Of some considerable importance as regards the assistance in readily identifying motifs (birds, fishes ....) concerns what I term as the typical representation of the outline. By this, I refer to a �common' or 'normal' view of the creature, whereby from its outline alone it is instantly recognisable. Such a feature is highly desirable, as it thus permits identification at a glance, and is invariably the signature of a high-quality tessellation. This feature 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, the creature it is representing should be immediately obvious. This test invariably succeeds,.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.

�

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 sentances 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 above. 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. Furtermore, examples are shown, redrawn from other people's tessellations, of motifs that simply are of an inferior standard.

�

�

Quadruped

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. 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.

�

�

Specifics

�

�

Dogs
Dogs are best portrayed in a profile view, from which the outline, no matter what breed, is thus obvious, as illustrated below. Alternative views, the 'head-on' or rear view, are not so discernable. For instance, with 'head-on', the tail would not be visible. When viewed from the rear, only the back of the head would be seen. This obviously lacks the more typical outline of a nose and muzzle. Consequently, such aspects make a dog more difficult to recognise in silhouette in this portrayal.

As detailed above, a sitting position is also ideal. In contrast, where the dog is shown lying down, this aspect is lacking in showing the elements. 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 utilise for tessellation purposes. Indeed, even the accomplishment of a generic dog is cause for praise.)

�

�

Insects

Escher generalities: � insects appear most typical from above �

�

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 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 close-up. Although such a view is 'valid', it is obviously a less frequently way of portraying an insect. Also, a �unnatural' front or back view would similarly be untypical. Again, the creature would have to be viewed at ground level

�

�

Birds

Escher generalities: �In addition, it has a characteristic shape, from above and below, from the front and the side.

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 are folded, of which the silhouette is then not so readily typical.

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 (Fig.1):

• Both wings in a up position, left
• Both wings in a down position, centre
• Both wings in a outstretched position, right
  

Fig.1

Regarding anatomy, it is anatomically impossible for the wings to appear in 'one up and one down' positions - the wings act as a unit. i.e. both 'up' or both 'down'. 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 are thus immediately recognisable as a bird at-a-glance.

Fig.2
An additional aspect that applies more specifically to the 'outstretched' wing is that variations of the interior are possible, concerning the 'viewpoint' of the bird. Upon taking an outline of Fig.1c, left, it can be seen that it is possible to add two distinct views of the bird, as when seen from above (centre) and below (right). Consequently, this possibility can thus be applied to a tessellation in which the wings have the same outstretched position. An example of this is Birds 1 No.5

Fish
Escher generalities :� A fish is almost equally suitable; its silhouette can be used when viewed from any direction but the front.

Fish are unique in the sense that their environment is not met with in every day life (excepting those kept as pets) unless deliberately looked for, i.e. to be found in water. Furthermore, even when their so found, they are still not readily viewed. Consequently, as they have no �typical' view, there is thus no one defining view. However, these are essentially best represented by being depicted in a sideways position, as illustrated. From this, the fishes elements of head, fins and tail are thus more recognisable than when seen head-on, from which only a rounded outline would be seen concerning the latter view.

�

�

Human Figures

Escher generalities:� the human form is most characteristic when seen from the front .

�

Specifics

Human figures are most typical represented by being seen �full on' i.e. face to face, or in profile, from which such an outline and what it would thus represent would be obvious. In contrast, a non-typical representation would be from the ground level up, with an outline that would be not so obvious (as the figure would be foreshortened) as with the more normal view as above. However, other poses are equally valid, as the human figure can adopt a myriad of poses, such as with the body bent at the waist, arms and legs bent, crawling, running, jumping. 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.

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 Human figure No.2

From this, the silhouette has the figure defining elements, head, arms, body and legs unanmbigously. 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.

�

�

Lizard

Lizards are best portrayed as seen from above, as being small creature a natural consequence is to look down to view these, and so typically these thus consequently have their typical representation in which the back view is shown. In contrast, a side or head on view would be untypical.