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 …..
Here are some crazy stairs. Look at the stairs leading up to the balcony, and at the foot of the stairs you’re looking down on them from above, whilst up by the balcony you’re looking up at them from below. Nothing wrong with that, in a perspective view, but these steps are in a parallel projection, which forbids it. As a result, the side of the steps that’s furthest from us, next to the outer wall down at ground level, has somehow twisted to become the side that’s nearest to the viewer up by the balcony, and vice versa. There’s a different twist to the stairs at the foot of the image. On those, if you start, say, on the right, you’ll find that the flat step surfaces have become vertical risers once you’ve passed the half way mark.
Update May 2012! There’s also a later version of this scene. I wanted to give it another go, because these stairs do have an extra twist to them …..
For years I’ve wished someone would make an animated cartoon in which the events depend on the kind of visual transformations we see in many illusion pictures. It won’t be easy. Salvador Dali loved effects of these kinds, and helped sketch out a scheme for a Disney movie (though not one with a real storyline) in 1945/6. It’s called Destino. It didn’t get made, until Disney’s nephew Roy Disney made a version in about 2000. I don’t think it was so successful, but it was a fascinating chance to see what works, and what is less successful when animated. Take a look at a trailer and decide,
I reckon Goo-Shun Wang’s wonderful, recent animation of a character trapped on an Escher-style, never-ending staircase is far more successful:
To explore the kind of effects I think might work in a narrative, I devised a couple of still-picture cartoon stories. Here’s a pair of frames from one you can view on the www, in which the characters are almost trapped on another never-ending staircase, when a spiral stair suddenly transforms:
Check out the whole thing at:
it also includes loads of hints on drawing illusion pictures.
Here’s a demonstration of one of M.C.Escher’s famous pictures, the Waterfall. (Just put Escher Waterfall into Google Images to see his version).
First of all, you need to understand how a famous “impossible figure” called the tribar produces its effect.
One the left, in the picture above, we see the tribar as an impossible figure. The top of the vertical bar to the left seems to be at both the nearest point in the image and the furthest point at the same time. In the image to the right, seen from a slightly different viewpoint, there’s no problem. The top of the vertical bar really is nearest to us. But seen as to the left, with the arm exactly aligned with the end of the arm to the rear, our brains go for the option that bars are connected as the most probable configuration – even though it’s impossible.
If you are good at fusing stereo picture pairs without a viewer, you’ll find these two images will show the tribar in 3-D. For a guide to how to view 3D picture pairs without a viewer, in “cross-eyed” mode, try:
There are other sites if you search on “viewing 3d picture pairs” or similar, and also animated guides on Youtube.
Now for Escher’s Waterfall. On the right below is my stripped down version. The water seems to be flowing uphill, and then pouring down to the bottom again. But then compare the right hand image with the small middle image: the configuration is just two tribars, one on top of the other. And on the left, with the vertical posts sawn off, so that our brains don’t have to connect them to the zig-zagging channels, the whole configuration seems to recede horizontally as it should, instead of stacking up impossibly.
Note added 16/5/17: There’s a brilliant movie demo of this on Michael Bach’s illusion site.