Actually, I am not a big fan of stochastic method since randomization is not an understandable thing for me. However finding the logic of "random" is pretty easy, since it's tightly related to the concept of probability. Imagine a dice with six faces and six numbers... the probability that the dice will show number 6 is 1/6. Throwing it 10 times increase the probability that the dice will show number six at least once. If we cheat the dice, and change the faces so that two faces has number six, the probability to get number 6 ( if we throw it 10 times) would increase to twice. The point is... however random things are, we still can control the randomization process with parameter.
In Diffusion Limited Aggregation, a "filament" will be added, if a particle (,which move based on brownian motion) collide with certain treshold of the seed point. It is arguably a stochastic method, where the filaments added randomly. However, this random method can still be controlled by certain parameters such as: the number of particles, the movement of the particles, the size of the treshold, the amount of the iteration, the vector direction of the particles etc.
So in other words, everytime we run DLA script, we can generate a uniqe form and still can get the form we want if we input the right parameter.. enjoy