Human Figures 2

Based on Girl 1

The examples show additional aspects of the Girl 1 tessellation, namely:

• • Experiments in 'improving' upon the initial figure 

  • The girl adapted to a Kaleidocycle 

  • Linear metamorphosis 

  • Hexagonal, ‘starburst’ metamorphosis

Experiments in 'improving' upon the initial figure
Before showing a definitive motif is an intermediary stage where, although the basic life-like tessellation is established, in this instance a girl motif, it might still be possible to improve upon the motif, as this drawing shows. Here, I try out various experiments in the desire for a potential improvement of the verisimilitude of the figure.
As ever, when making one change, this also affects the ‘other’ side of the line. For example, raising the hemline of the dress also affects the hair, changing its length (and vice versa). This, simply stated, is a typical trade-off in designing – will changing one aspect affect the other, and to what degree? For example, if one change is made that is only slightly for the better, if the other side is affected disproportionately, i.e. much worse, then overall the tessellation is made inferior than it was before, and so this would not be proceeded with.
Another experiment shown is at the bottom of the dress, where, rather than being of a ‘smooth line’, is instead shown pleated. On the other side of this line, it can be seen that this results in the hair being made wavy. Again, is this an improvement? Arguably, it is, on both counts. A dress can be made pleated, and hair is naturally wavy, so both factors arguably improve on the initial, somewhat simplified outline. Although in this instance the improvement here is slight, by such small, though significant advantages, the figure is noticeably enhanced.
Therefore, critical judgment comes into play as to aesthetics overall when experimenting in this way.

Kaleidocycle
Here I show the girl motif adapted to a Kaleidocycle. This is designed for two pieces to be joined together at the tabs. Colouring is left to the user.

Compositions
Upon completion of a life-like tiling, it is possible to develop this, both metaphorically and literally, with compositions based on the underlying tile. In this particular instance, with the girl motif based on a rhomb, the obvious formats are of a rhomb and hexagons (the latter of three conjoined rhombs).
Now, it will be observed that both the tile and motif are mirror symmetric along the long axis (aside from the crossing of the legs, for reasons of aesthetics, which I consider a pedant quibble as regards symmetry). Now, an obvious thought is that if this is so, when undertaking a development, it would be very pleasing to retain this feature. That is, a development from a rhomb to the girl motif, all the while preserving the mirror symmetry of the rhomb. Can this be done? Yes. So, on the premise that a symmetric development is superior, I here show some compositions based on this type. The examples below show two different compositional forms, a ‘linear’, and a ‘hexagonal starburst’.

Girl linear composition
The premise of this is of a linear development from rhombs to a girl motif, all with the interpretation of (symmetrical) development. This example more clearly follows Escher’s example, namely Metamorphosis I, albeit with subtle differences, concerning the shading, rather than that of the more important development process. As can be seen, in my version, the development at all stages is mirror symmetrical, and so aesthetically is most gratifying indeed, for obvious reasons. Naturally, an asymmetric development would be less pleasing on the eye.
Of interest is that Escher, using drawing 4, Chinamen, shows a somewhat like development, Metamorphosis I, which (disregarding the town) is essentially a development of rhombs to a Chinamen. Here, although the motif is indeed mirror symmetrical (aside from the patterning on his shirt, which I consider a pedantic quibble as regards symmetry), the development proceeds in both a symmetric and asymmetric manner. Ideally, of course, this would be symmetric throughout. An open question is why Escher did this. Upon my own investigation, Escher could have shown a symmetric development for his Chinaman, and so here it is obvious that he blundered. (In his defence, this was the earliest work of all this 'development' type, and so one could thus expect that as he was still developing his procedures, he overlooked this superior possibility.) This makes for an ideal comparison between our respective efforts. Simply stated, Escher's is non-symmetric, whilst my own is symmetric, i.e. inferior and superior respectively. Again, another instance of Escher’s occasional shortcomings. He wasn’t perfect…

Girl Hexagonal ‘Starburst’ composition
The premise of this development is of a ‘starburst’, within an overall hexagonal format, this being derived from the unification of three rhombs, of which the connection is obvious.
The premise is of a (symmetrical) radial development from a centre point (a ‘Big Bang’, if you like) with the development proceeding from the centre outwards, with rhombs per se, to eventually the outer rim, with fully-formed (symmetrical) girl motifs, all the while retaining the symmetry in the interim.
Note that it is possible to reverse the process if one would so wish, with the rhombs on the outer, with girls at the centre. However, I consider this to be the ‘weaker’ of the two options, if these are compared directly. The reason for this is that from the human perspective, the more ‘interesting’ (and numerous) life-like motifs (girls) are shown, rather than ‘less interesting’ rhombs.

Page History
12 December 2025. Upgrade from Classic Sites.  The conversion did not require a widespread revision. Captions had become 'free floating' (detached), which I reattach. Corrected basic errors in the text with Grammarly, pending a later in-depth review. In general, the piece is overdue for a review, although it has broadly stood the test of time.  

No date was given for when the page was established, but it was at least 2010 ( I lack the will to plough through checking numerous years for when exactly).

Last Updated: 26 May 2010