Escher notes on the drawing ‘triangle system: 3 motifs, each with one colour’, an apparently simple statement which does not do justice, as this has been more carefully planned than that text suggests. Although individually the motifs here are nothing out of the ordinary, the underlying concept that is portrayed is indeed of more significance, namely the three elements of Air, Water and Earth. Undoubtedly, such a unifying theme gives a very pleasing tessellation of subtlety when this is thus known, of which without such foreknowledge is not obvious. 
    Perhaps somewhat surprisingly given the pleasing concept above, Escher did not choose to utilise this drawing for a print.

Coloration and Rendition 
Three-dimensional, minimum, three colours: red, blue and dark yellow. All of the motifs have a high-quality rendition, with shading to suggest three dimensionality, with black outlines.

Coloration and Rendition
Three-dimensional, minimum, three colours: red, blue and green. Escher can quite obviously be seen to have taken considerable care and attention over both of these aspects, and this is an example of the top echelon of such exactitude. The coloration per se of the butterflies, with coloured dots of the other two colours of the composition arranged in a systematic manner results in a most pleasing effect. The rendition is particularly fastidious, with fine detail involving the veining of the wings resulting in a most realistic motif. Therefore, both of these elements combine to give a particularly high quality tessellation. Of interest is to compare both of these aspects with an earlier butterfly, drawing 18, of which the difference in quality of finish for roughly comparable outlines is pronounced.
    G.C. Shephard (above) discusses the mathematics of the coloration, giving an example with seven colours, and suggesting that if Escher had known this, then this would have been preferred. However, Shephard neglects the practical aspect, as his colouring scheme would entail a considerable increase of motifs, of a time consuming nature, that in Escher's day, although possible would not thus be a practical proposition. Certainly, with the computers of today, such a large number of motifs of necessity would not be a hindrance to such a scheme. Shephard’s arbitrary patch shown does not repeat each orientation of the butterfly, resulting in the colouring scheme not being shown to its best advantage.

DRAWING 71 [TWELVE BIRDS]
Baarn, April 1948
India ink, coloured pencil and watercolour
Discussed in: Symmetry Aspects, page 22.
Related graphic work: Sun and Moon, April 1948 (cat. 357). Liberation, April 1955 (cat. 400).

Escher notes on the drawing that this consists of ’12 motifs of various forms; all are repeated in mirror image (glide reflection), more or less according to system VC’, thereby establishing the premise of the tessellation. In contrast to the preceding drawings, which generally consist of either one or two motifs, Escher here appears to have made a conscious attempt to considerably improve on such relatively few distinct motifs, as this has no less than twelve distinct bird motifs. Without doubt, Escher must have set himself the challenge, not necessarily of twelve motifs per se but of a quantum leap in their number. Undoubtedly, he admirably succeeds in this matter, as overwhelmingly the motifs are generally on a par with his usual standards, albeit two of these are marginally inferior. However, this is a minor quibble, of which, by the sheer number of high quality motifs thus pales into relative insignificance. 
    Such a large number of motifs for the outlines thus demonstrates how relatively easy bird motifs are to compose, due to their inherent ambiguity of outline as discussed in Essay 3, Motif Choice, Birds. In contrast, a tessellation of, say, a comparable number of human figures would result in too many gross distortions to be of an acceptable worth. Ideally, Escher would also have composed a fish example of the same type, thus forming a ‘unifying’ pair, as these are another motif of similar relative ease, of which was obviously well within his capabilities, as these are thus equally suitable in theory, of which such an example would have nicely complemented the birds.

Coloration and Rendition 
Three-dimensional, minimum, two colours: red and grey. A considered, high quality coloration and rendition, with shading suggesting three dimensionality, with a black outline.

Escher notes on the drawing ‘2 motifs, transitional system IA-IAA; See nos.18, 22, 29, 30’ referring to the underlying tessellation system and not the motifs themselves, albeit coincidentally drawing 30 is also of a boat and fish (of which the underlining presumably signifies this).
    As both motifs have a natural connection to each other, i.e. of water, this tessellation is of a pleasing, unifying theme. However, in this instance, the boat and fish are inherently of different scales, and thereby not ideal, albeit such matters are obviously impossible in this particular situation.
    As regards the aesthetics of the motifs, the fish is somewhat contrived, albeit in contrast the boat is surprisingly good, especially so for an inanimate motif. The boat portrayed is typical of those berthed around the Mediterranean, examples of which appear in Escher's prints of the period.
    An aspect of note here is this is the first usage of a white delineating line around the outlines, and furthermore of considerable unit thickness, far exceeding the previous black lines. An obvious question to ask is to why Escher so chose to do this. Presumably, this was for an experiment, or even for just a change, and thereby seeing if such an effect is an variation or improvement. For whatever reasons, although Escher did indeed utilise this on two further occasions, with drawings 79 and 94, he did not essentially continue in this matter, probably for reasons of practicality, as it is far simpler to draw a black line than to have a white one, as no ink is opaque enough for a ‘pure’ white line.

Coloration and Rendition 
Three-dimensional, essentially minimal, brown and multicolored. An interesting aspect to the coloration and rendition is that for essentially the first time (discounting the shells of drawing 42) the (fish) motif is of a multicolored nature, with a basic blue body supplemented by brown and green tail and fins. As such, this is a pleasant change from the essentially monochrome colourings of previous drawings, albeit there are drawbacks to this, in terms of discerning the motif, as discussed in Essay 8, Coloration and Contrasts.

Curiously, this sheet of paper has two drawings on it, which although not unique (see drawings 47 and 48; 49 and 50) is not a common feature, and furthermore are of the same style, albeit of different motifs, which thus suggests a connection. Escher notes on the drawing ‘system IA See 38, 74 and system IA See 38, 73’, respectively of each drawing, this referring to the same symmetry system and not the motif. However, a more direct connection between the motifs is not readily discernible.
    A somewhat fanciful portrayal of a flying fish, with the dual shortcoming of the fish’s mouth and head being somewhat contrived.

Coloration and Rendition 
Flat, minimum, two colours: black and white. Minor rendition - somewhat carelessly, Escher missed adding interior detail to two of the motifs.

Coloration and Rendition 
Flat, minimum, two colours: black and white. Minor rendition.

Although somewhat fanciful, the lizard-like motif is pleasing as all of its elements are in broad proportion to each other. Furthermore, both front and hind legs are each individually of the same length, thereby raising this in quality from others of this ilk that is not so well proportioned.
    An aspect of note is that concerning the symmetry, whereby for the first time a simple rotation about the mid points of a rhombus occurs. This is similar in nature to the very earliest drawings, albeit paradoxically these are more complex than this later one.

Coloration and Rendition 
Flat, minimum, two colours: black and white. Minor rendition.

Escher noted on the drawing ‘2 motifs, system IV, variant 2 (the points where 6 motifs come together lie in this case at the vertices of a rhombus; this is not necessary) (Instead of A, B can also arise)’ this referring to how different lattices can produce this, of which Escher illustrates in schematic form below the main drawing. Curiously, this has a variation, drawing 76A (discussed below), whereby both motifs can face the same direction, instead of both left and right as here.
    Although this drawing is not of the highest quality, as both motifs are somewhat contrived, this still has merit as it consists of two distinct motifs, a more difficult type to achieve, and so consequently the occasional shortcoming can to be overlooked. Additionally, as both motifs are inherently of different sizes, a disparity of scale thus arises, albeit of course this is unavoidable.

Coloration and Rendition 
Three-dimensional, minimum, two colours: light brown and light blue. A relatively considered coloration and rendition with a black outline, which effectively enhances the tessellation.

Although this cannot be considered a proper tessellation, in that it contains only a fragmentary sketch of two motifs, as Escher has indeed given this a number it is thus included for discussion purposes. Essentially, this can be regarded as an off-shoot of drawing 76, in which Escher shows a possible variation concerning the motifs, in which these are shown all facing the same direction, whilst in contrast, the other drawing has the motifs in two opposite directions.

Coloration and Rendition
Not discussed, as due to the inherently sketchy nature such comments would be inappropriate.

Escher notes on the drawing ‘system VIB (see no. 36)’, referring to the same symmetry system and not the motif. As the motif is highly fanciful, this is thus a tessellation of inherently lower quality, further exacerbated by the motif per se in itself of poor quality, as the body is twisted in relation to the arms and legs. In addition, the front and rear legs are of different lengths, albeit a minor redeeming feature being these are of the same respective sizes.

Coloration and Rendition
Three-dimensional, minimum, two colours: blue and light green. A considered coloration and rendition, disproportionate as to the motifs inherent quality.

DRAWING 78 [UNICORN]
Baarn, October 1950
Coloured pencil and watercolour
Discussed in: Symmetry Aspects, page 72.
Related graphic work: [New Year’s greeting card, 1951, L. and K. Asselbergs], October 1950 (cat. 371).

Escher notes (in the form of a query) on the drawing that this a ‘new system?’, as it does not belong to any he has investigated.
    Although fanciful, this is better than most of this type, as the elements of the motif are more easily recognisable, and furthermore are in proportion. Indeed, an exemplary example of the quality that is possible.
    Escher utilised this for a greeting card, making subtle changes to better fit the format.

Coloration and Rendition 
Three-dimensional, minimum, three colours: red, yellow and greenish-grey. A considered coloration and rendition, with shading to suggest three dimensionality, with a black outline.

Escher notes on the drawing ‘triangle-system I B3 type 2 (variant of no. 70)’, of which the main difference concerns that of the colouring, this being of a more complex mathematical nature for its own intrinsic sake. 
    Another aspect to this is that Escher employs a white delineating line, in contrast to black, albeit there appears to be no specific reason as to its necessity.

Coloration and Rendition 
Flat, three colours (in combination): yellow, light brown and dark brown. Each butterfly is coloured in three elements of body, upper and lower wings, with the lower wing colour also appearing as coloured dots on the upper wing. From this, secondary effects of coloured circles appear (better seen if the drawing is viewed from a longer distance than of normal reading), reminiscent of his abstract studies of interlacing circles. Minor rendition of shading to suggest three dimensionality.

Escher notes on the drawing ‘system IA; combination of 73 and 74 [under three motifs shown] congruent forms’, these motifs ‘adapted’ to the outline. This tessellation is interesting not due to the quality per se but of the idea, namely that of an outline that is so ambiguous that it suffices for two distinct motifs, and is shown in combination in the main drawing, and also illustrated separately below the main drawing. Such examples are very difficult to compose for obvious reasons, and therefore where such occur these are thus of more interest than with a more orthodox tessellation. Consequently, due to the dual demands the motifs are not necessarily of the highest quality, as these motifs indeed show, albeit still of a recognisable nature.

Coloration and Rendition 
Flat, two colours: black and white.

Coloration and Rendition
Flat, non-minimum, four colours: pale red, pale blue, pale yellow and white (unstated). Due to the way that Escher has composed this, a single colour would suffice. However, as the motifs appear in four distinct orientations, although minimal he chose four colours to better emphasise the number of motifs. A considered rendition, with fine detail.

Both motifs have shortcomings due to their contrived nature, with the birds body being unnaturally twisted, whilst the fish is poorly defined, the upper fin not essentially being distinct from the body, along with the lower right fin being anatomically incorrectly placed too near the tail. 
    Due to the inherent low quality, it is perhaps surprising that Escher chose this for further work (above), as he has far superior drawings of the same combination of motifs that could have been utilised instead.

Coloration and Rendition 
Flat, minimum, two colours: grey and off-white. A somewhat muted choice of colours. Minor rendition, of interior and black outline.

Escher notes on the drawing ‘Free plane-filling, based on rectangular system, with 36 different motifs. (design for mezzotint)’. Consequently, Escher here sets himself with a challenge, in which he revisits a previous idea of composing a tessellation with multiple motifs (drawing 71) with a new type, namely with no restriction as to choice and number of motifs. Strictly speaking, this is shown not as a tessellation, as there is no repeating unit, although this could have indeed been made as such. As such, the motifs are highly fanciful, essentially of necessity due to the demands of the idea. Although this could have been shown as a tessellation Escher chose not to do so, as if so attempted, the motifs would have been of relatively poor standard, possibly unacceptably so. As this is then, in Escher's own words, a 'free plane filling...', the motifs extremities around the border thus have more freedom in that greater attention can be paid to their veracity, as there is more room to manoeuvre.

Coloration and Rendition 
In contrast to the other numbered drawings, this was intended as a study for a print, hence the detailed rendition (and mirror image date and monogram), of which coloration therefore has no place. Consequently, as the print is of a highly rendered nature, the drawing is thus shown in a similar degree of quality.

Last updated 14 November 2005 (minor reworking 23 November 2006) 

Coloration and Rendition 
Three-dimensional, minimum, two colours, black and off-white. Minor rendition, almost of a casual manner. Cross-hatching in a ‘rough and ready’ way represents the scales of the fish. Although the bird motif does possess a rendition of sorts, to all intents and purposes this is non-existent, as it can barely be detected.

Coloration and Rendition 
Three-dimensional, minimum, red, yellow and blue. Possibly for maximum contrast, Escher chose to utilise so-called primary colours of the furthest (equal) spacing around the colour wheel. A high quality rendition is shown, perhaps disproportionately so considering the relatively no more than acceptable quality of motif.

Escher notes on the drawing ‘system VIIID and IXD (improvement of no. 39)’, referring to the motif. Escher here explicitly revisits an earlier tessellating idea of drawing 39, of which the motif in that drawing is adapted to the confines of a square rather than the previous rectangle. Presumably, Escher means by improvement is that the motif is now symmetric, of which whilst the previous example appeared to be so at a casual glance, this was in fact illusory and not so. Perhaps more correctly this should be regarded as a variation, as improvement arguably suggests a change to the drawing itself (as Escher himself stated when he ‘improved’ earlier drawings). Whatever the terminology, improvement/variation does indeed occur, due to the symmetry of the motif, and not due to any other reason, such as the rendition, as the respective renditions are comparable.
    A pleasing feature is the segmentation of the antenna and legs, this thus reflecting a real-life bug, thereby effectively enhancing the tessellations portrayal in this matter.

Coloration and Rendition 
Three-dimensional, minimum, two colours: blue and reddish brown. A high quality rendition, with shading to suggest each individual segment of the antenna and legs. As with drawing 39, examples of this type, where the extremities splay out from the body, are notoriously difficult to discern (of which Escher noted in Regelmatige vlakverderling), as this tessellation shows. Ideally, a defining black line around the motif should have been utilised to improve this aspect, and not the almost incidental thin line as shown.

DRAWING 87 [TWO BIRDS]
Baarn, July 1952
Ink and watercolour
Preparatory drawing: Magic, page 163.
Related graphic work: [New Year’s greeting card, Eugène and Willy Strens, 1954], October 1952 (cat. 383).

In style, this is somewhat similar the bird motifs of drawing 84, as the same serrated idea for the wings and tail is utilised. Arguably, this is a better example to so use, as this consists solely of birds rather than birds and fishes, the latter of which is a motif perhaps not so suitable. Indeed, both wings and tail are ideal, and as this thus leads to a more accurate representation of a bird, such a portrayal is to be favoured where possible. However, Escher's example is rather simple, in effect a broad statement of the principle. 
    Oddly, both birds interior contain only a modicum of detail, consisting solely of an eye and a line for the beak – quite why he did not add more detail, as was his usual practise is unclear. In contrast, the related graphic work (above) shows more detail, in that a body is shown.
    Another oddity is that upon delineating the motifs with a thin black line, he then added a thicker one to the front edge of the wings, resulting in a most unedifying drawing. Quite what he was aiming for with this is unclear.

Coloration and Rendition
Flat, minimum, two colours: green and white (unstated). No rendition at all.

Escher notes on the drawing ‘system IIIA (see 11)’ referring to the motif (which is alike) and not the tessellation system (which is not). Escher here effectively revisits a previous drawing, utilising the seahorse motif for a different system. As such, the motifs are very much alike, the main difference being this later one is of a slightly simpler nature, in that it can be coloured in two colours instead of the preceding three of drawing 11. Another difference is that this utilises the ‘feathery’ appearance of recent bird and fish motifs reflecting real life.
    The somewhat ‘spoiling’ square grid patch superimposed upon this was probably added in conjunction with the related work (above).

Coloration and Rendition 
Flat, minimum, two contrasts of the same colour, light and dark blue. No rendition.

In contrast to Escher's tessellations whereby a straightforward repetition is shown, he here shows two possibilities side by side, with the composition divided by a implied diagonal from top left to bottom right. Although either of the fishes can be said to be derived from the other, it is more correct to assume that the ‘feathery-finned’ fish arose as a variation of their less exotic counterparts. Consequently, although related, the question arises as to whether such examples should be regarded as distinct or worthy of being drawings in their own right. In this instance, Escher chose not to show distinct drawings but instead combined the two types in a single composition. Which of the motifs is ‘best’ is subjective, as the fish are of a stylised manner, a flatfish type. Both have pros and cons – the ‘non-feathery finned’ fish could be regarded as somewhat ordinary and plain, whilst the feathery one, although ‘livelier’ is anatomically open to question as regards veracity. Although Escher did not state explicitly which he preferred, as the related work (above) shows the ordinary one this was thus presumably favoured.

Coloration and Rendition 
Flat, minimum, two colours: two-tone, dark and pale green. No rendition.

This essentially is a variation of the flatfishes of drawing 89, and quite why Escher chose to do this is unclear, as the differences between the two is most small. Precisely, the underlying grid has been changed from a kite to a quadrilateral, along with an increase in the number of distinct lines, from two to four. Of most notice is that the fish no longer meet nose to centre of tail but nose to outside of tail. Consequently, due to the changes, the fish is thus non-symmetrical, of which for a flatfish type is an inferior portrayal.

Coloration and Rendition 
Flat, minimum, two-tone: dark and pale crimson. No rendition.

Last updated 14 November 2005