
Baarn
1952
p2mm
Baarn
1950
c1m1
Baarn
1953
p2gg
Baarn
1963
Baarn
1964
p4gm
Determine the Pattern Type
and Then Replicate This Design
p4mm
Belvedere
May 1958
Lithograph
Man with Cuboid, 1958,
Wood Engraving
Relativity, 1953
Woodcut
Lithograph
Relativity, 1953
Woodcut
Lithograph
Mobius Strip II (Red Ants), 1963
Ascending
And
Descending
1960
Lithograph
Drawing Hands, 1948, Lithograph
Creation
Keukenhof Garden