Some heckin' cool particles. See it live!
The renderer is roughly speaking a ray-tracer, and it is implemented as a WebGL fragment shader.
First, we define a scalar field assigning a "density" to each point in
space. Formally, if the particles have positions r1,...,rn, and we want to
calculate the scalar field at a point v, the scalar value is given by the sum
of 1/(1+|v-ri|^2).
Each of these terms are big when v is close to the given ri, and each term
slowly fades to 0 as v gets far away. So, the scalar field represents how
much a particle fills a location v in space.
Then, to render, I apply the same principles of ray tracing. To be able to do ray tracing, I need to be able to calculate the "light" coming in along a ray.
Instead of following the rays backwards until they hit an object/light source,
I compute the line integral of the scalar field over this ray. Rather than doing
this numerically, I can actually explicitly find the integral. It turns out to
be arctan something or other.
On the physics side of things, each particle just has some sort of simple gravitation (inverse square law), a nearby repulsion force to bullet through paper sort of effects, and some ad-hoc friction.
I'm using something like verlet integration I guess? It's just doing euler's method except averaging velocities instead of using initial/final velocity in a timestep.