Areas

Area 6. Geometrisation of the Plane

On his first visit to the Alhambra in 1922, Escher took an interest in the Islamic decoration of the Nasrid Palaces and their division into basic geometric figures. The reproduction of these infinite figures which Escher encountered in the tiling and plasterwork exerted a decisive influence on his subsequent works. In his travel journals, he compiled various minutely detailed sketches and drawings of the tiling and mosaic decorations, endeavouring to decipher the rules of their composition. He was particularly struck by the manner in which the geometric figures on the plane were repeated without leaving gaps between them. From this and his subsequent visit to the Alhambra in 1936 stemmed his interest in what he would call the division of the plane into regular figures and the use of patterns to fill the space leaving no interstices.

Following his journey to Spain, the division into congruent figures that he himself acknowledged as one of the main thrusts of his oeuvre became one of his most utilised instruments with which he would achieve astonishing compositions. The works concerning the geometrisation of the plane constitute painstaking works only possible after years of meticulous experimentation. As he himself would say “the only reason for their existence is one’s enjoyment of this difficult game”.

The series Regular Division of the Plane (1957) and Plane Filling I (1951) and Plane Filling II (1957), which we can see in this section, reveal the difficult balance between the motifs in the compositions. Though the works appear to be very simple at first sight on account of the use of basic figures such as horse riders, horses, birds, fish and insects, the final product is complex, since the representation of the figures is based on the dynamic interplay between black and white. To unravel the repeated pattern, the viewer must focus on a figure within the composition.

Escher’s work plays continuously with the ambiguity, dissociation, metamorphosis, recomposition, invention and transgression of the figures in the plane, which he would later bring to the space.

TILLINGS AND THE FRACTAL THEORY

Escher took the world of tessellation to an art. Tessellation or the division of the plane in identical shapes consists of filling the plane with forms that can be regular or irregular with no overlaps or gaps. From movements on the plane, Escher was able to achieve various designs on this long journey of multiplying forms.

The mathematician H.S.M. Coxeter, a friend of his, suggested that he develop new patterns to cover a surface starting from regular geometric structures. He also created various designs over circular limits according to the model devised by the mathematician H. Poincaré, which allowed him to represent an endless surface in a restricted circle. This method of work was very demanding and Escher had to dedicate an enormous amount of time and create many preliminary sketches for each one of his works.

Works

  • Development I
    Development I
  • Sky and Water
    Sky and Water
  • Sun and Moon
    Sun and Moon
  • Horses and birds
    Horses and birds
  • Fish and frogs
    Fish and frogs
  • Plane filling I
    Plane filling I
  • Plane-filling motif with fish and bird
    Plane-filling motif with fish and bird
  • Two intersecting planes
    Two intersecting planes
  • Fire, New year’s greeting card 1955.
    Fire, New year’s greeting card 1955.
  • Water, New year’s greeting card 1956
    Water, New year’s greeting card 1956
  • Earth, New year’s greeting card 1953
    Earth, New year’s greeting card 1953
  • Air, New year’s greeting card 1954
    Air, New year’s greeting card 1954
  • Liberation
    Liberation
  • Regular division of the plane I
    Regular division of the plane I
  • Regular division of the plane II
    Regular division of the plane II
  • Regular division of the plane III
    Regular division of the plane III
  • Regular division of the plane IV
    Regular division of the plane IV
  • Regular division of the plane V
    Regular division of the plane V
  • Regular division of the plane VI
    Regular division of the plane VI
  • Plane filling II
    Plane filling II