The Processes of Creating Representational Tessellations

1.Background� 2.Abilities �3.Motif Choice� 4.Aesthetic & Non-Aesthetic 5.Typical Representation �6.Contrasts & Colouration� 7.Speciality Tessellations� 8.Media

Part 2

Design Process

(both under construction, to be illustrated)

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So, upon having outlined the background to ones interest in tessellation, a relevant question to ask is what sort of abilities are thus in order to produce representational tessellations. Now, it may very well be thought that people from any of the above scientific backgrounds would be at a great advantage as when compared with the artistically inclined, as they would be inherently aware of the rules underlying tessellation. However, despite many eminent professors having taken an interest, none can be seen to have produced anything that can be said to even approach Escher's in quality, or furthermore of noticeably inferior examples. Indeed, all the quality examples of tessellation since the time of Escher have been composed by the artistically inclined, and not consequently from the much more likely scientific field. Now, why should this be so? What, in essence, makes somebody a representational tessellator? As such, I believe the foremost requirement is to be one of which I describe as shape recognition. More precisely, this refers to the ability to �see' or recognise some sort of creature or inanimate object in an arbitrary shape. As such, this is can be found at the most basic levels of children's games, such as looking at clouds in the sky and then by using ones imagination trying to �see' such things. A similar occurrence is looking at the moon and then trying to �see' motifs, most noticeably illustrated by the familiar �man in the moon.' Furthermore, Escher also played likewise games, adding various motifs to paint on the wall in his bathroom to amuse his children, as recalled by his son George in M.C. Escher: Art and Science . Indeed, despite being such a simple pastime, with the thought in mind that such matters are too frivolous or childish for the scientifically inclined, such pastimes even occupied Leonardo da Vinci, who amused himself in this way. (A quotation on this matter by da Vinci is in the book Escher The Complete Graphic Work, page 160.) However, as the above �shape recognition' games have referred to shapes that are not in any way per se to do with tessellation, one may thus feel justified in asking as to how all this pertains to tessellation matters. Well, quite simply, such ability in �shape recognising' can in effect be �transferred' to tessellation, as when faced with an given, arbitrary tessellation such ability can thus be duly applied. However, such ability seems to be lacking in most people, or perhaps is lying dormant, awaiting a prompt. As to my own abilities in this matter, I do indeed distinctly recall that at a young age, approximately 10-15 years of age (unfortunately, I cannot be precise), I was indeed aware of such an ability. However, this was of an isolated example, of which that until becoming interested in tessellation I had no use for. Specifically upon observing a map of the British Isles, I thus recognised such a shape. Can you use your imagination here and see a bird, fish�? As such, once pointed out it appears so obvious, and is noticeable at each view of the map (answer given below). Indeed, as the map occurs every day with the weather reports, millions of people have had the opportunity to see this, but have not apparently recognised the shape I have noticed.

Of interest is just how soon should one expect life-like tessellations of an at least �reasonable' standard to be produced. Upon examining Escher's tessellations and background to this matter, a �probationary period' of May�June 1936 can be discerned, whereby a relatively intense period of study was undertaken. Essentially, this involved copying patterns from the Alhambra and the mezquita in Cordoba (from recent visits to these places). Upon returning home and showing these to his brother Beer, who recognised their connection to crystallography, and this was then followed by an active search of crystallographic journals by Beer in seeking out existing tessellations, of which most notably an article by P�lya was influential, with a direct study of the diagrams by Escher himself being undertaken. From this, his first �proper' tessellations then emerged (negating a brief period of study which produced a mere handful of tessellations of 1922 and 1926 or 1927, the latter essentially �abandoned' and subsequently numbered 1 and 2) quickly followed, resulting in a whole host of tessellations in the style of which he has become renowned. Indeed, these �early years' resulted in a veritable outpouring of periodic drawings, of which with subsequent years, for a variety of reasons, he was never able to match in such quantities. Essentially, it can be said that he developed the �knack' of life-like tessellation very quickly, and indeed high-quality examples emerged remarkably quickly, such as with periodic drawings No.18 and 20 (which later were utilised for his renowned prints Day and Night and Sky and Water I). Therefore Escher's �probationary period' can be seen to be most short, a matter of a mere seven months. Such a �pause' and subsequent study echoes my own studies, whereby in 1986 I merely �dabbled,' lacking any real mathematical understanding worthy of the name, before in July 1987 I made a more concerted effort. However, it was not until February 1988 that anything of true, original tessellations emerged, albeit still mostly rudimentary, although �promising' in their nature. Indeed, one of my favourite motifs, of Girl 1, No.1 dates from this period. Likewise as with Escher, this marked a watershed, with my own �outpouring' of tessellations quickly following, albeit still not in a generally finished state as with his numbered drawings.

Therefore, from all this, it can be seen that essentially one either intuitively understands tessellations or not at a relatively early stage in ones �tessellation career.' Essentially, if the early efforts are �encouraging' this thus naturally results in further study, whereas if no improvements are initially forthcoming (as Escher found in 1922), ones enthusiasm is naturally lessened, with the likelihood of pursuing such matters, at best, being put aside, or more probably abandoned in favour of other pursuits. However, pleasingly, age is not an apparent factor per se, as Escher himself began his own studies at the relatively late age of 38.

Furthermore, upon establishing tessellation of a reasonable standard, it can be seen that progression as to inherent quality does not continue with the passing of the years, as may have been thought, but essentially remains static. Certainly, �refinements' do indeed take place, but there is no arrow-like continuum. For instance, utilising Escher's examples, a periodic drawing from the 1930s could quite easily be mistaken for one of the 1960s. As such, this is not due to a lack of ability, but is rather a consequence of the specialised nature of representational tessellations in which the underlying symmetry �forces' outlines that at times leaves a lot to be desired as regards representation. Therefore, this simply has to be accepted as a matter of course, albeit this should not be used as an excuse for slip-shod work that is quite plainly of an unacceptable standard.

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