Regelmatige vlakverderling (The Regular Division of the Plane, Escher's Own Writings on TessellationTranslated into English in Escher: The Complete Graphic Work)

Of note is Escher's writings (and more rarely, film) on tessellation, of which, perhaps surprisingly, do not in any way concern themselves with the creation process per se. For example, his major work on the matter, in Regelmatige vlakverderling (The Regular Division of the Plane) is essentially a comment on the examples given (with frequent digressions of unrelated matters), albeit these were specifically designed for the purposes of the book. How the designs came into being is not addressed.

Other writings by Escher include comments he composed for his book The Graphic Work of M.C. Escher, of which this includes 14 of his numbered tessellations. However, these appear very much merely as background sources for the tessellating-based prints, albeit admittedly, being not graphic art in themselves, than their omission of discussion can be argued as natural, being intrinsically subsidiary to the book. Whatever, these are not discussed in the book. Another of Escher's major writings concerned a series of lecture notes for a American tour reproduced in Escher on Escher, in which he discussed both prints and his tessellations. However, once again these do not address the 'how' aspect, bur rather are comments, of a decidedly brief nature. Aside from these three books, Escher's other writings on the 'How' aspect is conspicuously absent. Why should this be so? As such, perhaps unfairly, I am somewhat suspicious as to Escher's motives in all this. Being generous, it is indeed possible that he was more interested in producing the tessellations, rather than in trying to explain how they came about. Indeed, his active period in tessellation was relatively short, curtailed in later life by ill health. Consequently, it may well be that he simply considered detailing such matters as a matter of being sidetracked, the drawings themselves being of more inherent importance. However, a counter argument can be put forward, in that as Escher frequently wrote about other graphic issues, well why not detail by far the most important aspect of his life's work, namely the tessellations themselves? Rightly or wrongly, I believe that Escher wanted to keep the 'secret' to himself, thereby not diluting his star. Furthermore, the preparatory drawings/sketches that underlie the genesis of the periodic drawings, that again would reveal the 'secret' rarely, if at all, are shown. Again, I am most suspicious as to why. In just about all publications on Escher, these are notably conspicuous by their absence. Indeed, most books completely disregard them. As such, the only source for such material that I am aware of is Visions of Symmetry by Doris Schattschneider, who at least does show a few examples, pages 106-108 and 111, albeit even so, only page 111, showing the Horseman drawing, directly relates to the genesis of that particular periodic drawing. During the course of designing the periodic drawings, Escher must have composed many hundreds, perhaps even thousands of such sketches. Therefore, what has become of this material? Did Escher mostly dispose of such studies upon having completed the definitive periodic drawing? This seems highly unlikely given his general approach, with thoroughness in attention to detail and record keeping. Oddly, in contrast to the paucity of the above material, the preparatory drawings for Escher's non-tessellating 'spatial structures' (such as Depth and Spirals) are shown in various books in abundance - why should there be such a discrepancy? Again, rightly or wrongly, I believe that the purpose behind all this is to keep Escher's star solely in the ascendancy, to the exclusion of other people. However, with the publication of all the periodic drawings, the 'secret' can be, if not gleaned, than glimpsed from the drawings.

So, How Did He Do It?

So, utilising Schattschneider's opening line in Visions of Symmetry, how did he do it? Without having seen the preparatory drawings underpinning the tessellations, it is not possible to state categorically that he utilised a certain method/s. However, the morsels given in Visions of Symmetry are most illuminating, of which beyond all reasonable doubt show that he started with no predetermined motif in mind, in which a framework of a tessellating tile had added to it a gently indented line, either of straight lines (as in the case of Horseman), or curved squiggly line. From this initial effort, if he could vaguely discern that the shape had some sort of likeness to a representational motif, he then continued to seek improvements in increasing its inherent quality by successively refining it. Quite how long this took, as a rule, is unknown. Possibly, some drawings were devised more quickly than others. Furthermore of interest are those examples that he considered as failures, which did not lead to a definitive periodic drawing. Interestingly, these are not shown. Quite simply, it is unbelievable that Escher attempted 137 efforts and had 137 successes, with no failures. Interestingly, the 'random line' method appears to be the only method Escher utilised, as the periodic drawings are quite similar in this regard, in that a simple underlying tessellating unit underpins the drawings. So, are there other methods? Well, yes.