These options enable customization of the simulation parameters. You'll notice that the original seeds in the simulation are black. Those which have aggregated are mostly red, except for the odd one which is brown. Those brown coloured pixels occur where more than one particle has joined the aggregate. Changing this parameters during the simulation can be interesting, however it will also change the appearance of the aggregate.
By default the simulation takes place on a closed topology, which means all of the sides are connection to each other--as if the square was really a sphere. Opening the topology means that the particles are free to leave the system making the diffusion much more sparse.
Add more particles adds another batch of particles to the simulation. This will often seed up the convergence, but can change the shape of the aggregate--especially if added later in the simulation.
The degrees of freedom specifies how many directions the particles can move in, and whether they converge only perpendicularly, or in increments of π/4 radians.