Tessellations
Who was M.C. Escher?
"I NEVER GOT A PASSING GRADE IN MATH, BUT I SEEM TO LATCH ON TO MATHEMATICAL SOLUTIONS WITHOUT KNOWING IT."
unusual angles, extreme close-ups, unexpected reflections
Other World, 1947. Wood engraving and woodcut.
How many different viewpoints are shown in this image?
Eye, 1948. Messotint.
Who or what is being reflected in this eye? What idea might this reflected image express?
Puddle, 1954. Woodcut, from three blocks.
"Several worlds can go on simultaneously, each unaware of the other." -M.C.Escher
In math, a plane is flat surface that goes on forever in all directions. A tessellation is designed to fill a plane, so it too is designed to go on forever.
Tessalation (Latin word meaning tile): a pattern of interlocking shapes, where positive shapes alternate with negative shapes
Reptiles, 1943. Lithograph.
"A whole universe of reptiles spirals out in circles toward infinity."
Symmetry Work 105, 1959. Ink, pencil, watercolor.
"To be dynamic, tessellations must have a clear direction for the flow of traffic."
Symmetry Work 85, 1952. Ink, pencil, watercolor.
"The frogs, bats, and fish in this work symbolize earth, sky, and water."
"I AM DRIVEN BY THE IRRESISTIBLE PLEASURE I FEEL IN REPEATING THE SAME FIGURES OVER AND OVER."
Three Types of Tesselations
Translation
The original shape is created than repeated again and again. The congruent shapes fit together like pieces of a jigsaw puzzle, shapes never overlap, and there are no gaps between them.
Rotation
The congruent shape is created, then repeated in a circular pattern.
Reflection
The congruent shape is created and repeated again and again. Only this time, the image is flipped and repeated backwards.