What is the name of this moving color pixels effect, for animating a painting? https://superrare.co/artwork-v2/spring-22267
The artwork in the link seems to be based on a painting of a woman, but effects have been added that assign a pixel to each block of the painting that shift in color and contrast across a certain number of frames as part of a gif animation, although the original painting itself doesn't move underneath.

is there a name for this effect?
and could someone breifly outline the steps of how it can be achieved
in software?
any popular examples where this effect is used or first introduced?
This effect is called Color Cycling (or Palette Shifting). Mark Ferrari has a great GDC talk where he demonstrates and explains the entire technique. You can view a bunch of his artwork based on this technique here.
The main idea is that each pixel is painted not with a single color, but as values of a look-up table to a palette of colors. The entire image then cycles through the palettes frame by frame. Assigning colors to each palette to create the illusion of movement requires a fair bit of artistry. Mark Ferrari does this in a software called Pro Motion, but this can be coded in a shader pretty easily.