The Processes of Creating Representational Tessellations

Part 2

Design Process

(both under construction, to be illustrated)

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1. Background

Although not central to the creation process, of interest is to how one arrives at the subject of tessellation. Now, as can be seen by the practitioners of the art, it is noticeable that a wide diversity of subjects can lead to an interest in tessellation, of which the following thus discusses:

Personal

As such, my own first �proper' introduction to tessellation (neglecting my schooldays mathematics lessons on the subject, which, although I can distinctly recall, I did not proceed further with) was through just browsing at random (in approximately 1983) a Readers Digest magazine, of March 1981. This contained a brief article on Escher titled �The Artist Who Aims to Tease' by Greg Keeton, pages 37-41, the article containing some prints of Escher's, most notably Day and Night, from which I then wondered how he did this. However, due to not understanding how to go about such matters, this thus remained at an interest level only, and essentially put aside. Not until much later did not turn my attention to tessellations in a practical sense, in 1987. Before this, I had an interest in art, of a mostly surreal nature, favouring the work of Salvador Dali (whom Escher also greatly admired), and laterally of op art. Consequently, I then gradually drifted into the world of mathematics, before finally beginning my tessellation studies, albeit still somewhat of a fragmentary nature, in 1987.

Art

Without doubt, an interest in art is highly desirable. However, this is not to say that anybody with an interest in the subject will be capable of producing worthwhile efforts in this field. As such, despite there being many artists the world over, the number of artistically inclined people interested in the subject is relatively small, and as a consequence of having such a very narrow interest base, the associated numbers producing tessellations thus results in a mere handful of so inclined people. However, in general terms, most people who do indeed arrive at tessellations via this way, despite an essentially non-mathematical background, perhaps somewhat surprisingly produce the most worthwhile examples. Incidentally, as detailed above, this is the route I took.

Mathematics

Obviously, an interest in mathematics is, again, highly desirable, albeit not necessarily of an advanced or indeed of even a basic nature. Escher admirably illustrates evidence of this, as he himself essentially picked up the rudiments required, despite his many protestations as to his lack of ability in this field, having not undertaken any mathematical studies since his schooldays. Not until considerably later, at the relatively late age of 38 did he essentially begin his interest in tessellations (neglecting some minor studies of 1922 and 1926 or 1927). However, despite tessellations being primarily in the domain of mathematics, so few mathematicians seem to be capable of producing any worthwhile representational examples. Indeed, a typical example of the shortcomings of mathematicians in this field, arbitrarily chosen, can be seen in Modern Mathematics by Patrick Murphy, pages 194-205. Although he is a splendid mathematician, far superior to myself, he can quite plainly be seen to be lacking in the representational aspect.

Architecture

As such, despite appearing as disparate subjects, another relation to tessellation appears to be architecture. Indeed, Escher was more than interested in the subject, apparently intending to make it his profession, attending the Haarlem School of Architecture and Decorative Arts (1919), although he quickly abandoned architecture aspect in favour of the decorative arts. Although no direct channel to tessellation can be found in architecture, its practise can be said to lead to symmetry aspects, from which tessellation can thus be seen as a near relation. A contemporary practitioner of like manner is Andrew Crompton of Manchester, England who has produced many fine examples, with further details on the links page.

Crystallography

Another avenue to tessellation appears to be crystallography, albeit in this field such an interest lies very much secondary to mathematics and art. However, some eminent crystallographers have been personally associated with Escher, notably Caroline H. MacGillavry, who did much to popularise his works, notably with the book Symmetry Aspects of M.C. Escher's Periodic Drawings. Interestingly, his half-brother B. G. Escher also took an interest in this in conjunction with his post as Professor of Geology, in which he taught crystallography (and also played a pivotal role in Escher's progress, introducing him to crystallographic journals containing tessellating diagrams). However, despite having the above advantages in both theoretical knowledge and indeed in personal contact, of which needless to say must be greatly advantageous, no representational tessellations of any kind or worth has emanated from the above people, or from their successors as far as I know.

Psychology

Despite not possessing an obvious connection to tessellation, aspects of psychology do indeed have a bearing on the subject, of which this interacts with tessellation in a mostly subsidiary way, notably with the aspect of figure and ground, essentially to be considered as an optional �extra' upon the completion of a tessellation. Various articles of these matters were apparently studied by Escher, latterly of which an article in Scientific American of July 1974 by Marianne L. Teuber sets out the various sources that were essentially available to Escher, albeit much of what Teuber relates was subsequently rebutted by his son, George, in a following letter to the journal.

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