This picture shows what happens when you add chromium salts to the alum solution before it crystalizes. Chromium is included in the resulting crystal structure and imparts a purple colour. The intensity of the colour will depend upon the amount of chromium included.

Note that the shape of the Alum crystal is the same as a pure Alum crystal. It looks a bit like two pyramids stuck together along one of the faces with slightly flattened tops and squared edges.

To see what a "pure" Alum crystal looks like, Click Here.