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Copyright 2005 by Sandro Corsi.
Created 2005-02-27. Last modified 2005-10-20. |
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Maurits Cornelis Escher (1898-1972) explored the artistic implications of several mathematical ideas. One of his earliest and most enduring interests was tessellations http://www.mathacademy.com/pr/minitext/escher/#tess, an interest reinforced by his encounter with islamic tile patterns. You can explore such patterns on your own with the program Taprats http://www.cgl.uwaterloo.ca/~csk/washington//tile/islam/ (its author, Craig S. Kaplan, not surprisingly has also developed an "Escherization" method http://www.cgl.uwaterloo.ca/~csk/phd/).
Adapting and extending ideas from mathematics and crystallography, Escher filled his notebooks with interlocking shapes, designed to fill the drawing surface without gaps http://www.tessellations.org/tess-escher8.htm
In the following links you'll find documented the process used to create several of Escher's works, all of them derived from a repeating pattern which was in turn based on a regular tessellation of hexagons http://library.thinkquest.org/16661/simple.of.regular.polygons/regular.4.html. This pattern (and more complex ones) can be created interactively in your web browser using the Pattern Blocks applet http://ejad.best.vwh.net/java/patterns/patterns_j.shtml
Escher went beyond the simple geometric shapes of regular tessellations by systematically altering the sides of the polygons he started with
http://library.thinkquest.org/16661/escher/tessellations.1.html
See how a tessellation of hexagons turns gradually into a tessellation of more complex shapes by watching this animation of celtic spirals.
http://www.geocities.com/davidschow/celtic/ani.htm
In this example the sides of the hexagons are altered symmetrically to sprout spiral arms. In Escher's drawings, they would instead evolve into the limbs and tail and head of a creature.
The repeating lizards pattern, Periodic Drawing e25 (1939) http://www.mcescher.com/Gallery/symmetry-bmp/E25.jpg or http://library.thinkquest.org/16661/gallery/escher/17.html, one of the drawings in the Regular Division of the Plane series. In addition to the artists' own later adaptations of this work, this design was also used for puzzle pieces http://iproject.com/lizards/lizards.html?mgiToken=CDA00E161D992AFDC5
An earlier version of the lizards pattern emerges from a checkerboard in Development I (1937) http://www.mcescher.com/Gallery/switz-bmp/LW300.jpg or http://www.nga.gov/collection/gallery/ggescher/ggescher-53928.0.html. This picture suggests the process of deriving the pattern from a regular tessellation of squares.
The lizards pattern radiates from the center of Development II (1939), first http://www.mcescher.com/Gallery/switz-bmp/LW310A.jpg. and final http://www.mcescher.com/Gallery/switz-bmp/LW310.jpg states.
The lizards pattern appears in a linear section http://www.mcescher.com/Gallery/switz-bmp/LW320B.jpg of Metamorphosis II (1940) http://www.mcescher.com/Biography/lw320_42_46.jpg, and a section http://www.mcescher.com/Gallery/recogn-bmp/LW446C.jpg of Metamorphosis III (1967-1968).
A variant of the lizards pattern evolves in the lower-left quadrant of Verbum (1942), http://www.mcescher.com/Gallery/back-bmp/LW326.jpg.
The lizards turn into 3-d alligators in Reptiles (1943), http://www.mcescher.com/Gallery/back-bmp/LW327.jpg or http://www.nga.gov/collection/gallery/ggescher/ggescher-47677.0.html.
Escher's influence is still strong. See just a very small sampling of designs inspired by his work: http://www.geocities.com/davidschow/HUB/Esample.htm
Some of the many books written about the art of M.C. Escher:
http://www.tessellations.org/tess-reference.htm
And a few tips on how to go about making your own designs:
http://www.tessellations.org/diy-basic1.htm
http://www.geocities.com/wenjin92014/escher/teaching.htm
http://www.geocities.com/williamwchow/escher/thinker.htm
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