Creating particle systems for advanced effects

A particle system is a special technique that uses many small particles (images or other graphic objects) to simulate effects that are hard to get using other render techniques. Examples are fire, rain, fog, explosion, and many others. Refer to the following image for an example:

Fire particle system

Particle systems might look difficult at the first glance because of the amount of parameters you can and often have to configure to create one, but the main concept is quite simple. You have a particle, in most cases this is just a small image, and you have an emitter that emits many copies of that particle.

Of course, there is not much sense in creating every particle at the same position, with the same size and rotation, since these particles will just overlap (just like if you add the same sprite many times in the same position) and all you will see is just one particle. This does not seem like a lot of fun. However, if we set the different movement...