Research – Tessellations

When looking at the idea of interlocking medals, and in researching the work of M. C. Escher I stumbled on the term “tessellations”. A tessellating image consists of a series of repeating, interlocking tiles which contain no gaps or overlaps. As always, Escher is one of the main artists in the field with his mathematical and geometric based art. Tessellations can range from very simplistic geometric images, or as in the case of Escher become much more complex.

An example of tessellating shapes

An example of tessellating shapes

two set tessellation

The interesting thing about these shapes is that they can fit together in different ways, each shape can be put together when facing horizontally or vertically, and so with the context of forming an image could have different permutations.

Fish tessellation - M. C. Escher

Fish tessellation – M. C. Escher

This is another more complex tessellation, where the picture has been rotated around 180 degrees in order to fit with itself. While this is certainly interesting, this does not incorporate the reverse side, which is very important in the format of a medal. This would mean that either all the medals in the set would need to be the same side up in order to fit together, and so doesn’t allow so much for the idea of interchangeability that I was hoping to capture. However, perhaps this would be simpler, as they would still be able to interchange in a sequence, for example 5 medals face up could still be arranged 3, 1, 4, 5, 2, and I would then not have to be trying to make the images fit both sequentially and on the reverse side. But this does mean that there would no longer be a strong interplay between the front and reverse sides, which I have previously discussed is a strong feature of the medal in my opinion.

escher pattern problems

Here, using some of Escher’s designs as examples, I am trying to resolve some of the questions I have in relation to tessellations. Many of the shapes I have seen, even though complex, fit together only with rotated versions of themselves, as with the previous example. Others, while seemingly reversed versions of themselves, when analysed closely are actually different shapes which are made to look the same by the imagery on the front, which would involve making a set of medals of different shapes, an idea which I do not like. It is important to me that for the cohesion of the set, that all the medals remain the same shape (with potentially some, but not drastic variation between the form). I don’t think that having a set, several of which cast to a distinctly different shape, would add anything to the piece and would likely only cause more confusion. What is it about those pieces that makes them different to the others? This may change if I did in fact have a reason for making them different conceptually, but doing so simply for the mechanic of having them tessellate is not a strong enough reason in my opinion and would only disrupt the message.

Crane tessellation - M. C. Escher

Crane tessellation – M. C. Escher

This is a much more promising example, where the same pattern has been reversed, and yet still fits together with itself. This allows for both different orders to be made of the medals in the series, and the combination of the front and reverse sides of the medal to be shown and investigated by the user. However, while Escher makes it look deceptively simple, the concept of creating a tessellating pattern, let alone one that can be reversed on itself and still fit, is frankly mind boggling to me and I’m not sure where I would even begin. Another question is, if I were to make a complex pattern as Escher has, what would I make it? Again, this comes back to the issue of imagery and motifs, and this might perhaps become more clear once I settle on this issue, but as of now I am still working in hypotheticals and so can’t think of any shape or form that would inherently strengthen the message of the piece. There is also the fact that it would have to be the same shape across all of the medals, and so therefore would have to transcend the message of each individual piece, of a singular point of change, and express the uniformity and continuation of narrative of the piece as a whole. It would need to be reflective of the fact the medals are a set, which come together to form a whole.

transitioning tessellations

This is another excellent example by Escher, although not using both the front and reverse sides, but of transitioning image while the form of the shape stays constant. This is exactly what I would like to achieve in my medals in terms of transitioning image, where change across the surface is gradual and almost unnoticed, until you compare the beginning and end which are distinctly different from one another.

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One Comment on “Research – Tessellations”

  1. “… the concept of creating a tessellating pattern, let alone one that can be reversed on itself and still fit, is frankly mind boggling to me and I’m not sure where I would even begin…”
    Hi, stumbled upon your blog. Interesting that you would use a tessellation to create your medal. Maybe I can help, if this is still an option. visit: http://www.canyousee.ca where I give tips on accomplishing the task of tessellations in all of the 17 symmetry groups.
    Francine


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