One of the first was "rain" [1] by semi-randomly walking blue pixels down the screen and not clearing the buffer. But then the screen would go all blue, so I made them pop up to the top and do the same walk but as black pixels. It came out as a rain-on-the-window effect:
https://x.com/Rendello_/status/1231426590380318729
Eventually, I started just using one pixel and moving it really fast to render scenes. This is basically what raster rending does anyway, but instead of doing every pixel, the random walk will only hit a subset of pixels every frame and will make a really cool scratchy effect.
In PICO-8: https://x.com/Rendello_/status/1258243668626063361
In TempleOS: https://www.youtube.com/watch?v=W-wpUcDFZaI