me it remains an open question whether [this work]
After disecting a selected piece of Eschers work from the previous page, our group then embarked on a task to come up with our own tessellations based on the mathematical principals we discovered in his work. Each member who created the tessellation then penned down their thoughts after their attempts.
Before we begin the group members fully admit that we are no M.C. Escher as such our tessellations can be considered a far cry from what Escher has produced. Then again, it was our first try at something Escher had devoted his whole life to.
addition, even though we knew the mathematical principals behind the
tessellations, we realised that coming up with one is a lot more difficult
than it seems, as we soon found out.
At first sight, my part of the project seems simple enough. I just need to draw a couple of grids, doodle some shapes and repeat the rest of the pattern. Escher’s work contained of several pieces on fish. Thus, I decided to let my subject, i.e. the form of tessellation, be the fish to try to experience and understand more of his concept on tiling using similar approach. Besides, fish seemed undemanding enough.
as I proceed on, I realize that it is easier said than done. Amidst
the frustration of getting the right shape and trying to fit each individual
tile with one another to prevent gaps, I began to appreciate the brilliance
of his work. Many considerations and manipulations had to be made in
order to reach the final piece. A good selection on the type of grid
to base your work on is of utmost importance. The wrong first step will
result in a painful journey later.
The creation of the final piece is mainly through the adjustment of shapes and our stylistic touch and deal not so much with any mathematic principals despite the end product deeming so otherwise.
I first saw this tessellation, it seemed pretty straight-forward: simply
a man under 3-fold rotational symmetry. However, upon closer inspection,
I realised it was pretty amazing how everything fitted so perfectly
into one another. For instance, the space beside one man's face is another
man's hat! When you zoom into the individual units that make up this
tessellation (triangles), they don't seem to make any coherent sense!
However, through the rotations into hexagons, they miraculously start
to form the shape of the men! It took me quite a while to digest the
picture and after analysing it, i realised it was certainly more than
simply rotating men! The amount of precision and detail that made up
the tessellation astounded me.
Though i realise that my tessellation is infinitely simpler than Eschers', coming up with the tessellation itself was not easy Some difficulties involved was resolving how the tails of the dolphins would all come together, and also the conscious attempt to not leave any empty spaces in between. The tessellation finally evolved through a lot of patience and manipulation. It is through the creation of our own tessellations that we appreciate the beauty and genius of Eschers' work to a much higher level.
Looking at Escher’s example of glide reflection (the horsemen) I figured that it would turn out to be quite a simple task. Just draw the object, reflect it, translate and maybe manipulate it a little to fit. However, it turned out to be a lot more complex than that. I had to make sure that no gaps were allowed and that simply by glide reflecting didn’t automatically mean that there would not be any gaps. The animation greatly simplifies how I came about with this particular tessellation but all I can say that it was a lot of trial and error and very little mathematics.
Ironically, I had originally planned to tessellate a series of elephants but somewhere along the way when I was sketching the tessellation out, I realized I could not squeeze the outline of the elephant in correctly. As such it somehow changed into a ram instead which brings me to the next point.
I could have placed any other animal or object into that outline of the ram and it would still tessellate. In fact, it is the outline that is the most difficult to come up with, after that what ever details go on the inside are very much non-mathematical and purely artistic.
In fact I would say that the actual creation of the tessellation is more art inclined than mathematics despite the final outcome having mathematical properties.
I honestly felt that I had the most complex tessellation of all to create. To dissect Angels & Devils was a heavy task let alone creating a tessellation that used its fundamental principals. To fit the elephant and the butterflies perfectly together was such a mind boggling experience that it took me ages to get to the final outcome. However, after much perseverance I finally managed to come up with something that was at least remotely decent.
conclude, I feel that the most difficult part in obtaining this kind
of tessellation is the process of finding out how a pattern is repeated
such that there are vertical, horizontal and glide reflections are all
involved. What Escher did was truely amazing and it is only after I
had a go at it did I fully appreciate his work.