How do I get the movement pattern of bullet hell games?

I've been struggling for some time trying to find specific tutorials about the mathematics and coding involved in the spreading patterns of particles/sprites/bullets/enemies in this type of games like touhou series, but without any luck. Any help is appreciated.

some examples who may apply for what I'm looking to achieve.

https://vimeo.com/126033836

I believe it's not too hard when you understand how to utilize loop. A Bullet usually move in one direction at certain angle. So a swarm of bullet spread from one point to point. Same principle with 'seeking bullet' too, only the angle of motion were updated each time.

I should make an example though, maybe tomorrow.

Here an example already exist:

https://dl.dropboxusercontent.com/u/659 ... aving.capx

https://dl.dropboxusercontent.com/u/659 ... ssile.capx

thank you for the answear, but it is still unclear how can I rotate, mix, multiply and work with reflectors in many ways, controlling everything from mathematical equations like the Fourier Transform, dragon curve, golden ratio, sorting and even fractals.

Here an example :

https://dl.dropboxusercontent.com/u/659 ... ttern.capx

See my posting below to get an idea how to reflecting bullet:

viewtopic.php?f=180&t=164607&p=996119&hilit=bubble+shoot#p996119

thanks, cheking your example and post as well!