It's the color scheme. I think in matplotlib it's called "hot". I do a lot of 2D kernel density plots that by having a black zero level and dozens of contour levels produce a smooth look with aesthetics similarities to this. I used to use that scheme because "heatmaps" but stopped because of the pulsing illusion.

I'm not sure if this image is real color or just lightness value and they used a color scheme for drama.

I think my eye is trying to bring it into focus. It is like when the camera on your phone can't quite figure out what it is looking it and keeps adjusting.

I suspect this is because it's extremely blurry, if you watch it on a large screen it might trick your eye into trying to refocus, obviously without success.

Interesting that so many people see this but for me it's absolutely static.

Yes, reminds me of the Eye of Sauron.

Yes, fascinating! If you shift the focus of your eyes from the outside to the inside of the hole, it seems to "pulsate"

looks like the image data was cleaned up with bicubic interpolation, or something of the like.

https://en.wikipedia.org/wiki/Bicubic_interpolation

I don't even have to move my eyes, I stare at it and it's constantly moving away from me. I had to check that it's not actually a movie. Strangest thing.

Yes, and I also see a spot in the shape of it after looking away, though that may just mean my monitor is too bright

Some time ago I've seen a picture over the Internet where the description said the more you see it "moving" the more likely you're stressed.

As for the black hole, looking it at full screen I see it pulsating a little.

Yes if you dance your focus around the image, it appears to pulsate. Probably your pupils constricting and dilating due to the high contrast in the image.

It does look like it pulsates to me! That's an interesting illusion :)

Stare at it till there are two, then have fun snapping them in and out.

Relieved it isn't just me

moving the picture on my screen caused some eye bug

You mean to tell me this is not a gif?!