For this work, Escher fixed the fish’s tail, and rotated its body around the fixed point to create the other fish. A rotation is when one point of the image is fixed and the rest of the image is rotated around that point. Rotation is used to create the tessellation. How has the flying fish shape been repeated in this tessellation? Can you find the fixed point around which the fish turn? Now look at Regular division of the plane no. The blue bird is then shifted vertically parallel to the mirror line. In this image, the white bird is flipped over the line of reflection – the mirror line – to create the image of the blue bird. A glide reflection is made up of a reflection and a translation. How has the bird been placed to make the pattern?Įscher has used translation and glide reflection. The original horse shape is maintained and shifted across the surface to create other winged horses that form the tessellation. 105 (Pegasus), 1959, in which only one shape is used. This can be seen in Regular division of the plane no. How have the horses been placed to repeat the pattern? Have they been flipped or turned?Ī translation is when an image is preserved and moved in any direction across a surface without turning or flipping it. Translation, reflection and rotation are ways to transform a shape in a tessellation. In maths a shape is considered transformed when it is shifted from one position to another while maintaining its exact image. To create many of these tessellations, Escher used mathematical transformations. He referred to his tessellations as ‘regular division of the plane.’ Over three decades, he created more than 130 tessellations incorporating repeating motifs of creatures and figures. Surprisingly, Escher didn’t do well at mathematics in school, but his complex designs have inspired many mathematical thinkers.Įscher was intrigued by tessellations – patterns that repeat without gaps or overlapping. Escher (1898 – 1972) is well known, but initially it was mathematicians and scientists who were most interested in Escher’s work.
Although I am absolutely without training or knowledge, I often seem to have more in common with mathematicians than my fellow artists.
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