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.
This seems to have exploded on forums and Reddit, but as of yet I cannot find a definitive source of the possible variations, and their locations.
So, What are the locations I need to trade with in order to get all the different patterns?
Best Answer
There are 18 confirmed patterns, and there are people who've managed to Catch 'Em All. Here's a YouTube video that shows them all caught:
These are the locations I've managed to piece together from firsthand experience and digging all over the internet, including various forums, reddit & tumblr posts (linked below).
Locations
Notes
Sources: