What materials can be used to make pictures / paintings, where the colors change as the direction of the sun and hence the angle of incidence of the sun rays hitting the art structure changes? I'm interested in both indoor and outdoor structures and materials. I was thinking of cardboard-or-similar material placed as vertically running painted wedges, but I'm not sure if that would work.
I think what you are looking for are called “chameleon paints”, but I cannot recommend you use cardboard. It is better to suited to non-flexible surfaces.
Check out chameleon car paint or search on amazon for it. Most automotive shops should stock it.
Another option might be to look for iridescent paints, but they just get a bit shinier depending on the angle that light bounces off the surface into your eye.
There are "optically variable inks" that change color depending of the direction of the light. They're used on currency as an anti-counterfeiting measure and have found their way into art. I know they're sold in bulk quantities (1-2 kg minimum); you can check out https://www.alibaba.com/showroom/optical-variable-ink.html. There may be resellers offering smaller quantities but I haven't researched it.
My understanding is that the chameleon paints (which are based on ChromaFlair pigments) described in Nothingismagick's answer are a different technology. However, counterfeiters sometimes use the paint to approximate the ink since the color combination used on US currency can't be purchased.