M.C. Escher and the History of Tesselations

             One of the sources of inspiration for Escher's designs is the Alhambra in Granada, Spain whose ceilings and walls are covered with beautiful ornamentation. During his lifetime M. C. Escher designed over a hundred tessellated patterns, many of which were transformed into the famous works of art that we recognize. Unlike the Islamic designs he saw, almost all of Escher's tilings were designed to resemble recognizable objects, usually living ones. In the Preface to Visions of Symmetry he writes, "without recognizability no meaning and without shade contrast no visibility." Escher means that he values both resemblance to actual objects and careful shading in order to draw attention to the specific shapes used.
             In spite of his lack of training in mathematics, Escher was influenced by developments in science and mathematics. Many of his works of art that involve topology, optical illusions, tessellations, and other advanced mathematical topics were created with mathematicians such as Roger Penrose, J. F. Schouten, H S. M. Coxeter, and J. W. Wagenaar. Escher truly loved his work and today people can understand the beauty of his designs. .
             "While drawing I sometimes feel as if I were a spiritualist medium, controlled by the creatures which I am conjuring up. It is as if they themselves decide on the shape in which they choose to appear" (Escher 8). .
             In short, a tessellation is any repeating pattern of interlocking shapes. Tessellations are also sometimes known as tilings. The definition sounds fairly simple, but the ideas involved in designing and understanding tessellations can grow very complex and interesting.
             If one were to cover a large surface with little pieces of material, they would probably choose to design a repeating pattern since repeating patterns are usually more neat than non-repeating ones. When the surface was completed, the finished product would have been a tessellation. Any repeating pattern of shapes that cover a plane without overlap is considered a tessellation.