The pattern a Vivillion will have when it evolves is based on the combination of language and location settings in the cartridge in which it was created. These settings can be manipulated to produce certain patterns, but under any given settings that cartridge will only be able to produce that pattern. When traded, the Scatterbugs and Spewpas "remember" the cartridge they were created in, and will evolve into their native pattern. Note that the 2 Event patterns cannot be bred.
For America, depending on where you live, you can produce High Plains (orange), Polar (dark blue), Modern (red), and Ocean (sunset) patterns.
A full list of current patterns, and an admittedly outdated map of known Vivillion areas can be found here: