Click on the green flag and be patient. All processes in nature take time. Some take a few billionths of a second, others, millions of years. 300 particles perform random walks in the plane. If a particle touches the central seed it sticks to the seed and itself becomes sticky. Any other particle may stick to the seed or one of the now sticky particles. Particle 'arms' are created that restrict further motion of the random walks. This leads to arms (called dendrites) being formed from the central seed. Five to ten minutes will usually create enough dendrite growth for you to see the process.
DIffusion Limited Aggregation does create a fractal with a typical dimension of 1.7. The Center dot acts as a seed (like a dust particle for a raindrop). A number of particles surround the seed and perform a random walk. If the particle hits the seed or a growth from the seed, the particle sticks and a new particle is added. I tried to keep the code as simple as possible so that you could easily understand the algorithm and create better DLA projects.