M. C. Escher
The Dutch artist M.C. Escher (1889-1972) created his graphic art based
on mathematics. Using translation, reflection, glide reflection and rotation
Escher produced intricate tessellations of patterns., geometric figures
and creatures of his imagination. Escher illustrated and expanded tessellation.
He also used symmetry, perspective, contrast and optical illusion to stretch
the viewer's understanding of the plane and of space. His violations of
perspective broaden the viewer's comprehension. The lithograph "Waterfall"
is an example. (click here
to see "Waterfall") Escher gives the illusion of a body naturally descending
down a path.
Upon closer examination,
it is clear that by manipulating shading and the use of perpendicular lines,
Escher has subverted what the viewer thinks of as "natural" and made the
viewer question how she views the world.
A simple way to create Escher-like
drawings:
1. Take a square piece
of cardboard (any shape will do, but a square is easiest for the first
time) and cut a shape out of one side.
2. Slide the cut-out shape
to the side opposite the one that it was cut from and glue or tape it so
that is responds to the area it was cut from. (For example, if you cut
a triangle one inch from the top of one side, the triangle should be placed
on the other side, one inch from the top.) Note: pieces may be cut from
either (or both) sides, but they must be placed accordingly on the opposite
side from which they were cut.
3. Repeat step 2 for the
other sides of the square.
4. Trace the shape you
have made. Slide the "stencil" left, right, up and down and continue to
trace. Your object should fit into itself and you should be able to create
a tessellation.
5. Use your imagination
to color, shade and decorate the translation tessellation you have just
made!
more information about
Escher is available in Doris Schattschneider's book, M.C. Escher: Visions
of Symmetry, and at the web site World
of Escher.