Carrot facts: Carrots were originally grown in their original colors of purple, yellow and white. In the 17th century, Dutch growers cultivated orange carrots, a variety that had more beta carotene causing the orange color, as a tribute to William of Orange – who led the the struggle for Dutch independence – and the color stuck. 

Purple carrot cake is a real dessert and I found it with a Google search. There are several recipes to be found! While I've not tried any personally I certainly would like to. Drop me a comment if you do!