According to Vivillon's Pokedex Entry, they have different wing patterns depending on their original location in the world:
Vivillon with many different patterns are found all over the world. These patterns are affected by the climate of their habitat
So I've been doing some research, and it seems the pattern is determined by the real-world location of the 3DS in which Scatterbug was first caught, in some countries down to individual states/regions.
So, What are the locations I need to trade with in order to get all the different patterns?