The Dutch tessellation whizz M.C.Escher was fascinated by transformations from one tessellation to another, for example in his series of prints Metamorphosis. I’m sure he would have explored animated versions if it had been practical in the 1940′s. So I’ve borrowed a couple of his motifs and animated them. I showed an animated transformation in an earlier post, but that was between two designs that shared the same kind of symmetry. (See the earlier tessellation tutorial for how these tessellations work. If you like technical detail, my earlier animation was of two motifs based on Heesch tessellation no. 11). Sticking to just that one kind of tessellation meant that the corners of each cell of the design had to remain stationary, and only the edges of the cells transformed. This new transformation is a bit different, because it’s not just a transformation from one motif to another, but between two different kinds of symmetry pattern – Heesch nos 17 and 18 in the tutorial – and the corners of the cells of the pattern are not fixed.

In the earlier transforming animation, the design transformed in space, across the image, as well as transforming in time. If I’ve got it right, (I’m not 100% sure about this), that kind of time plus space transformation is not possible in an animation if the corners of the cells of the tessellation change position, as in my new tessellation above. So in this new animation, there’s no change from cell to cell across the design, and all the cells transform together.

I’m fascinated by the artistic possibilities of these kinds of animation, and one aspect of it is to do with what you might call the dance rhythms of the animation. Here’s a variation on the new animation, speeded up and with an added wave that gives a quite different kind of pulse to the design.

These animations are bit monochrome for the moment – colour is on the way, but I’m on a steep learning curve with file sizes, compression etc.

The illusion of movement when a series of images is animated is one we take for granted nowadays. However, here’s a small world first (I think) as new example.  It’s a new Leonardo cartoon.  Actually, there is a Leonardo cartoon already, THE Leonardo cartoon, in London’s National Gallery.  But that’s not a movie. Art historians use the term cartoon for full size drawings for paintings.  But now here’s another Leonardo cartoon, and this one is an animated movie. Maybe a bit short, that’s all.  

Leonardo often made anatomical studies from viewpoints in a strict sequence as if moving round the specimen. Some years ago leading Leonardo scholar Martin Kemp pointed out that one famous set of studies, of the shoulder and arm with superficial muscles exposed, contains so many drawings it’s almost cinematic. In fact there are nine views, from three different sheets, which can just about be combined. The drawings are in the British Royal Collection. They have a great website, and here’s one of the Leonardo drawings, showing four arms.

Nine views is just barely enough for a slightly rapid animation.

Leonardo’s observation is so consistent that I only had to adjust overall proportions and contrast a little bit in some cases, in order to combine drawings from different series. It might be possible to make a smoother animation with more adjustment of the images, but I wanted to interfere with them as little as possible.

An effect that in some ways is even better is possible, with just the last two frames in the sequence.

For Leonardo in general, a fun site is the BBC one.  The Wikipaedia Leonardo entry is very good too, with stacks of detailed info.

My short movie may be the first made entirely from a sequence of Leonardo’s own drawings, but it’s not the first based on individual drawings.  Some brilliant, very professional animations were made from Leonardo drawings, for a show at London’s V&A museum in 2006/7.  (I believe the animation was done by Aardman of Bristol).  They developed their own sequences of images from individual drawings, of geometric shapes or machines, which they projected as 3D reconstructions, and then rotated and combined by computer.  I’ve found only one example still on the WWW, but it’s a beauty, based on his drawings of the regular geometric shapes called regular solids.

Here’s a new kind of never-ending stair (I think).  It’s like the famous never-ending staircase seen from above by M.C.Escher, called Ascending and Descending.  However, in this new staircase instead of figures doomed to go downstairs for ever we have penguins destined to walk away from us forever.  It’s based on the geometry of the object in my post on paradoxical size-constancy.

Here’s an animated version:

Like Escher’s famous impossible staircase, (and also as with the impossible tribar), the effect depends on our seeing a scene from a viewpoint from which points that would be at different distances from us seem to connect up. Here’s a view in more usual perspective of one configuration that would give rise to the ever receding staircase above. The trick depends not just on getting the alignment just right, but also on suppressing the usual perspective cues.  Size diminution with distance is the most important one.  The other is aerial perspective, in which contrast flattens out and colours get bluer with distance. I’ve put them both back below.

For more on staircases like Escher’s famous picture Ascending and Descending …..

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Heads that present one character one way up and another when rotated have been favorite illusions for over a century. Here are two heads from a cartoon story I devised about a boy who gets stuck in a weird hotel. The receptionist and chef, (Mr. and Mrs. Turner …. ) seem OK at first, but then transform into two sinister old men when their heads rotate.

For an animation of Mr. and Mrs. Turner see below:

There are loads of great rotating heads at:

http://members.lycos.nl/amazingart/E/6.html Rotating Heads

I love tessellations. Here’s quite a complicated example, with a transformation running across it, and an added graphic twist.

Want to try your own tessellations? There are software short-cuts you can use but to really get the hang of them, do them by hand, with a graphics package on a computer. (I use the graphics facility in a full version of Photoshop, but any capable graphics package should do the business. You will need to be fairly handy with it before you start doing tessellations, however). Or you can also really do them by hand, with tracing paper and pencil.

For an extended tutorial, see my tessellation tutorial, or visit another page with outstanding “how-to-do-it” demos.

Note added in March 2011!  If you are new to tessellations, first watch my later post with an animated demo of how tessellations work.

or for demos plus brilliant examples:

http://www.tessellations.org/mygallery16.htm (great examples)

For M.C. Escher’s tessellations see:
http://www.mcescher.com

Here’s my animated tessellation: