We can also turn the duplicate through 60 degrees about the point C, and we notice that again it covers the original pattern exactly. If we shift the whole plane over the distance AB, it will cover the underlying pattern once again. The whole surface is covered with equilateral triangles. In the next figure, there is a simple design. He build his own system and wrote about it in 19. He read books about ornamentation, and mathematical treatises he could not understand, although he liked and used the illustrations they had. He made copies, together with his wife, of the Moorish tessellations, and on his return home he studied them closely. For the second time he was impressed by the enormous possibilities lying in the division of a plane surface. But in 1936, accompanied by his wife, he paid another visit to the Alhambra. He wasn't satisfied by his results, so for 10 years he wasn't interested anymore in this topic. He made his own sketches, as one can see in the next figure:įig 3: Sketches made in the Alhambra, pencil and coloured crayon (1936) Then, in 1926, having some acquaintance with the Alhambra on the occasion of a brief visit, Escher was impressed by the Moorish frescos, although not all of them had figures that are true tessellations. The heads have a theatrical air about them, false, unreal, 'fin du siècle'. Eight different heads are shown, four of them right way up, and four upside down.

The most detailed and fully developed production from this period is the woodcut 'Eight Heads' (1922). The idea of covering the entire surface with figures was not due to the influence of his mentor. He had a predisposition to the discovery and application of the priciples of tessellation, as it can be seen from early works (while he was studying under de Merquita in Haarlem). Here is one of his first attempts:įig 1: First attempt at regular division of a plane, with imaginary animals (1926 or 1927) He himself was saying that: 'it is the richest source of inspiration that I have ever tapped, and it has by no means dried up yet'. No other theme has been as popular in Escher's work as the periodic drawing division, which is related to the mathematical concept of tesselation of the plane. Escher's Tessellations of the plane, Section 8

Reflection tessellation