ESSAY 3
MOTIF CHOICE
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Concerning the motif, as there is a wide diversity of animal life, with many species, it may be thought that any motif would be as suitable for tessellation purposes than with any other. However, in practise this will be found to be not so, with birds and fish prevalent, not only in Escher's work but with his successors as well. (A noticeable assistance in comparing the frequency of specific motifs is being provided by Patrick Snels, who is currently compiling a database (albeit this is still under construction), of examples from people who are composing representational tessellations of a more or less worthwhile standard.) Now, an obvious query to ask is why that these two specific motifs should be so admirably suited, as a priori there is nothing unique about their respective outlines � why should not other motifs, say human-like figures or dogs, to give two disparate examples, all consisting of the �same' essentially curved lines not be equally so suitable? As such, this has a lot to do with what I term as �ambiguity of outline' in which for an arbitrarily given outline birds and fish are to be found the most suitable. The following thus sets out to answer this question in relative detail by discussing various aspects pertaining to this matter with a variety of motifs in turn.
Of interest would be Escher's views on the subject, of which he said unfortunately (all too) little, contenting himself with the brief passage in Regelmatige vlakverderling, stating that:
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My experience has taught me that the silhouettes of birds and fishes are the most gratifying shapes of all for use in the game of dividing the plane. The silhouette of a flying bird has just the necessary angularity, while the bulges and indentations in the outline are neither too pronounced nor too subtle. In addition, it has a characteristic shape, from above and below, from the front and side. A fish is almost equally suitable; its silhouette can be used when viewed from any direction but the front.
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However, although somewhat brief, this at least contains the basics, but from the viewing and examination of his works, the same conclusion could equally well be reached. What is required is a more exact discussion, with the merits of each creature discussed separately (as below), along with as to why each �element' (e.g. birds, with beak, wings, body and tail) is so suitable.
Of assistance in drawing motifs is having to hand suitable �field guide' books, from which the different �elements' of the creatures can readily be compared.
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1.1 Birds
Ambiguity of Outline
Simply stated, the above motif, in contrast to any other type of creature (exempting fish), can be seen to have a certain inherent amount of what I term as ambiguity of outline, of which such an aspect is of fundamental importance. By �ambiguity', this term is thus applied to the various �parts' or �elements' that go into the making of an arbitrary bird, of which I detail below. For instance, a bird may possess a short, medium or long wingspan, and yet is still instantly recognisable. A likewise argument can also be put forward for other regions of a bird. For example, the tail region, with different types and also similarly with the length of the body � with noticeable differences between, say, disparate birds such as a sparrow and albatross, all of which any �field guide' book will confirm. As a result, seemingly whatever combination is utilised, the outline remains bird-like. From this, there is thus literally an abundance of such �ambiguities of outline', with which, in comparison with any other type of creature, disregarding fish, any other motifs simply do not possess. Therefore, when applied to tessellation, such �ambiguity of outline' simply gives more opportunities for this particular motif.
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Elements
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Beak
A most convenient feature of birds for tessellation purposes is that the beak can be so varied, in length, width and shape, as illustrated below. In essence, any protuberance (within reason) can be regarded as a valid, life-like beak, and so consequently the task of �adapting' to a tessellation is greatly facilitated. Consequently, there occurs considerable 'ambiguity of outline'.
Another feature of the beak is that although it is most frequently shown closed, a different portrayal is also possible, in which it is shown in an open or gaping position. Consequently, this can be taken advantage of as the situation demands (which is somewhat of a rarity). Escher utilised this feature on only a one occasion, with drawing 76a, whereby the open beak defines the horses' ear as well.
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Wings
Again, as wings can be depicted in a multitude of poses, I here concern myself with generalities rather than attempting to cover an impractical 'every concievable possibility'. Tremendous variety of the wing is to the fore, not only concerning the shape but the length as well, as illustrated below. For example, due to differing needs, evolution has provided birds varied types, such as long and pointed, rounded and 'swept back' wings. Consequently, there is thus plenty of scope for ambiguity of outline.
As always, reality should always be striven for, and generally the wings are shown simplified without individual feathers. As such, there is nothing wrong with this, and indeed, of necessity it is frequently the only practical solution. However, on occasions it is indeed possible to show the wings in detail, echoing a real-life birds. Specifically, this refers to showing the individual serrations of the wings (and/or tail) when the circumstances are appropriate, as below. Escher utilised this device on two of his bird drawings, Nos, 87 and 92, although portrayed somewhat crudely.
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Legs
A typical feature of the bird examples is that the legs are omitted, essentially of necessity, as due to their spindly nature such lines are impractical to incorporate in a tessellation. Essentially, the legs are �unimportant', as the greater proportion of the bird is made up of the body and wings. Furthermore, in flight the legs are tucked into the body, of which they are even less distinguishable. Indeed, the �omission' of the leg is not necessarily a matter of expediency, as in flight, as seen from above; the legs are hidden from view by being held along the body. Of Escher's 15 bird examples (not including those with other motifs in addition), only two (Nos.17 and 19) can be seen to have legs, these occurring not as a by-product but as a necessity of their respective tessellations.
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Tail
As with the wings, variety is noticeable. Here different lengths, along with different shapes all combine to offer variety. For example, tails can be long and narrow (kestrel), short (golden plover), rounded (tawny owl), forked (swift) or fan shaped (great tit), and yet all remain inherently bird-like. Again, such vagaries thus offers the possibility of the desired �ambiguity of outline'. However, as the tail is generally of a smaller size than of the wings, this will be found not to be quite so important as with the wings.
As with the wings, on occasions more detail can be shown, in the form of individual serrations of the feathers, as discussed above.
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As the birds elements thus has considerable ambiguity of outline, it is thus possible to assemble these onto a arbitrary body.
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Summary
Consequently, this particular motif thus has an abundance of ambiguity of outline (in contrast to say, a human figure, where for instance any significant departure from correct proportions would result in a ridiculous appearance).
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Distinct Views
A further aspect to this choice of motif is that it permits the drawing of two distinct views, applicable when the motif has its wings outstretched, with the bird taking the form of an approximate cross, and indeed this can be most rudimentary. From this, a �under' and �over' viewpoint is thus possible, as shown in diagrammatic form below. As a consequence, this aspect thus adds to the possibilities for any given bird tessellation that possesses such a cross-like outline, as the tessellation can now be any or all of three types, namely of �under', �over' or �under and over' in combination.
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3.2 Fish
Ambiguity of Outline
Fish are motifs that are ideal for tessellation purposes, and indeed arguably of the simplest of all to achieve. This is due to their ambiguity of outline, in which a fishes body has consideration variation, along with fins and tails. Quite simply, a fishes body can be either long/narrow/squat and yet still remain true to life. In addition, the fins differ in their shape and number, with two, three of four all being common. Furthermore, the tail can be just about any shape or length within reason, and yet again still remain true to life, all of which any �field guide' book will show. Therefore (as with birds), seemingly whatever combination of the above elements is utilised, they all remain fish-like, with the result that there are thus simply more opportunities of �ambiguity of outline' and hence more tessellation examples. Indeed, it is arguable that fish motifs are the most ambiguous of all, and as such, it is simply a �quirk of fate' that more are not shown on the fish page category.
Escher shows numerous examples of fish, some noticeably stylised as seen in a unnatural position, as from above rather than the more naturally recognisably sideways view. Such examples are relatively easy to compose, and are not particularly praiseworthy. Ideally, examples of this type should be avoided in favour of the'classic' viewpoint.
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Elements
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Body
Perhaps of most significance is the shape of the fish's body. Quite simply, there seems to be no �typical' body � any shape is possible. Consequently, such variety thus leads to considerable opportunity for such motifs.
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Fins
Again, ambiguity abounds � just about any shape is acceptable.
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Tail
Although the tail is somewhat more defined as according to a usual outline, considerable variety still exists.
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Mouth
Although of an essentially unimportant nature, on occasions the mouth can utilised, specifically when in a gaping position. Essentially, when so open, the mouth can define another outline, of which Escher shows this with drawings 29, 72-73, 84 and 120.
However, although it is possible to compose a most unlikely fish using these elements, none the less the ideal remains to be that the fish should be �typical', and not too outlandish.
3.3 Human Figures
Ambiguity of Outline
Motifs consisting of human-like figures are noticeably less frequent than with the more commonly found birds and fish, which thus retorts the question as to why, as all three are possessed of essentially curved lines, and thereby it may be thought that there is no intrinsic difference between them. However, as can be seen by observation, there is a distinct lack of such tessellation motifs, of which the reason pertains to the previously discussed ambiguity factor. Now, in this particular aspect the outline of a human figure is to be found decidedly limited. For example, any slight deviation from the correct proportion of the body, with say the arms being noticeably longer in proportion to the body, thus results in a ridiculous outcome, of what is self-evidently anatomically incorrect. Such an analogy is also applicable to any other body part. In short, correct proportion is a necessity. In contrast, as the previously discussed birds and fish have an abundance of ambiguity, all whilst remaining in proportion, hence their more frequent occurrences. Therefore, due to the above practical difficulties, the drawing of human-like motifs (if of a decent enough quality) is cause for praise, as it is a strict test of ones tessellation capabilities to compose such figures. Indeed, it is noticeable just how few such quality human figure motifs are to be found. As such, I frequently see so-called human figure examples of gross distortions and strange protuberances that should be best kept unseen and not displayed in all their supposed glory. As such, the �quality question' arises, and on many occasions this aspect is neglected in the attempt for an obviously desirable choice of motif.
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As an indication as to how difficult it is to compose such motifs, even Escher himself only composed four clearly �unambiguous' figures (periodic drawings Nos.3, 4, 5 and 21). Furthermore, these are to a certain extent examples of the above discussed �compromises', as the figures are in various ways out of proportion but not to a gross intent that would render them as unacceptable.
On occasions, it is possible to introduce �fantasy people', with such examples being angels and devils, and as these only exist in the imagination, there is thus plenty of scope (ambiguity) in this aspect. A frequent device with these is to equip the figure with wings, of which any wing-like outline will be acceptable within reason, as this is a non-critical aspect per se. Therefore, such examples have further �ambiguity of outline' and so are thus relatively easy to undertake in the context of human figures.
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An aspect of composing human figures that is noticeably different from all other life-like motifs is that the human figure is shown clothed, and not in its natural state as with other motifs.. By such additions, this thus adds to the ambiguity factor, of which such matters are a decided assistance in what is a most difficult motif to achieve.
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Now, as human figures are somewhat �complex' for tessellation purposes the following breaks down the various aspects that pertain to the above difficulties of this motif.
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(i) Clothing
The clothing of the figure obviously opens up considerable �ambiguity of outlines,' with various styles and fashions possible, of which such choice is obviously fertile ground for tessellation purposes. Furthermore, as males and females wear different types of clothes, some gender differences occur. Generalising and simplifying, the male wears suits and the female dresses, of which there is an obvious difference in outline between the two garments. In short, the female apparel, with a shorter or longer hemline, along with different possible fashion possibilities, thereby has more variation or ambiguity of outline, whilst in contrast, the males clothing, with the angular lines of his suit and trousers, is therefore less variable, and so possesses fewer such possibilities of ambiguity. However, where specifically a geometric tessellation is considered, the angular lines are indeed more suitable to the male figure, because of the wearing of the suit and trousers, which can thus be depicted as essentially straight lines. Therefore, although there are various nuances on this matter, the fact remains that as a general principle, a female motif is easier in theory to compose than a male.
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(ii) Head
A somewhat minor aspect that specifically pertains to the head of figures that possess mirror reflection symmetry is that it will be found possible to include minor variations, if so desired, by the process of what I term as �symmetry breaking.' Now, with an arbitrary mirror symmetrical outline, it is natural to draw the head as seen �full-on,' thereby preserving the overall symmetry. As such, this is all well and good and perfectly valid. However, such a �view' should not in anyway be regarded as �cast in stone,' as the head per se is not part of the outline, which is instead formed by the hair. Therefore, this thus opens up the possibility of variations, as the head can thus be drawn in different views, as turned slightly to the left and/or right. An actual example of this can be seen on the angel of Human Figure No. 4. Because of this, there is now three possible heads, of which I describe as �full-on', �left' and �right,' and thereby if utilised in combination an appropriate tessellation consisting of motifs in three orientations should thus be chosen. Of my own examples, the most appropriate for this would be No.1, as it possesses all the necessary attributes, albeit not shown in this way.
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(iii) Hair
Of considerable assistance n the composing of figures will be found is in the hair, despite this not perhaps being what is a �fundamental aspect' of the human body, as with, say, arms. Quite simply this aspect has considerable �ambiguity of outline' with different hairstyles, along with short or long, flowing hair, of which the latter can frequently be employed to advantage. This is due to the long hair, which in outline is obviously non-critical, as it is not of any great importance per se as to its waves or curls. An example of my own that illustrates this principle is shown with Human Figure No.1, where the hair is adjacent to the leg of a neighbouring figure. This being so, it is obviously of more importance that the leg is anatomically correct than the hair, and so the hair can thus be of the above ambiguity aspect.
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Furthermore, as alluded to in the introduction, as the female generally has a longer, more flowing hairstyle (in contrast to the shorter hair of the male) and so this thus makes a female motif more likely than not.
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(iv) Hats
When designing the motif, a very common occurrence to be found is that frequently the motifs will be seen to be wearing a hat, of various proportions and styles. As such, this is not due to a fixation in dressing the figure with this apparel, but is instead to do with obtaining a better resembling figure. Typically, but not necessarily, the head will terminate at a vertex, resulting in the figure being distorted, and so, consequently, the �addition' of a hat is thus utilised to alleviate what would otherwise be an inferior figure. Consequently, this arises to suit the tessellation, and the inclusion is not of any importance per se beyond this. Quite simply, this refers to the previously discussed �ambiguity of outline', as by their very nature this can vary, as a specific outline is in general not a necessity for a hat (unless called for) and thereby thus offering up more possibilities of composing a more realistic figure than otherwise.
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Of Escher's four examples, Nos.3, 4 and 21 terminate at a vertex, with Nos. 4 and 21 possessing such hats, of which, although a very small sample to survey, gives some indication of their necessity of inclusion. No. 3 has the hairstyle �adapted' at the vertex. Indeed, such �hat wearing' is a device I frequently use myself, as seen on the appropriate page.
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Arms
As arms are of a spindly nature, such aspects are most trying in attempts at adapting for tessellation purposes. (Such difficulties of a spindly nature, of a different type of motif, birds legs are discussed above.) Although different poses can be utilised, such as these being shown outstretched or bent at the elbow, in general terms these will be found to be somewhat contrived. Consequently, the difficulties in portraying arms are circumnavigated by the possibility offered up by clothing, in which the difficulties of this aspect can effectively be disguised, with the only the hand showing.
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Legs
As regards legs, these have much in common with arms (along with the same problems), both being of an essentially spindly nature, albeit the leg is slightly more substantial in mass. However, it remains essentially spindly, and so difficult to incorporate in a representational tessellation. Again, as with arms, the legs can be shown bent, but will likewise generally appear to be contrived. Essentially, the same way of circumnavigating the problem as with the arms can be employed, this time �obscuring' the legs either partially with a dress/skirt or completely, with trousers.
�Two for One'
Another aspect pertaining to the human figure is that an additional feature is sometimes possible, essentially of an optional nature, is of what I term as a �two for the price of one' type principle. Quite simply, the most common view of humans is when seen �full on' as in face to face. However, another view, equally valid, although less so in an aesthetic sense, is the back view. Now, as the outline of a human figure is appropriate to both views, such a possibility arises of combining these in a single tessellation, hence �two for the price of one'. Of course, in accommodating both of these, the symmetry of the tessellation must of necessity be taken into account. For example, a tessellation where the motifs all side by side or are in two orientations would be ideal. Less so would be an example whereby the motif appears in three orientations, as it is obviously inappropriate for this particular instance. A typical example of the latter can be seen on human figure No.1.
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However, despite the most thorough attempts in composing such motifs that are essentially in proportion, of necessity �compromises' of outline are still generally in order. Therefore, such �disproportionate aspects' essentially have to be accepted with equanimity, as it remains most difficult (if not impossible) to compose a human figure having absolute correct proportions, and so consequently, some marginally, but not grossly inferior examples are thus �permissible' as a matter of course.
3.4 Dogs
Dogs are another tessellation motif that in comparison to the previously discussed birds and fish are of appreciably fewer in number, and indeed, they pale into insignificance when so compared. Again, the obvious question to pose is why that this should be so, as arguably with the previously discussed �ambiguity of outline', there at first consideration seems to be potential in this aspect, with different breeds possess widely different outlines. For example disparate, arbitrary dogs such as corgis, bulldogs, greyhounds with different body sizes, legs, tails all thus appearing to have to have possibilities. However, as examples of this motif are conspicuous by their absence, with even Escher only showing two such examples, namely No.16 and 97, such matters thereby require investigation.
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Now, perhaps the most noticeable difference between the �more frequent' birds and fish and �less frequent' dogs is that the latter has legs, of which as previously discussed, being of a spindly nature make for a most trying set of circumstance for composing representational tessellations of this or indeed any motif. Indeed, as the leg is fundamental to this creature (this being in contrast to the birds leg, which is inconsequential), the animal can hardly be portrayed without it, as they make up a considerable proportion of the animal. By their very nature, legs are long and angular, of which such an aspect has essentially no �ambiguity of outline' � in effect, the legs must be drawn as anatomically correct, with no leeway, as otherwise the motif will appear ridiculous. Such matters are thus difficult to incorporate into a tessellation. Although it is possible to circumnavigate this difficulty by showing a dog in different poses aside from the �classic' sideways portrayal, such as lying down or curled up, such positions generally make for a contrived representational tessellation. Therefore, because of this, the number of dog motifs that attain the required standard as regards quality is thus very small indeed. Far too often dogs can be seen that fail the quality test and so consequently are of an unworthy nature for showing, and yet they still appear, unfortunately.
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Note that although the above text pertains to a dog in its own right, the material can also largely be applied to any other arbitrary quadruped, such as cats or tigers or indeed any other animal having a similar four-legged outline, as essentially the same explanations are applicable, and therefore such specific text would largely be redundant.
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Lizards
Another relative common creature to be found is a lizard, with Escher showing many examples. As such this is a type of creature that is best portrayed and recognised as when seen from above, rather than in a sideways position, such as with dogs.
Dinosaurs
A relatively easy type of creature to compose is that of dinosaurs. The most notable aspect that makes dinosaurs ideal is that running along their backs are a series of plates (the purposes of which are disputed, for protection or heat loss) that are ideal for purposes of ambiguity of outline. A view on any book on dinosaurs will show considerable variation, all of which is fertile ground for tessellation purposes. Essentially, as the plates are a non-fundamental aspect in terms of their portrayal, in contrast to, say, the head, this thus allows what is bordering them to be shown more anatomically correctly, as shown below. Furthermore, anatomically there is great inherent variety of the creature, for example long/short necks, tails, legs, tusks, all of which can combine to offer ambiguity of outline.
3.5 Imaginary Creatures
This category refers to motifs that although consisting of animal-like elements do not in fact represent a defined creature (such as with a bird of fish), but are instead are designated as �imaginary', in that one's imagination is left with free reign to compose speculative examples. A typical occurrence of this is to utilise elements from disparate, unrelated animals, and essentially combine these for a unique creature, say, a dogs head on a lions body. A further possibility is to give the creature wings. Another example would be of creatures taken direct from mythology, such as centaurs. Hence the description of examples of this type as �imaginary'.
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As may be envisaged, examples of this type, possessing no inherent pre-determined proportions, therefore possess considerable �ambiguity of outline' and within reason, there is no restrictions imposed upon the creature's portrayal. Consequently, examples of this type, with inherent ambiguity are thus relatively easy to compose, of which their low assessment rating (of Category*) thus reflects this.
3.6 Unidentifiable Motifs
On occasions, more specifically with representational tessellators of an inherently lower quality, there will be found examples of creatures in the broadest sense of what I term as of a �unidentifiable motif,' whereby although vaguely reminiscent of some sort of motif, this cannot be identified as essentially recognisable, such as with birds, fishes, lizards�. (Note that this does not include the �imaginary' creature category, which is altogether another matter.) As such, these examples are thus be regarded as of the lowest possible quality, and indeed strictly speaking, I consider this type to be unacceptable, essentially unworthy of the dignity of the title �representational tessellation.' Essentially, all the tessellator is doing here is that after composing a non-representational tessellation, this is then supposedly made animate by the addition of an eye(s), along with a few vague, suggestive body markings. Such efforts are obviously inferior to the more life-like examples, and hence essentially unacceptable. As such, examples of this type may be understandable in ones �early' days of attempting representational tessellation (indeed, they are hardly unavoidable as a result of experimentation, and I have many examples myself, but are designated as essentially �not for show').
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Interestingly, Escher's examples from the �early years' do not include any of this type, from which this thus indicates that he was aware of the triviality and ease of such a type from the very beginning, and so he did not concern himself with such �unworthy' examples. Presumably, in his early days, whilst experimenting, he must have composed some examples of this type, but what became of these has not been stated. Curiously, somewhat oddly, in later years he did include some examples of this type, with drawings Nos.36, 103 and 116. (No.36 was undertaken for a specific purpose, of a �missing' symmetry type that Escher desired to include for the sake of completeness).
3.7 Multiple Motifs
Less frequently accomplished is a representational tessellation can be seen to be composed of two (or more) distinct motifs, such as a bird and fish or cat and dog, to give two arbitrary examples. An obvious question to ask is why this should be so. The explanation of such rarity is that in general terms, by introducing additional motifs, by whatever method you so utilise, the number of lines involved of necessity increases, and thereby the difficulties lay. Quite simply, by increasing the number of lines this thus results in additional difficulties, as the outlines has to represent yet another motif, and furthermore ideally all of the same quality as regards the veracity of the motifs. A further obstacle to overcome is that the motifs should ideally be in proportion to each other, as this makes for a sensible and not absurd combination. Utilising Escher's drawings for comparison, drawing 22, of birds and fish is ideal, as both are in proportion. In contrast, drawing 30, of fish and boats is clearly lacking, and thus can be regarded as inferior in comparison. Now, as evidenced by the lack of good-quality tessellations of even one motif, of the simpler, less numerous lines required, the introduction of additional lines, of obvious necessity for multiple motifs, is thus more difficult, albeit by no means impossible, to achieve.
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However, putting the �practical difficulties' aside, bird and fish motifs in unison remains ideal for this, due to their own �ambiguities' as discussed above. Furthermore, in such a combination, if of a sufficient quality (as with drawing 22), the serendipitous contrast of the two motifs, with concepts such as �above and below' or �sky and water' in mind, lend themselves aesthetically to a superb natural composition, of which Escher took full advantage, admirably demonstrated by his print Sky and Water I. Indeed, it really is of purely fortuitous circumstances that the above motifs in combination are to be so appropriate, and lend themselves so readily to such concepts.
3.8 Familiarity of Motif
Another aspect of the motif is one that I shall term as familiarity of motif. This refers to the knowledge of the animal in terms of its portrayal. As such, this can be divided into two distinct types:
�� Animals that are familiar in everyday life, e.g. cats and dogs
�� Animals that are rarely, if ever encountered in normal life, e.g. giraffes and kangaroos
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From the former group, the proportions of the animal come readily to mind, whereas with the latter, although pictures of these will have been seen, the exact proportions of the animal is not fixed in the mind. For example, is the proportion of the giraffe's neck to the length of its body the same, or is it two, three times as long? Likewise with a kangaroo - for example, is its tail length the same as of its body, or is it again, two, three times as long? As such, only an animal enthusiast with knowledge of a wide variety of animals can readily judge the veracity of resemblance of the motif to the actual animal. Therefore, in certain aspects this factor can work to the advantage of the tessellator, as faced with an unfamiliar animal in an tessellation, people will accept this at face value and not go to the trouble of comparing this with an actual picture, whereby its possible shortcomings would then be evident. Therefore, the tessellator thus effectively gains potential credit for a supposed accurate portrayal from the general lack of knowledge of such creatures. However, this of course should not be used as an excuse for possible slipshod work, in effect taking advantage of the general ignorance in such matters. Undoubtedly, the aim remains, as always, in portraying the animal in question as close as is possible to its natural appearance.