Tessellations by xuyuzhu


									*Created by Kay Wagner, Ph.D., Edina
Public Schools, Edina, Minnesota
Drawn images may be used freely, fair
use laws apply to all other images
Creating Tessellating Art

     • Artwork inspired by M.C. Escher
      Tessellations are arrangement of shapes that
cover the picture without overlapping and without
leaving spaces.
      Typically, the shapes making up a tessellation
are simple similar regular shapes, such as the
       M.C. Escher developed the
    tessellating shape as an art form
  Escher was a graphic artist, who specialized in
woodcuts and lithographs.
    He was born   Maurits Cornelis Escher
in 1898, in Leeuwarden, Holland.

   His father wanted him to be an architect, but bad
grades in school and a love of drawing and design
led him to a career in the graphic arts.
Escher Self-portrait
Map showing where Escher was
He was unknown until the 1950’s
  But by 1956 he had given his first important
exhibition, was written up in Time magazine,
and acquired a world-wide reputation.

   Among his greatest admirers were
mathematicians, who recognized his work as
pictures of mathematical ideas. This was amazing
because he had no formal math training.
  Escher saw tile patterns that gave
     him ideas for his art work
     His interest began in
1936, when he traveled to
Spain and saw the tile
patterns used in the
He spent many days
sketching these tile patterns,
and later claimed that this
“was the richest source of
inspiration that I have ever
World map sowing Spain
    Alhambra Palace
   The Alhambra is a walled city and fortress
in Granada, Spain. It was built during the last
Islamic Dynasty (1238-1492).

   The palace is lavishly decorated with stone
and wood carvings and tile patterns on most of
the ceilings, walls, and floors.
Alhambra Castle
Alhambra consists of palaces
built by several rulers, each had
his own.castle.
The Alhambra Palace is a
famous example of
Moorish architecture.
It may be the most well
known Muslim construction.
Islamic art does not usually
use representations of living
beings, but uses
geometric patterns,
especially symmetric
(repeating) patterns.
The idea behind several of the buildings of
Alhambra was to create a Paradise on earth.
 Escher used the geometry in his
   art that he saw at Alhambra
   As his work developed, he drew great
inspiration from mathematical ideas he read
about, often working directly from geometric

    He was also fascinated with paradox and
"impossible" figures, and developed many
intriguing works of art.
Convex Concave
   Lithograph, March 1955
    Escher was fascinated by every
         kind of tessellation
    In 1957 he wrote an essay on tessellations.
Mathematicians, had shown that only the
                regular polygons,
triangle,           square,          and hexagon

   could be used for a tessellation . Escher used
these basic shapes in his tessellations.
 Sometimes Escher changed the
        basic shapes
By “distorting” the basic
shapes he changed them into
other figures.
The effect can be
both startling and beautiful.
Escher Horses
Lets make a simple tessellating
Begin with a simple geometric
      shape - the square
Change the shape of one side
Copy this line on the opposite
Rotate the line and repeat it on
     the remaining edges
Erase the original shape
  Add lines to the inside of the
shapes to turn them into pictures.
Add color to enhance your picture.
By repeating your shape you create a
         tessellated picture
Escher liked
what he called

where shapes

changed and
interacted with
each other.
Another example
of metamorphosis
Lets make a simple tessellating
Begin with a simple geometric
      shape - the square
Change the shape of one side
Repeat the line on the opposite
Change the shape of the top
Repeat this line on the bottom
Erase the square
 Turn shape looking for two
hidden animals, flowers, fish,
      insects, or birds.
Draw a line that separates the two
 hidden shapes you have found.
Add a few lines that bring out
    your hidden shapes.
Separate the two shapes so you
  can use them one at a time
Make four versions of each shape, each
      version with more detail

   The most
 detailed shape
can be changed
   quite a bit
   Make four versions of each shape
          with more detail

The most
detailed shape
can be changed
quite a bit
 Color all of one
type of shape the
same basic color
Line up the simplest shape with
  the most complex along the
Line up the next most complex
    with the next simplest
Add the next row in the same way
Completed Tessellation
Completed Tessellation
Completed Tessellation

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