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The Science of Escher
Though M.C. Escher contended that he knew virtually nothing about mathematics, even having gone as far as to declare that he was ďabsolutely innocent of training or knowledge in the exact sciences,Ē (Schattschneider 67), his art work commonly incorporates the use of many recognized elements of science and mathematics. It has been argued that Escherís natural accessibility and his popularity with young art patrons is due to the Escherís use of symmetry, his use of metamorphosis, and his focus on representational elements of science in his work (Donato 31).
Though Escher appeared unwilling to address it during his lifetime, it was evident that his work was supported by elements of science, including the use of mathematic formulations and specific geometrical patterns. If he did not study science, he at least studied visual constructions, and determined his artistic perspective after evaluating the distinct nature and geometry and color configurations of ancient arts. The link between Escherís creations and tile patterns of the Alhambra in Grenada as well Islamic art demonstrates the imbedded nature of his developments and the focus on science and math (Schattschneider 67; Watson-Newlin 43).
II. Escherís Perspective
Even as a child, art historians suggest that M.C. Escher had a visual focus that directed him towards the study of patterns and symmetry (Schattschneider 67). In his younger years, Escher had an affinity for creating patterned drawings that led him to the study of patterns in the tiles of the Alhambra in Grenada, as well as to study the geometric drawings in mathematical papers and in the need, to pursue his own perspective and unique ideas for the tiling of a plane (Schattschneider 67).
It was Escherís focus on the coloring in his drawings of interlocked tiles that later interested mathematicians and crystallographers when evaluating his color symmetry (Schattschneider 67). As a result of his focus on these elements, Escherís work has actually been utilized since the late 1950s to illustrate some of these mathematical and scientific concepts (Schattschneider 67). In 1954, at the International Congress of Mathematicians in Amsterdam, Escherís works were prominently displayed as representations of particular mathematical concepts, and the publication of his first book The Graphic Work of M.C. Escher in 1959 marked his further insurgence into the world of math and science (Schattschneider 67).
Though Escher contended that his focus on these elements came not from a knowledge of science, but from a keen understanding of the geometric laws demonstrated in nature, the preciseness of his work and the way that many pieces express specific scientific premises has been a major element of evaluation and speculation in terms of Escherís work (Schattschneider 67). Escher was fascinated by what he considered to be the ďregular division of the planeĒ which provided the scientific basis for his conceptualization of symmetry in art (Schattschneider 68). During his lifetime, Escher created over 150 color drawings that demonstrated hi scarcity to draw nature, especially animal forms, into symmetrical and non-representational works of art. His drawing Triangle System 1B3, Type 2 (1948), for example, is a colorful and systematrical drawing of butterflies that links the abstract and nature inextricably through Escherís perspectives on the symmetry in nature (Schattschneider 68). His artistic creations often provide a sense of dichotomy or paradox both in nature and in the world of man (Duran 239). The resulting art works demonstrated the link between the progression of his design of symmetry and his representational process. Some have argued that the direct nature of Escherís designs are linked to the way Escher perceived nature, more than as demonstrations of a knowledge of math or science.
III. The Use of Symmetry
Symmetry is the structural concept that shapes many mathematical and scientific processes (Schattschneider 68). Though Escher liked to make his drawings appear to have a random construction, a closer look at the particulars of his design orientation demonstrate a clear sense of symmetry (Schattschneider 68). In the example of Triangle System 1B3, Type 2 (1948), Escherís butterfly design is based on six alternating colored butterflies that move around the flow of the drawing in a circle. Though the symmetry is not immediately perceivable, it is directed through circular symmetry, and provides a unique visual perspective and continuity in the drawing.
Escher is also famous for using symmetry as a means of demonstrating the infinite, and his drawing Circle Limit IV (1960) uses negative space and the picture of a gargoyle incorporated into circular symmetry in such a away that it appears that the circular construction continues with out end (Schattschneider 68). Escher also considered this element of negative space as a representation of duality, which corresponds with the mathematical concept of negation, that each statement has a counterpart or negative correlate (Schattschneider 68). In math and in the drawings of Escher, this concept of duality suggests that each element has a complement, and that the link between both provides a complete definition (Schattschneider 68).
This concept of duality is also the fundamental element in what has been described as Escherís technique of tessellation, which features patterns that have equivalent weight given to both the positive and the negative images (Walczak 29). Tessellations have been defined as ďrepetitive designs in which positive and negative shapes are of equal importance and consume the entire surfaceĒ (Walczak 29).
As an extension of his perspective on symmetry, Escher also pursued the use of self-similarity, based on the mathematical concept of the recursive algorithm (Schattschneider 68). Escherís illustration entitled Square Limit (1964) is constructed using a recursive scheme, or a set of directions that is applied to each new object on and on so that the representations and the transformations appear without end (Schattschneider 68). The final product is a picture that is self-similar, but that has a clearly differentiated final objects when compared to the first image transformed (Schattschneider 68).
Escher addressed many other scientific principles in the design of his work, including dimension, relativity, reflection, and infinity, and underscored the way in which art can demonstrated more complex scientific principles (Schattschneider 69). But it was also Escherís contention that this was not his intent, and instead, that this link was simply the culmination of his individualized perspectives on the particulars of nature and focused on the way that other cultures recognized these same scientific and mathematical elelemts within their artistry.
IV. The Geometric Shapes, Escherís Perspective and Islamic Art
The geometry of nature and of art were primary concerns for Escher, who demonstrated these elements through the use of metamorphosis, geometric progression and visual plane distortion techniques to demonstrate these elements (Doornek
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