algo

(a) create a looping fireworks animation (non interactive). You will need to reset or restart particles every so often.
(and then we’ll figure out how to save this as a screen saver for your mom!)

(b) since you know how to position things in a circle using the formula:
x = x_orig + radius * cos (angle);
y = y_orig + radius * sin (angle);
think about how you could use sinusoidal information to start all the particles with some interesting positions / velocities. Instead of using random, use sinusoidal information (in any way you want) to make the sarting positions/velocities of these objects interesting.  can you use sin/cos to make the movement or drawing of the particle more interesting?

(c) Besides evidence to the contrary, particles don’t have to be just circles!  you can draw them however you want.  Can you create an interesting effect with transparency or by using images?   Can you use parameters, like velocity to control the way these objects are drawn (like, they get smaller as they slow down, or more transparent, using angle of the velocity to rotate, etc).  Think about trying to create a natural phenomenon or make something really nice looking.

advanced:

(d) hook up the drawing code (from the lissajous example) to a particle so that the particle draws a trail of where it has been. see if you can make this trail fade out (like a comet) : ) Use alpha or some other method…

(e) Make a funky, expressive drawing tool with particles.