Tattoo ink lives in the space between living skin cells. The concept is to choose pigments which are stable because they don’t interact with the processes inside the human body. Black pigments based on iron are very stable and have been used in tattoos for centuries. Iron based pigments for red, essentially powdered rust, exist, but it’s a more burgundy shade of red than some art requires. To get a bright red, you need cadmium (or perhaps mercury, which can be toxic and isn’t used in large quantities). Alas, our buddy cadmium is very hard to make inert in the body. All the little garbage collector cells in the body like to try and remove it, which can smear it out of position. It’s almost impossible to laser, if you ever want your tattoo removed/modified/… .
Yes, there is an easy way to avoid this, get tattoos in black, blue, or green. The copper based compounds used in blue and green shades are much more stable in the body.
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