I can safely answer this one. These are considered light-interference pigments, so it's both the light and the angle. Changing the angle shifts the color, but moving into a different lighting will also change the colors. Unlike holographic pigments that thrive in full-sun, chromatic pigments often "shine" best in indirect light, where you can see more of the shift at once.
Oh, and here is a fun fact that all us mermaids should REALLY love!! There is a trick for photographing chromatic nail polish in a way that shows the most colors possible: put your nails underwater! The refraction of the water actually bends the light in such a way that you see more colors at once. So a true multichrome tail has the potential to look STUNNING underwater.

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