I’ve just found a visual illusion that gives a striking impression of motion from a static image. It’s entitled ‘this picture is not animated’, which, like anything eye-catching on the internet, immediately made me check whether it was or not.
With many of these sorts of illusory motion images, you can ‘stop’ the motion by simplying viewing them through a very small aperture.
Putting a pin through a piece of paper and viewing it through the hole does the trick, but so does making a small viewing hole with your fingers.
As you can see yourself, the picture stops ‘moving’ when viewed like this, but starts again as soon as you view it normally.
This also prevents stars from twinkling when you view them at night. The traditional explanation of ‘star twinkle’ is that the light gets bounced around as it travels through the atmosphere, giving it the twinkling effect.
In fact, by looking at them through a small hole, you’re preventing any effects caused by your eyes moving about.
The fact that the illusion stops moving and the stars stop twinkling when you do this, suggests that the way our eyes scan across the visual scene is an important part of why we see the false movement in these sorts of images.
Because of this, you can ‘speed up’ and ‘slow down’ the false movement in the visual illusions by changing how often you move your eyes.
UPDATE: Thanks to celeriac for posting a link to a scientific paper which explains this effect.
Link to striking movement illusion.
Mind Hacks 
This unattributed illusion was created by Akiyoshi Kitaoka at Ritsumeikan University in Japan. He has a very large site of illusions here:
http://www.ritsumei.ac.jp/~akitaoka/index-e.html
The mechanism of the illusion in question is explored in this paper (Conway et al. J. Neurosci 25(23):5651-5656):
http://www.jneurosci.org/cgi/content/full/25/23/5651
Since stars’ twinkling is readily observed by telescopes whose imaging devices are fixed solidly to the earth, I don’t buy eye movements as having much to do with twinkling. However in the case of the almonds illusion, any refreshing of the image on the retina (such as by eye movement) will elicit the illusion.
I guess there’s two phenomena here. The first is the fact that light is indeed affected by the atmosphere, the second is whether the naked eye is sensitive enough to detect this phenomenon. The fact that the pinhole trick remarkably reduces the twinkling effect, suggests that they may be different.
A group called the Neural Correlate Society sponsors an annual competition for the best visual illusion (one that speaks in some way to the “neural underpinnings of visual illusory perception”).
Their extensive archives of winners and notable mentions going back to 2005 is where I first discovered the motion-without-animation illusion above, and their site showcases many other interesting illusions.
http://illusioncontest.neuralcorrelate.com
(check out the “Image archive” link)