Of some considerable importance as regards the assistance in readily identifying motifs (birds, fishes....) concerns what I term as motif representation. Essentially, a motif can be shown in two distinct ways, simply described as typical and atypical, to be striven for and avoided respectively.
• Typical refers to a ‘common' or 'normal' view of the creature, whereby from its outline alone it is instantly recognisable.
• Atypical refers to a 'unusual' view of the motif, whereby from its outline alone it is unrecognisable.
Pleasingly, these criteria can easily be determined with the minimum of effort. All that is required is to take the outline of a single tile and 'colour' it as in a silhouette. From this 'silhouette test', the creature it is representing will either be recognisable (typical) or not (atypical). This test invariably succeeds in determining this matter, albeit very occasionally there can be an exception. This occurs when the motif is seen turned upon itself (such as a fish, where the body and tail are not necessarily shown elongated), from which the silhouette is thus not necessarily as clear as when seen in profile.
The typical aspect feature is highly desirable, as it thus permits identification at a glance, and is invariably the signature of a high-quality tessellation. In contrast, the atypical aspect is essentially a formless shape, the signature of a low-quality tessellation.
Escher briefly alludes to this aspect in Regelmatige vlakverderling, (Escher The Complete Graphic Work, page 164), firstly in a general sense in which he discusses the different types of recognisable objects that are most suitable for motifs, and secondly by specific creatures:
…Secondly, the outline should be as characteristic as possible. It should clearly identify the nature of the object; preferably the silhouette should be so striking that the object can be recognized even without any detail, which always has an disturbing effect on the figure as a unit… and .… The most usual shapes are those of living creatures. However, for animals the question immediately arises, from what angle should they be viewed so that their silhouettes are as characteristic as possible? Quadruped animals are usually most easily recognised when viewed from the side, while reptiles and insects appear most typical from above and the human form is most characteristic from the front.
However, although the above is indeed relevant, and indeed I concur with all its sentiments, these few sentences were as detailed as Escher gave of his thoughts on the matter. Although this may be said to have the benefit of succinctness, in matters of understanding the issue, it is far too cursory, lacking in detail and any illustration. Such matters require a more thorough, in-depth approach as regards the various intricacies than the brief offerings Escher has given us. Therefore, below I discuss this in more detail, firstly in a generalised sense, based upon Escher's statements, repeating relevant Escher quotes above, followed by a more in-depth discussion, liberally accompanied by illustrations, of my own views on the matter. Furthermore, for demonstrative purposes examples are shown, redrawn from other people's tessellations, of motifs that simply are of an inferior standard.
The illustrations below show these aspects in 'two-motif' units, with a line drawing of a actual motif, additionally shown as a silhouette to the immediate right. This is for the purpose of recognising the motifs outline immediately, without any 'distractions' of finer detail. The purpose of this is to see if the motif can be discerned by its silhouette alone.
Escher generalities: …In addition, it [a bird] has a characteristic shape, from above and below, from the front and the side.
Firstly, birds are somewhat unusual in that their typical representation can be shown in a variety of ways, which partly explains their suitability for tessellation purposes. As such, they can be portrayed in flight, either from above, sideways or below, with the wings shown up, down or parallel, or perched on the ground. All are readily identifiable. However, ideally, birds should be portrayed in flight rather than alighted on the ground. By so doing, all the 'elements' that make up a bird, such as the head, body, wing and tail will be thus seen as individual elements. In contrast, when grounded or perched, the wings, the most typical feature of this motif, are folded, of which the silhouette is then not quite so readily recognisable.
Concerning the portrayal of flight, although the bird can be seen from numerous orientations and angles, it will be found that essentially there are only three basic positions. All of these are as good as the other as regards typical representation:
Both wings in a up position, left
Both wings in a down position, centre
Both wings in a outstretched position, right
Furthermore, the drawing of the birds' interior, of the head and wings has variations as regards the detail, to be discussed in a forthcoming essay.
A point to note concerning the anatomy, is that it is impossible for the wings to appear in 'one up and one down' positions - the wings act as a unit. i.e. both 'up' ,'down' or 'outstretched'. To portray the bird in this manner would be incorrect. The illustrations above show these three positions as a 'two-bird' unit, with a line drawing of a actual bird, additionally shown as a silhouette. This is for the purpose of recognising the birds outline immediately, without any 'distractions' of finer detail. From this, each of these is thus immediately recognisable as a bird at-a-glance.
An atypical representation would be to show the bird either 'full-on' or from the rear when perched. Both of these views would not show the most important element, the wings, and so consequently the silhouette would be less identifiable.
Escher generalities :… A fish is almost equally suitable; its silhouette can be used when viewed from any direction but the front.
Fish are best portrayed in a sideways position, as then all the elements that make up the creature, head, body, fins and tail are immediately identifiable.
Essentially two atypical representations are when seen from directly above or below and head on or rear, neither of which makes for straightforward identification. When seen from above (or below) an 'elongated ellipse' will be formed, of which although the head and body are indeed shown, are thus essentially shapeless i.e. they lack definition. When seen from 'head-on', the body length is hidden by the fishes head, and so consequently, a 'rounded ellipse' is all that is seen. When seen from the rear, the tail is shown as a inconsequential 'slither', with a rounded ellipse for the body. Essentially here, elements 'merge', resulting in a silhouette that is essentially formless, unrecognisable as a fish.
Escher generalities:… the human form is most characteristic when seen from the front .
Human figures are best portrayed ‘full on' i.e. frontal, or in profile, from which such an outline would be obvious. From this, its 'elements', of head, body, arms and legs would be immediately identifiable. Upon the basic premise, variations are possible, as other poses are equally valid, as the human figure can adopt a myriad of such poses, with the body bent at the waist, arms and legs bent, activities such crawling, running and jumping, and yet still remain instantly identifiable. Furthermore, in contrast to the animal world, the human figure is typically seen clothed, and so this also adds more possibilities. Consequently, the discussion for this motif is fraught with difficulties in attempting to cover a multitude of variations.
In contrast, an atypical representation would be as seen from above, with only the top of the head and shoulders visible. Another examples would be from the ground level up, with an outline that would be not so obvious (as the figure would be foreshortened).
Consequently, the figure is best seen either full on or from the side. Less clearly defined would be poses where the elements of the figure merge with the body. For example with the arms in front of the body. In this situation, the arms would obviously not be seen in outline, and so the figure would be less typical.
Perhaps the best illustration of this point is to examine one of my own tessellations, namely from Human Figures, No.2.
From this, the silhouette has the figure defining elements, head, arms, body and legs unambiguously. Such matters therefore 'elevate' the tessellation in terms of inherent quality.
Now, when the above is thus applied to tessellations, frequently the motifs outline, due to the inherent symmetry ‘restrictions' necessarily involved, can be seen to leave a lot to be desired, from which such appropriate typical representation can only assist in matters of unambiguous determination of motifs. Such analogies also apply to other motifs.
(No Escher generalities)
Dogs are best portrayed in a profile view, from which the outline, no matter what breed, is thus obvious, as illustrated below. Ideally, the tail and legs would be distinct, with the front and back legs set slightly apart, to emphasise three-dimensionality. When one leg is hidden by the other then three-dimensionality is then obviously lost. The diagram below illustrates both these aspects, with the rear legs shown slightly apart, with the off-front leg hidden by the leading leg. (However, to 'accommodate' three-dimensionality in a tessellation is fraught with difficulty, and so the legs on the far side of the body are thus usually shown hidden or very close together, with no visible space between them.)
Another 'typical representation' is offered by the possibility of showing the dog in a sitting position. Although all the elements as detailed above are not so readily visible, enough of these remain to render the silhouette as unmistakably of a dog.
Yet another position commonly to be found is when the dog is lying down. However here, in contrast to the above poses, this aspect is lacking in showing the elements, as all the elements 'merge', as shown below. Although in the line drawing a dog is readily discernable, in silhouette a essentially formless shape occurs - if asked what this is, a dog would not be identifiable.
In contrast, alternative views, the 'head-on' or rear view, are not so discernable, as the elements will also 'merge'. For instance, with 'head-on', the tail would not be visible, as would the length of the body. Also, distinguishing features of the head would not be so apparent, such as the muzzle in profile. When viewed from the rear, only the back of the head would be seen, with the body being omitted. This obviously lacks the more typical outline of a profile view. Consequently, such aspects make a dog more difficult to recognise in silhouette in these portrayals.
Furthermore, if the outline is recognisable by a certain breed of dog rather than a generic one, then this is the indication of a tessellation of the highest ranking. (However, such a desire is most difficult in practise, as dogs are a most difficult creature to use for tessellation purposes. Indeed, even the accomplishment of a generic dog is cause for praise.)
Escher generalities: … insects appear most typical from above …
Insects are best portrayed as when seen from above, from which the outline is thus obvious. From this, its 'elements', of head, body, wings, abdomen, legs and antenna are all immediately identifiable. The most notable feature of an insect is that of its intrinsic small size, of which when it has alighted on a object is thus more typically viewed as from above, and therefore this type of creature is thus more instantly recognisable as when so represented in this way.
In contrast, a sideways portrayal would not show as a typical insect, as the only way of viewing this would be to align the view directly at ground level, and furthermore a close-up look would be required. Also, a ‘unnatural' front (i.e. head on) or back view (behind) would similarly be untypical. Again, the creature would have to be viewed at ground level. Although such views are 'valid', it is obviously a lesser way of portraying an typical representation of this motif.
(No Escher generalities)
Lizards are best portrayed as seen from above, from which the outline is thus obvious. From this, its 'elements', of head, body, legs and tail are all immediately identifiable. The most notable aspect of viewing an lizard is that of its intrinsic small size, of which when it viewed is thus more typically viewed as from above, and therefore this type of creature is thus more instantly recognisable as when so represented in this way.
In contrast, a sideways portrayal would not show as a typical lizard, as the only way of viewing this would be to align the view directly at ground level, and furthermore a close-up look would be required. In addition, an ‘unnatural' front (i.e. head on) or back view (behind) would similarly be untypical. Again, the creature would have to be viewed at ground level. Although such views are 'valid', it is obviously a lesser way of portraying a typical representation of this motif.
Escher generalities: …for animals the question immediately arises, from what angle should they be viewed so that their silhouettes are as characteristic as possible? Quadruped mammals are usually most easily seen recognised when viewed from the side …
Quadrupeds are indeed more easily recognisable when viewed from the side, as the disparate diagrams below illustrate. Essentially, when seen from the side, neglecting scale matters, one quadruped is very much like another. Consequently, it will be found that this can be of benefit when composing motifs, as for instance a dog that is not quite right may then be transformed into, say, a cat. Although other viewpoints are possible, such as 'head on' or as seen from the rear, these are not the best for silhouette purposes. For example, when seen from the side, the creatures head, body, legs and tail (if applicable) will all clearly be discernable. In contrast, if viewed head-on or from the rear, these elements would not be so distinct. For example, the head will merge into the body, and the body length will not be apparent. Another untypical viewpoint would be when the quadruped is lying down or sleeping. This is because its legs and tail (if applicable) would be tucked into the body, essentially merging if seen in silhouette. Consequently, these elements would not be seen on the silhouette, therefore rendering the creature less recognisable. In contrast, where a sitting position is shown in profile, this is more acceptable, as all the elements remain on view.
Some quadrupeds have different breeds, of which if by outline alone the type is thus recognisable then this adds to the inherent quality of the tessellation. For example, say of dogs, if a St. Bernard can be recognised, then this is thus better than a generic dog, all things being equal in terms of inherent quality of the two types of dog.
Created: 24 January 2006 (substantial extra material). Last updated: 25 August 2009. Minor revision: 9 August 2010. Changed wording, 'untipical' replaced by 'atypical'