## The Graphic Work of M. C. Escher (part 1)

2013/04/13 § Leave a comment

“He who wonders discovers that this is in itself a wonder. By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I had made, I ended up in the domain of mathematics. Although I am absolutely without training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.”

(Maurits Cornelis Escher)

#### SELECTED WORKS

##### The regular division of a plane

Drawings that “show how a surface can be regularly divided into, or filled up with, similar-shaped figures which are contiguous to one another, without leaving any open spaces”:

**The function of figures as a background.** “Our eyes are accustomed to fixing upon a specific object. The moment this happens everything round about becomes reduced to background.”

“In the horizontal central strip there are birds and fish equivalent to each other. We associate flying with sky, and so for each of the black birds the sky in which it is flying is formed by the four white fish which encircle it. Similarly swimming makes us think of water, and therefore the four black birds that surround a fish become the water in which it swims.”

**Infinity of number.** “If all component parts are equal in size, it is impossible to represent more than a fragment of a regular plane-filling. If one wishes to illustrate an infinite number then one must have recourse to a gradual reduction in the size of the figures, until one reaches — at any rate theoretically — the limit of infinite smallness.”

“The area of each of the reptile-shaped elements of this pattern is regularly and continuously halved in the direction of the centre. where theoretically both infinite smallness of size and infinite greatness of number are reached. However, in practice, the wood-engraver soon comes to the end of his ability to carry on. (…) In this particular case. the halving of the figures is carried through ad absurdum. The smallest animal still possessing a head, a tail and four legs is about 2 millimetres in length. From the point of view of composition, this work is only partially satisfactory. In spite of the central limit, it remains only a fragment, because the outer edge of the pattern has been arbitrarily fixed. So a complete composition has not been achieved.”

“A diminution in the size of the figures progressing in the opposite direction, i.e. from within outwards, leads to more satisfying results. The limit is no longer a point, but a line which borders the whole complex and gives it a logical boundary. In this way one creates, as it were, a universe, a geometrical enclosure. If the progressive reduction in size radiates in all directions at an equal rate, then the limit becomes a circle.”

“Here (…) we have the components diminishing in size as they move outwards. The six largest (three white angels and three black devils) are arranged about the centre and radiate from it. The disc is divided into six sections in which, turn and turn about, the angels on a black background and then the devils on a white one, gain the upper hand. In this way, heaven and hell change place six times. In the intermediate, ‘earthly’ stages, they are equivalent.”

**Story pictures.** “The chief characteristics of [these] prints is the transition from flat to spatial and vice versa. We can think in terms of an interplay between the stiff, crystallised two-dimensional figures of a regular pattern and the individual freedom of three-dimensional creatures capable of moving about in space without hindrance. On the one hand, the members of planes of collectivity come to life in space; on the other, the free individuals sink back and lose themselves in the community.”

“At the top right-hand corner a jolly young lad comes popping out of his house. As he rushes downstairs he loses his special quality and takes his place in a pattern of flat, gray, white and black fellow-shapes. Towards the left and upwards these become simplified into lozenges. The dimension of depth is achieved by the combination of three diamonds which give the impression of a cube. The cube is joined on to the house from which the boy emerges. The floor of a terrace is laid with the same familiar pattern of diamond-shaped tiles. The hilly landscape at the top is intended to display the utmost three-dimensional realism, while the periodic pattern at the lower part of the picture shows the greatest possible amount of two-dimensional restriction of freedom.”

##### Inversion

“It was stated in connection with [the last print] that a combination of three diamond-shapes can make a cube. Yet it still remains an open question as to whether we are looking at this cube from within or without. The mental reversal, this inward or outward turning, this inversion of a shape, is the game that is played in the two following prints.”

##### Spatial rings and spirals

“Three unbroken knots are here displayed; that is to say three times over a simple knot has been tied in a cord the ends of which run into each other. The perpendicular cross-section of each knot is different. In the top righthand example the profile is round, as in a sausage; the top left one is cruciform, with two flat bands intersecting each other at right angles; below is a square, hollow pipe with gaps through which the inside can be seen. If we start at any arbitrary point and follow a flat wall with the eye, then it appears that we have to make four rounds before we come back to our point of departure. So the pipe does not consist of four separate strips but of one, which runs through the knot four times.”

“An endless ring-shaped band usually has two distinct surfaces – one inside and one outside. Yet on this strip nine red ants crawl after each other and travel the front side as well as the reverse side. Therefore the strip has only one surface.”

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