i have an urgent experiment and i want to know if a Calico Fantail Goldfish will change color if food color is added to its diet and surroundings.

If you mean food coloring, it should not change the color of the goldfish whether in food or the water. Food colors degrade fairly quickly are aren't taken up by the tissues in the fish that create color. Now, adding natural caretonoids to the diet such as from carrots, orange and green veggies, etc. can brighten up the color of goldfish. They will not however change the genetic makeup of the colors or their pattern. Goldfish do change colors over time although calicos such as a calico fantail have probably completed their color changes much faster than other varieties and should not change their pattern anymore once they are a few inches long. Color changes from diet will be most obvious in the white areas of the fish which may turn yellowish for example if lots of B-carotenes are added. Being water and not fat soluable, unnatural food colorings will not have an effect.