You can as long as you change your region-settings before starting the new game. My 3DS is locked to the PAL region and I have access to all of Europe, Australia, New Zealand and large parts of Africa. Because of this I think I can get 13 of the patterns just by restarting. Modern, High Plains, Elegant, Moonsoon and Savanna are the only ones I can't get by restarting, but the 3 first mentioned are already very easy to get through trading.Resetting doesn't work unfortunately, so yea. :( it's region locked meaning you can't actually do that unfortunately.