A good place to start is with multiple compositions. You can mimic this effect using just solids and blend modes. I would start with one composition and animate the lines of one particular color first, then duplicate that composition and switch the colors. Repeat until you have covered all the colors desired, then place all the color bar comps into a larger comp and play around with the blend modes until the desired effect is seen. A good book to pick up, that talks about in detail about a project similiar to this is “Adobe