Michael Bach a scientist of visual function, and he made a clever site that shows off 141 optical illusions — using interactive doodads that let you tweak different parts of the illusion, to figure at what point the illusion breaks.
This interactivity, these breakpoints, turn out to be incredibly useful in grasping the quirks of our visual machinery. Everyone's perceptual apparatus is tuned slightly differently, so being able to tinker with the illusion is a great way to let us individually see how and where the illusion coheres.
A good example is the "stepping feet" illusion, where a pair of yellow and blue feet appear to be periodically speeding up and slowing down, relative to one another, as they orbit the center of a circle …
Bach lets you click on a button to remove the black-and-white background, showing how the two feet are precisely in sync; so you can toggle back and forth and try and spy what your brain is doing. (Sorry that gif is so fuzzily low-rez — I'm lame, couldn't figure out how to save it in higher rez. They look much more sharp on Bach's site.)