The reason we don't have a formula for it is because it can't exist. The same thing can never exist twice, whether it's brains, blades of grass, mountains, loaves of banana bread, Volkswagens, or anything else.
If you have a formula for my sense of self then you also have a formula for as many exact copies of my sense of self as you have material to make them out of. There is nothing in the formula that determines which is which, just as there is nothing in a recipe for banana bread that determines which loaf is which.