It wouldn’t be easy to find two more different artefacts than these.  On the left is a silk velvet embroidery made in Italy about five hundred and fifty years ago.  On the right is a shield from Koave in Papua New Guinea, made in the last hundred years.  Yet they both use exactly the same graphic device, a figure/ground effect.

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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.

I wrote in an earlier post about how effective decorative motifs can be if they are ambiguous visually or in some other way a bit of a challenge for perception.  Why that should be is a mystery, but here’s another of my favourite examples, decoration from a pot made in Corinth, Greece, about 595 BCE.

The pot’s in the British Museum and I guess it’s about 70 cms high.  Here’s (nearly) the whole thing. 

What’s unusual about this decoration is the way the rosettes and other little decorative motifs in between the animals have expanded to fill almost all the space.  In earlier Corinthian decoration, they were much smaller, just little motifs floating in the pale space round the animals.  Over two or three decades, painters made them fill more and more of the space, until they left only an outline round each animal. I reckon that shows up better in a version of the first picture which I’ve played around with, and reversed so that the pale outlines are dark.

What’s perceptually puzzling about that, I reckon, is that the brain can’t quite decide whether, in this reversed version, these are animals with strong, dark outlines on a pale background, or pale animals silhouetted on a dark background.  If you like doing your own paintings, it’s a brilliant effect to play with, and works just as well with modern motifs, human figures, cars, aeroplanes, umbrellas, you name it.  

I reckon some images look beautiful because they bamboozle the brain processes we normally depend on to make sense of the world.  I don’t know why  that can help make patterns and pictures look beautiful. Nor do I think perceptual puzzlement is the essence of art, or anything like that.  But just from a practical point of view, if you are an artist (or a composer, poet or architect), a motif that’s puzzling can seem to offer a stepping off point for aesthetic effects.

Here are two beautiful examples from architectural decoration, both just about 500 years old.  The first is the dome of the Mausoleum of Sultan Qaitbay in Cairo.

What’s puzzling about this is that a single line segment can be part of the edge of an object, such as a star, and at the same time part of a line that meanders over the whole surface.  Edges don’t behave like that in everyday vision.  Here’s the dome with added lines, left below, to show what I mean. Look at the segment that is labeled with both blue and yellow lines.  

Then note that you can do just the same with the lines that outline the octagons on the ceiling in the picture to the right – every edge is also part of a fan of lines.  That ceiling is in Christchurch Cathedral in Oxford, and we even know who designed it – William Orchard, the Master Mason.  Now we’d call him the architect.  Here’s a picture showing a bit more of the ceiling.

I don’t think it’s just the puzzling features that make these patterns so beautiful.  Interlace patterns like these look like small segments of patterns that go on for ever, and in both Christianity and Islam were a metaphor for perfection and heaven.  And that’s how I reckon artists turn perceptually puzzling effects into something more than amusing images – they choose motifs that are also metaphors for some deeper meaning.

You may be more familiar with interlace as a technology for managing video images.  For interlace as a pattern motif in christian art, see the Wikipedia article on Celtic Knots.  Or try here to find out about interlace patterning in the context of islamic faith.

Everyone loves ambiguous pictures. The most famous one from academic psychology is the duck/rabbit illusion. Here’s my version of it.

But if you want chapter and verse on the original, try:
http://mathworld.wolfram.com/Rabbit-DuckIllusion.html

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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.

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:

What is a tessellation?

Any regular pattern consists of identical areas, which repeat without overlaps or gaps. An obvious example would be tiles on a wall. However tiles are usually geometric shapes – rectangles or squares as a rule, though triangles or hexagons would be possible too. In a tessellation, the cells can have wiggly edges, but still fit together like jig-saw pieces.

If you try to make a pattern like that out of any old shape, you will either end up with gaps or overlaps:

To make cells that tessellate, you have to follow a recipe. There are a whole set of recipes, but to get an idea of how they work, take a look at just one.

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