For those who don’t know, a favicon is the graphic that shows up in the location bar and bookmarks of modern browsers. They’re great visual clues that help you remember what’s on a page.
It is possible to have this icon animated, at least for some browsers. DON’T DO IT.
Animated graphics are designed to catch your eye. Once your attention is caught, you’re supposed to understand a message and respond. That response takes you to a web site. If a favicon is up, then you are already on the site, so animation just catches your eye and distracts you from the site. Anyone who thinks distracting viewers from paying attention to their site should get out of the business and consider a career as a utility pole.
The other possible thought behind an animated icon is that in a sea of tabs and bookmarks, the animation calls attention to your site. That might work, but if every icon is animated, then the result is a sea of irritation, so it’s not a strategy that will work for long. As far as tabs are concerned… I just visited these sites, I can recognize your icon without having it wave at me. In fact, the second time it interferes with my attention, your tab will get closed.
Summary: Animated favicons have lots of drawbacks and little upside. Just say no.