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An Essay on M.C. Escher's 63 Tessellating-Based Prints 31-63 |
[31] AIR Bool 383 October 1952, drawing 92, February 1954 The second of the series of the cards, with bird motifs representing air. The background to this is not of the greatest clarity. Schattschneider in Visions of Symmetry states that drawing 87 is the source for this, but, although of a similar nature, this is not strictly so, as the birds are based upon a kite in the print instead of the quadrilateral of the periodic drawing. More exactly, the birds here pertain to drawing 92, of 1954. However, the prints in the series are all apparently of 1952, and so there is a discrepancy in such chronological matters. Possibly, Escher did another version of drawing 87, of a study nature, (utilised for the print here) and subsequently, in 1954 redrew as a finished example. Again, the motifs remain essentially unchanged in the print; the only minor difference being the bird’s interior body has now been more clearly defined.
[32] FIRE The third of the series of the cards, with devil-like motifs representing fire. Escher here makes minor changes to the underlying source drawing, as the motifs possess tails of a more sinuous nature, and furthermore at the extremities of the print, having more freedom they are much larger, and they also have their pointing fingers more marginally raised. In addition, to fit in more with the cards square format, the two lower devils have been drawn accordingly with this in mind.
[33] WATER The fourth and final of the series of the cards, with fish representing water. Escher makes minor changes to the extremities of the outer fishes to accommodate the format of the card.
[34] TREES AND ANIMALS A somewhat mysterious woodcut, based upon one of Escher’s few non-animate tessellations, which is itself somewhat unusual in its tessellating nature. Escher here utilises the leaves of the source drawing for compositional purposes, of which the natural association is with trees, and therefore composes a print based upon this theme. Perhaps the most notable aspect of this print is that of the mirror symmetry, and indeed, this is the first print of its type with this aspect to the fore (although other prints display mirror symmetry, this is very much of a secondary nature). As with the preceding cards, this appears to have been adapted to fit in the constraints of an apparently arbitrary rectangular format (as this was a non-commissioned work). As such, the print is somewhat enigmatic as it is not obvious at first glance at what is being portrayed here. Indeed, different interpretations can be put on this, and whether by accident or design it reminds me very much of one of those pictures whereby amongst the scenery various features are hidden or disguised in some way, in which the viewer is then invited to search for, upon which here birds and squirrels can be found amongst the foliage. Indeed, if this is what Escher was intending here, this is admirably demonstrated, but the above interpretation of my own remains speculative. Further motifs are to be found in the lower half of the print, and essentially these are added as of a necessity, to fill-in what would be black or white space, of otherwise a block of ‘colour’. However, almost certainly, if I have interpreted the print correctly, Escher would ideally have been omitted these if possible, as they are not germane to the composition per se. Therefore, this aspect can thus arguably be described as somewhat non-aesthetic nature, as the lower bird motifs are redundant, having been added for the purposes of expediency.
[35] DONKEY In contrast to most of Escher's works of an animate form, this is an example of the non-representational type, consisting of a series of what can be described as letter E’s. Presumably, as Escher would have previously known this particular tessellation, as it occurs frequently in various publications, he did not therefore need to compose anew. Concerning the print itself, the centre has been omitted to accommodate a braying donkey, of which without further clarification such an appearance may appear somewhat obscure, of which the tessellating letter E represents Ezel, the Dutch for donkey. This was undertaken for the purpose of a booklet for Grafisch ABC, of which to illustrate his name the letters M and E (Maurits Escher), of which a subsequent print (Bool 393, of a non-tessellating nature) shows the letter M. Due to the relative simplicity of the print, there is nothing here of any real significance as regards compositional matters.
[36] FISH This vignette was created for an invitation card for an exhibit of Escher's work at the Stedelijk Museum, Amsterdam, of 27 August-26 September 1954, in conjunction with the International Mathematical Conference of that year. Again, it is of a most simple type, indeed the simplest possible, as he utilises drawing 99 with no inherent change, effectively choosing, somewhat strangely, a non-symmetrical composition of a ‘block’ of so-called ‘fish’.
[37] LIBERATION This lithograph shows the concept of liberation, and although Escher frequently said that his works were not of a metaphoric nature, the title perhaps epitomises the ending of the relatively recent war. Such matters aside, the print consists of an unfurled strip of paper from which, after having gone through a series of transformations from an intrinsically formless beginning of grey, to equilateral triangles of a contrasting nature, their lines gaining in angularity until a tessellation fragment of birds is thus formed. From this, the birds are then increasingly released from their confinement, hence the concept and title of a liberation. As such, an exemplary print in concept, of which the essence of the idea is immediately clear.
[38] FISH A vignette, commissioned for use as a greetings card. Again, this rigidly adheres to the periodic drawing, as no changes are made concerning the motifs, the composition being of a order 6 rotational nature.
[39] SWANS This has similarities in style with two earlier prints, Two Intersecting Planes of January 1952 in that the motif is shown in a flattened state, essentially alike as with a jigsaw puzzle piece and with the Horseman print of July 1946 in terms of composition. Quite what idea that is being portrayed here is not clear. Even amongst renowned mathematicians, there is disagreement, with Ernst and Senechal (above), stating this is based upon a Moebius band and a cylinder respectively. Escher briefly commented upon this (giving neither of the above two proposals), published in Visions of Symmetry, page 309, whereby he states that its main purpose is to simply demonstrate principles of glide reflection without having anything of a more meaningful nature in terms of composition.
[40] DIVISION As such, the source for this is unclear - although the motifs are based upon an earlier drawing, No.35 of July 1941, these do not resemble these in the strictest sense, as Escher here ‘splits’ them, of which a subsequent periodic drawing, as above, is more relevant. Again, it is likely that these are derived from a study that was not shown as a finished numbered drawing until later, hence the apparent discrepancy of the dates. Such background matters aside, this print is interesting in a number of ways, as it marks the return, in broad terms, of a ‘developmental’ nature, albeit here, the motifs are of a reduction of a self-similar nature. This was the first such example, the last having been undertaken in February 1939, and indeed this here was followed by a succession of like prints. Undoubtedly, the most noticeable aspect of this print is the ‘style’ of the motifs of what I term as of a ‘curtailed’ nature, of which the effect is most odd, and indeed Escher did not utilise this again – as such, due to this factor, it is most difficult to assess this in terms of its ‘success’ or not. Indeed, this is one of the few prints I have not been able to recreate in order to understand how Escher went about his compositions. Consequently, due to lacking any real insight, the following merely states a few observations on this. Firstly, although obscure, the print is clearly systematic, of a self-similar nature, with lizards being ‘curtailed and combined’ to produce the effect. Now, quite whether this is good or not in an aesthetic sense is debatable, and it may very well be that Escher is using this simply as a tour de force in self-similarity for the sake of it, and so without further knowledge of what Escher is portraying here any further speculations by myself seem inappropriate.
[41] NEW YEAR’S GREETING CARD PTT A commissioned work, undertaken for PTT the Dutch, Postal, Telephone and Telegraph service. Escher here, in contrast to his previous tessellation-based commissions, apparently especially devised this for the specific purposes of PTT rather than his ‘usual’ way of selecting from an existing periodic drawing.
[42] SMALLER AND SMALLER An example of an ‘self-similar’ composition, with the lizard-like motifs reducing in size in a systematic way as they approach the centre, hence the title of Smaller and Smaller. As such, presumably by default, this is a straightforward exercise in demonstrating the principal of reduction, as apart from the four outer lizards that are released slightly from the grid (more precisely their extremities), the others remain in situ. Although drawing 35 is indeed the source, it can be seen that Escher varies this slightly for the print, with the lizards’ eyes centralised and minor changes made to the arms and legs. This particular print marks a watershed in Escher's development, as from this point he concentrates on ‘infinity’ type of prints in contrast to the ‘story element’ of his earlier ones.
[43] FISH A vignette designed for an exhibition card of four graphic artists (including Escher) held in the Stedijlk Museum, Amsterdam, of January-February 1957, and was this was later re-utilised with two further exhibits. Curiously, the motifs here have no underlying periodic drawing, and so, presumably, Escher had previously undertaken a preceding study that he did not pursue to the defining stage of a numbered drawing. Again, this shows a straightforward exercise of a reducing nature, as the motifs remain in their grid without becoming ‘active’ in any way.
[44] REGULAR DIVISION OF THE PLANE I As to the print itself, Escher here shows the concept of a development in the broadest sense of the word, as upon beginning with a uniform grey this is then transformed by a series of ingenious stages to a tessellation of birds and fish by means of a ‘winding strip,’ presumably formed for the format of the rectangular page. This is essentially a more concise way of showing a metamorphosis rather than a ‘long strip’ as with his previous examples of the same kind. Such a simple description given by the above does not do justice to such a splendid composition, as this essentially requires a deeper analysis as to its intricacies, of which Escher wrote in relative depth of each stage in turn in his book. Although perhaps further comment is therefore superfluous, below I simply state each stage in simple terms: 1. A beginning of grey, with no definition of tessellation whatsoever. Undoubtedly, a tour de force of Escher’s skills is thus displayed here.
[45] REGULAR DIVISION OF THE PLANE II
[46] REGULAR DIVISION OF THE PLANE III
[47] REGULAR DIVISION OF THE PLANE IV Escher here once more illustrates the principles of glide reflection, utilising the Bulldogs tessellation, of which an counterchange is also shown.
[48] REGULAR DIVISION OF THE PLANE V Escher here once more illustrates the principle of glide reflection, probably with a motifs specially composed for the purpose of the book, as there is no numbered drawing of this, albeit a ‘considered sketch’ with axes of rotational symmetry are denoted (page 167) which accompanies the plate, of which a counterchange is to be seen.
[49] REGULAR DIVISION OF THE PLANE VI Escher here illustrates principles of a self-similar reduction of an apparently arbitrary ‘house-like’ shape that presumably was composed specifically for the convenience of the book, following the rectangular format. This took the form of a variation of an earlier print; Smaller and Smaller, whereby a sequence of diminishing right angled triangles act as the framework for the motifs (and is later repeated in the Square Limit print). Interestingly, in contrast to almost all of his works whereby he insisted on contrast (to aid the definition of the motifs), this example, which of necessity requires a minimum of three colours, breaks his self imposed rule. Presumably, this is on account of retaining the consistency of approach of the series of prints, all of black and white and shown on a grey background.
[50] PLANE FILLING II Escher here repeats an earlier idea of 1951, namely that of ‘free filling,’ possibly as an attempt at building upon the earlier example, as this one contains more motifs. As this print has much in common with the preceding one, the comments are also relevant to this as well, of which I thus defer to.
[51] WHIRLPOOLS Although that I state that this has no direct drawing as its source, elements of the fish motif can be found in a vignette of Escher's for an exhibition card of 1956 (Bool 414). This Woodcut engraving and Woodcut is interesting in a number of ways. Firstly, it is the first overtly spiral print that is based upon tessellating elements, of which such a feature in combination became a major pre-occupation with Escher. Interestingly, Escher here combines a spiral with reduction, as here he chose an ‘appropriate’ symmetry drawing (presumably in a study state) to accomplish this aspect, with fish moving in opposite directions resulting in a most pleasing composition.
[52] PATH OF LIFE I As such, another of the spiral types, albeit somewhat disguised by the colouring scheme Escher chose, as the outer ring of motifs are divided in their colouring, whilst the inner motifs are essentially shown as of contrasting nature. Typically, the fish motif here (and also of the succeeding prints of the same theme) is of a noticeably poorer quality than with most of his prints, and the reason for this is that as the motifs are somewhat distorted by the reduction process, a ‘vague, ambiguous’ motif outline is of a necessity. In addition, it will be observed that he typically shows a view in which one looks down upon the motifs, essentially showing a symmetrical appearance, this presumably being more suited to the composition. Such examples, more than any other of his tessellating-based prints, are obviously more inclined to a mathematical audience, and hence their general lack of relative popularity as compared with his more favoured works such as Day and Night whereby the content, although unusual, is more readily grasped by a non-mathematical audience.
[53] PATH OF LIFE II The second of the three prints based upon a spiral ‘Path of Life’ theme. Again, Escher utilises the same periodic drawing (102) as with the preceding example, with all of its aesthetic shortcomings and, as with Path of Life I, this is very much alike in its style, the main difference that this consists of four such spiral loops. Ernst in Magic Mirror, page 106 rates this print very highly indeed, and of the ‘infinity’ theme (and not just of the Path of Life series) he considers this to be aesthetically the best.
[54] SPHERE SURFACE WITH FISH Somewhat curiously, Escher chose to illustrate this with possibly his poorest tessellation in terms of quality, as the so-called ‘fish’ are most rudimentary, the example given being of what I have termed (in Processes) as a shape with eyes, in effect of a worthless nature. Quite why he chose this self evidently poor quality motif remains unclear. In his writings, this aspect is not specifically mentioned. Speculating, as this is one of his few of a geometrical outline, such a choice was dictated by the composition, as lines of longitude and latitude on the globe more naturally suit a geometrical tessellation outline, with curved motifs perhaps being unsuitable on this particular occasion.
[55] CIRCLE LIMIT I The first of a series of four prints based on an figure as shown in ‘A Symposium on Symmetry’ by H.S.M. Coxeter pertaining to the hyperbolical plane, of a somewhat complex, mathematically advanced nature, as discussed in more detail above. Essentially Escher thus utilised the framework for his own purposes, replacing the straight lines and arcs with a rudimentary indefinable geometric motif, of noticeably inferior quality. Again, as with the ‘spiral’ examples, this was probably dictated by the necessity of a ‘vague, ambiguous’ outline due to the restrictions of the reductions. Interestingly, Escher apparently created these motifs on an ad hoc basis for this from previous studies, as there is no numbered drawing preceding this, albeit subsequently, in April 1964, he did indeed complete definitive examples. Disregarding the complexities behind the framework, aesthetically the print leaves a lot to be desired, and indeed Escher was also unhappy in this aspect, pointing out the shortcomings. Firstly, the motifs are of a very poor quality, and although termed as ‘fish,’ this description bears only a most tenuous resemblance to the creature. Indeed, these are of the type of which I sharply criticise in Essay 1, essentially consisting of an outline with eyes, thereby of the lowest possible quality. In the print, Escher has placed the eyes in two distinct ways, effectively reversing the placement in relation to each other. Quite why he did this is unclear, as more naturally the motifs would be uniform in their placement of eyes. Another shortcoming, as Escher pointed out, is that there is no ‘flow’ to the motifs – more specifically the motifs ‘meet up’ head to head, resulting in a ‘jarring’ effect on the eye – aesthetically better would be to have the fish for any one line all swimming in the same direction. However, as this was Escher's first print of this particular type, it is unrealistic to expect perfection in such matters.
[56] CIRCLE LIMIT II The second of the series based upon a circle limit theme. This is one of Escher's lesser known works, rarely published, probably on account of its aesthetics, as it consists of a series of crosses of a somewhat disjointed or distorted manner, this is thus generally overlooked.
[57] FISH AND SCALES Quite what Escher is portraying here is unclear, and although he did indeed comment upon this woodcut, this is really only of a simplified statement of a ‘mutation’ nature. As such, this is a typical example of what I term as ‘clever but obscure,’ lacking the more elegant simplicity of his more popular prints. However, in contrast to most of the ‘obscure’ examples, this retains a certain elegance of its own, as the fish emerge and increase in size, and indeed Escher classified this amongst his ‘infinity’ types. However, Ernst clarifies the essence of this with an excellent explanation, in Magic Mirror, page 34 of which due to the inherent complexities of the print I thus essentially defer to, with the comments following being of generalities. From this, the print can be seen to be based upon a grid of Escher's own devising, of which he had previously utilised for an non-tessellating based print (of considerable complexity) Print Gallery of 1956, whereby certain aspects are ‘blown-up,’ as in a bulge. A most pleasing compositional aspect to Fish and Scales is the association of ideas with fish developing from the scales of a ‘mother fish’ thereby resulting of a satisfying, logical connection. All in all, although the background to this remains of a difficult to follow nature, aesthetically it retains much of merit.
[58] CIRCLE LIMIT III The third of the ‘circle limit’ series, of which aesthetically in terms of the composition Escher improves upon his earlier effort, as here the fish flow in the same direction, whereas previously they abutted each other. Indeed, this example was Escher's favoured one of the genre, of which he stated as such. In addition, the fish motifs are more realistically rendered, albeit still much remains to be desired, possibly, but not necessarily, dictated by the demands of the framework. As with Circle Limit I, this woodcut does not have a proceeding numbered drawing, and only subsequently (1964) were the motifs utilised for this shown as a numbered drawing.
[59] CIRCLE LIMIT IV The fourth and final woodcut of the theme, albeit here this particular one stands as an example in its own right, as Escher is not concerned with the aesthetics of the ‘flow’ aspect of I and III. Although Escher preferred III as the best, personally I favour IV, as here the motifs, of angels and devils, are more readily discernable, as well of being in compositional terms opposites, thereby suiting the two-colour contrast. In contrast, the preceding motifs consist of essentially indefinable creatures, generously described as ‘fish’ by Schattschneider. Interestingly, Escher chose for this composition a considerable earlier drawing from 1945, which thus suggest that he trawled through his ‘reservoir’ of drawings searching for a suitable example for what he had in mind. Furthermore, these are shown without too obvious a distortion of their respective outlines, which in terms of aesthetics is obviously a decided gain.
[60] FISH A pleasing compositional element to this is how cleverly Escher suggests a vignette effect solely by the use of black and white lines, and in addition, their sinuous nature is reminiscent of waves, thereby placing the fish in their natural environment.
[61] SQUARE LIMIT As to the print itself, fish-like motifs pertaining to the framework thus reduce in size towards the edge, of which again, as with the Circle Limits I, III and IV these are viewed as seen from above. As such, the reason for such a relatively poor fish-like motif is that the demands of the framework require a line that is of a certain sinuous nature. As such, it may be quite reasonably thought that any tessellation based upon a right-angled isosceles triangle, possessing the correct symmetry (of which a 180° rotation along the hypotenuse, with 90° at the apex) would suffice. However, this is not so, as upon trying to do so with one of my own tessellation, the distortion was too great to be regarded as acceptable, resulting in a mal-formed creature. Therefore, a certain amount of ambiguity is ideal, as in Escher's fish motifs here.
[62] PATH OF LIFE III The third and final print of the series, with the same idea of birth, growth and decline being retained, in a series of six spiral loops, albeit here he utilises different motifs. Interestingly though, he once more uses an ‘ambiguous, vague’ motif, this thus once more suggesting that a more realistic creature would not be suitable for the framework.
[63] METAMORPHOSIS III This was effectively Escher's swansong, of which he effectively returns to the task of tessellation per se after a lengthy period whereby he concentrated on his tessellating ‘spatial compositions.’ Indeed, one may be forgiven for thinking that Escher had essentially reached the end of composing tessellations and had no further examples left to give. However, here Escher well and truly sets such matters aside. Furthermore, in his later years, Escher was dogged by ill health, and this, more than any other reason, explains the relative lack of new prints or drawings of whatever subject. Again, as with Metamorphosis II, the small-scale reproductions in most books do not do justice to the majesty of this, of which the full size print should ideally be seen to more readily appreciative of the print. However, an example of worth is to be found inside the dust jacket of Magic. Discussions of this print can be found in Visions of Symmetry, pages 254-258, accompanied by Escher’s letter to Gerd Arnzt that sets out ‘background matters’ and his proposed lecture text, for the tour of America in 1964, that due to ill health never materialised. |
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