An lesser aspect, albeit still worthy of note concerning examples of representational tessellations is one of which I term as aesthetic and non-aesthetic examples. These are defined as tessellations whereby the motif/s remain in a upright orientation in relation to each other. Such a classification has a bearing of which tessellations are assessed as of a lesser or better quality, along with their potential application to the next ‘optional' stage of using these for ‘picture compositions' and/or effects such as counterchange. For illustrative purposes, Escher's tessellations are discussed below.
Orientations of Motifs
During the course of designing tessellations, a variety of polygons, along with different principles of symmetry (translation, reflection and glide reflection) are employed. As a result, the motif, depending on the polygon and symmetry principle can appear in a variety of orientations. Consequently, the motif can appear upside down in relation to contiguous motifs, and, again depending on the type of motif, this thus leads to incongruous situations. For example, using drawing 8, Horse, it will be seen that these are shown in both upright and upside down orientations. Consequently, aesthetically, as this is plainly a ridiculous orientation of a horse, or is, as Escher stated (albeit not directly referring to this tessellation) ‘… an absurdity' (in his notebooks, Visions of Symmetry, page 77). In contrast, examples where the motif(s) remain upright, as in drawing 18, Birds, are self evidentially better, of which these are thus described as aesthetic. As such, the above descriptions are thereby applied arbitrarily whatever the underlying tessellation system is, and therefore examples can occur whereby the motif itself is quite superb or alternatively very poor, and yet can still be described as aesthetic or non-aesthetic as according solely to the orientations of the motifs.
As mentioned above, such matters of orientation should be taken into account if the tessellation is used for a subsequent purpose, as in picture composition, in which the motifs are 'developed', and/or with a counterchange, as was Escher's general custom. For example, the horses of No.8 are less than ideal, as upon a 'picture composition' the motifs will appear upright and upside down – an absurd situation, as why should a horse appear in such an unnatural orientation? In contrast, the birds of No.18 are ideal for this purpose, as the motifs will remain in a sensible, upright orientation. Consequently, in this matter, only the most appropriate example would be selected for such additional matters, as Escher himself did, as he 'ignored' the unaesthetic horses whilst choosing the aesthetic birds, which were used for the print Day and Night.
Created:13 December 2005