Animated brushes are officially called ‘image hoses’, and they're quite fun. They are basically brush tips with multiple image files.
The typical way to make them is to first draw the ‘frames’ on a small canvas, per layer:
You can use the Alt + shortcut on the layer thumbnails to isolate layers without hiding them.
When done you should have a mess like this.
Go into the brush settings (F5 key), and go to predefined brush-tips, and click stamp. You will get this window.
And then use style animated and selection mode set to random.
Krita uses Gimp’s image hose format which allows for random selection of the images, angle based selection, pressure based selection, and incremental selection.
When you create a brushtip, Krita will automatically switch to it for the current brush, but you will always be able to find it in the predefined brushes tab.
And now you can use it to paint trees! (for example)
You can also use animated brush tips to emulate bristle brush tips that go from very fine bristles to a fully opaque stamp based on pressure, like a dry paintbrush might do. Or make incremental patterns like the ones you see on porcelain.