The Tessellations of Maurits Escher
Escher’s tessellations are of a degree of magnitude above most other people in
the field, although in terms of ability I put him below Makoto Nakamura. On eight
of the nine determining aspects of ability and understanding of the issues he
scores heavily, with criteria as listed in the introduction:
inherent quality of the motif (silhouette)
the whole motif (excluding ‘heads’)
number of tessellations in the body of his work
(5) X A
tendency to the more difficult to achieve motifs (human figures)
or shaded tessellations (excluding wireframes)
colouring of tessellations
(9) ✓Borderline (where appropriate)
Escher’s tessellations possess eight of the nine desired attributes.
Recognisable in Silhouette
aspect of recognisably of the motif, as seen in silhouette is fundamental to
the premise of a quality tessellation. Although not all of Escher’s
tessellations are immediately recognisable in silhouette, for the most part these
are indeed mostly discernible. However, this is not to say that the
tessellations are overwhelmingly so, as he includes many ambiguous silhouettes,
far more than I would have liked. For example, he has numerous instances of
flatfishes, of which I detail below. Indeed, he is far below Nakamura in this
regard, albeit still of a better standard than most people.
Lesser artists struggle with this concept (inexplicably so,
given its simple premise), and fail to recognise its importance and
unfortunately delude themselves as to equating interior life–like interior
detail with a exterior outline.
(2) Shows the
tessellations in all instances are pleasingly of a ‘complete’ motif
(like Bailey, Bilney, Crompton and Nakamura). The ‘head’ only type is implicitly
excluded, as this category is lacking in any challenge of worth, being all too
easy. Oddly, Escher never wrote why he excluded this type
Lesser artists frequently do not understand the difference
between the two types, and undertake such ‘head’ only examples (on account of
their less challenging aspect), and unfortunately delude themselves as
to equating these with the more challenging whole body motif.
(3) The number of tessellations
Escher shows 137 examples, well above the arbitrary benchmark figure of 50, but
considerably below Nakamura (268), who shows many more, of a like comparable
standard. Given such a reasonably high number, one might expect that these
would not all of the same highest quality, and to an extent this occurs. For
example, Escher included many flatfish type examples that are simply unworthy
of him, these being particularly easy to accomplish, as they are essentially just
shapes with detail added, rather than of an identifiable motif in silhouette. However,
although the quality is occasionally questionable, by far the majority show
true worth, and so he is not just interested in showing high numbers with
disregard for the inherent quality.
Typically, lesser artists will show a large number of
inferior examples, and consider that such large numbers outweighs quality.
Variety of Motifs
shows 32 different motifs, of which although relatively high is still below Bilney
(39), and Nakamura (39). Although the commonly to be found bird and fish motifs
occur (which accounts for approximately half his output), he does nonetheless
show creatures not usually shown, such as Horseman, Unicorns, Beetles, Sea
Lesser artists frequently shy away from undertaking such
variety, showing simpler to achieve birds and fish to the exclusion of variety,
and unfortunately delude themselves as to equating these with the more
praiseworthy variety of motifs.
(5) Challenging Motifs – Human Figures
The more challenging and interesting human figure is mostly
ignored, with only four examples. However, many other examples of a challenging motif can be
seen, notably with Horseman and Beetles, and so he scores heavily here, despite
having few human figures. Even so, I would have liked to have seen far more of
the human figure motif. One would have expected Escher to have realised the
fundamental importance of this motif (as exemplified by Nakamura, who shows no
less than 70 examples), and addressed this. To show just four examples
is not nearly good enough. Their inclusion would be of far greater importance
than numerous, unrecognisable, unworthy, flatfish.
Generally artists, for other
reasons than the desire not to repeat themselves, shy away from such challenging
motif examples (on account of their degree of difficulty).
or shaded tessellations
All of Escher’s
tessellations are pleasingly shown coloured (like Bailey, Bilney, Crompton,
and Nakamura). No inferior wireframe examples are shown.
Lesser artists frequently show wireframe examples, for no
good reason (from which one can only conclude is that they do not understand
colouring of tessellations
All of Escher’s tessellations are pleasingly shown
with map colours, one of the few artists who do so (like Bailey). Of note is
that other leading tessellators, such as Bilney and Nakamura do not always do
Lesser artists frequently disregard this aspect for no good
reason (from which one can only conclude is that they do not understand the
style, as regards finish, is of a consistent approach, with just the right
amount of detail, with little if any variation of note. (Nakamura, for
instance, shows examples varying from minimalist to highly detailed.) Generally,
he uses single ‘strong’ colours without any three-dimensional shading. Some
examples have a more detailed rendering, such as Butterflies, but aside
from this, and negating his early work where he was still establishing his
style, they are noteworthy for their sheer consistency throughout the years.
For instance, there is no difference in the rendering of the early drawing 18,
of 1938, and his very last, 137, of 1972. As a rule, generally a simplistic
finish is to be preferred, as too much detail hinders a clear interpretation of
Lesser artists frequently render their tessellation in too
much detail, believing this ‘improves’ the tessellation, when frequently it
does exactly the opposite, resulting in a most trying viewing, in which there
is to much detail for the eye to take in (from which one can only conclude is
that they do not understand the issues).
generally uses a decided borderline, and where not, uses ‘strong’
colours that do not require such usage. Other, fewer tessellations, typically
of his early studies, of 1937-38, have what I term as an ‘incidental’
borderline, of which although this is discernable, is negligible, on account of
its essentially hair-like nature that is not an intrinsic feature of the
However, the omission of a borderline cannot be said to be
a fault as such, in that the inclusion or exclusion is down to personal choice,
depending on the circumstances of the tessellation. Undoubtedly, this is
secondary to the tessellation itself, and so of less importance to other, more
fundamental issues, as detailed above.
from the plane tilings, Escher did not unduly concern himself with more ‘involved’
tilings devised by mathematicians, such as with the Archimedean, Voderberg
spiral, and the 17 plane symmetry types as a distinct body (in contrast
to Andrew Crompton, the first, I believe, to present the 17 plane symmetry
types as a concerted grouping). Indeed, the only instance of such ‘involved’
types was that of a tiling of rhombs as devised by Roger Penrose, the quality
of which was unbecoming of Escher, titled as a ‘Ghost’, which is nothing more
than a formless shape with elementary eyes.
Admittedly, he perhaps had less access to these papers than
is possible today. On the other side though, he had many mathematical contacts,
who must surely have pointed out such opportunities. Of note is that Escher did
discover self similar tilings, albeit these are not discussed here, as they are
outside the remit.
out a single, or indeed a ‘top ten’ of Escher’s works is a somewhat invidious task,
in that various aspects come into play, militating against a straightforward
selection. Therefore, in no particular order of merit, particular examples of
his that I like (with the drawing number in brackets): Chinaman (4), Camels
(6), Squirrels (7), Dogs (16), Birds (18), Fish (20), Imp (21), Birds and Fish (22),
Reptiles (25), Fish (32), Angels/Devils (45), Two Birds (47), Lizards (56),
Optimist/Pessimist (63), Winged Lions (66),
Butterflies (70), 12 Birds (71), Unicorns (78), Seahorse (88), Swan (96),
Bulldogs (97), Birds and Fish (120), Birds and Fish (121). Notable, and praiseworthy here is the sheer
Pleasingly, he shows a wide variety of motifs,
certainly not the highest of all, but indeed amongst the highest.
although I am positive on Escher’s tessellations, this is not to say that his
don’t have some shortcomings, in that some examples I have reservations with. For
example, I take issue with a decided preponderance of flatfishes. These are
nothing more than formless shapes with eyes, and are unworthy of him. Furthermore,
these are not even truly flatfishes, as true flatfish posses eyes not
symmetrically placed as portrayed by Escher. This shortcoming is even more
surprising, given that these date from his more mature period, when he had many
years of experience, and so would be expected to be aware of their lack of
worth (i.e. they lack any challenge of note).
Of note is that some of his earliest work, of 1927, is
essentially worthless, but this is only to be expected, and should not be
regarded as a criticism per se. indeed, I am loathe to comment on these, these
being his first efforts, more properly regarded as initial probing. I only
discuss these as they are included in the numbering. Similarly worthless is the
‘Ghost’, as discussed above.
Another shortcoming is the lack of human figures; again,
one would have expected Escher to have realised the fundamental importance of
this motif (as exemplified by Nakamura, who shows no less than 70 examples),
and addressed this. To show just four examples is not nearly good enough. Their
inclusion would be of far greater importance than numerous, unworthy, flatfish.
However, shortcomings per se are very much in the background,
with his work typically being of good quality, whatever the motif.
was a very good tessellator, but by far without fault. As detailed above, he
understands the various issues underpinning the composing of inherent quality
of tessellations. Indeed, he explained these in writing, a feature not
frequently to be found in other tessellators. That said, he never even remotely
explained the genesis/creation process per se. Pleasingly, he mostly, but not
invariably, composes challenging motifs (albeit generally not of human
figures), or at least rarely shown, with many examples as detailed above. Against
that however, there is a decided absence of the more challenging human figures,
with only four examples.
Although most of his tessellations pass the above criteria
tests, these are padded to an extent by the flatfish type, of a markedly lower
degree of quality (and are in themselves highly stylised, no true-to-life
flatfish appear like these), few of which any other tessellation artists of worth
deigns to show. However, even when not of the highest standards, then these are
still generally of a higher quality than with other people.
Although it goes without saying, the advantage Escher had
was of being the first in the field (negating Koloman Moser’s handful of
rudimentary efforts barely worth mentioning). Consequently, this has distorted
the issue of ability per se as against simply being the first person to
do this, with the first awarded undue reverence. All too often, all we ever hear
about is Escher, Escher, Escher, with no one else’s work deemed worthy. When
judged solely on his tessellations, then on the issue of ability there
is not such a dichotomy. The facts and figures speak for themselves. Other
people can indeed match and better him!
Last Updated: 3 April 2010