Blue food coloring came from indigo, or from Prussian Blue. Prussian blue originated in the early 1700’s, and the name is said to have come from the actual dye used to color the Prussian military uniforms. (Prussian Blue has been approved to help rid the body of radioactive contaminants, but the CDC has noted that the Prussian Blue coloring is not the same as the FDA approved compound Prussian Blue, i.e. you cannot self-medicate using artist’s colors.)
According to Wikipedia, the formula for Prussian Blue is:
Indigo is made from plant extracts, and from synthetic processing.