Unique at-home Science Experiments! with Physics Girl

One reason why the food coloring didn't stretch uniformly in milk like it as it did in water, could be that milk contains of droplets (emulsion) of lipids suspended in water. The dish soap might also interact with those lipid droplets, randomly distributed in milk that could lead to different patterns. 

Fun fact: These droplets scatter all spectrum of light so effectively that milk appears to be white.