I don't think you need much explaining here... why won't they stop moving!

What: This effect, and honestly the largest body of work you’ll see when you look into both optical illusions and illusory motion has been created by Japanese artist Akiyoshi Kitaoka, a true master of the art. If the illusion didn’t immediately hit you, there is no animation at all happening within the illusion, it’s 100% your brain playing tricks providing a weird spinning motion in the peripherals of your vision.

How To: You can change the colors, spacing, and sizes here, all of which should largely still give you the same effects, although if you remove the contrasting a lot the motion should largely fade away.

Explain it: It’s mentioned a few times on Optical Toys that its a little abstract, but again the Wikipedia description gives a relatively clear outline to the current thought reasons:

Apparent motion in optical art has been suggested to be caused by the difference in neural signals between black and white parts of an image. While white parts may produce an “on-off” signal, the black parts produce an “off-on” signal. This means for a black part and a white part presented simultaneously, the “on” part of the signal is separated in time, possibly resulting in the stimulation of motion detectors. [2]

Cites and Extras:

I've researched these illusions in my spare time but am clearly not any kind of expert and my explainations are pretty smooth brained, if you find something mis-cited, earlier examples, or general mistakes please new let me know via, be kind!