The classic book references for programming shmup bullet patterns (in Japanese) are シューティングゲームアルゴリズムマニアックス and シューティングゲーム プログラミング, but in general, a lot of this stuff is folk knowledge and isn't communicated well outside of trial and error until you get something passable. I would suggest looking up web tutorials and game source code and learning from that (also will mention the Development sub forum on shmups.system11.org being quite useful).

Thank you !