DLA models the growth of clusters such as snowflakes and soot particles. These particles grow by accumulating mass on their perimeter. This applet demonstrates this concept.
Tips on working the applet:
Pick DLA Cluster to view the actual cluster
Pick Fractal Dimension to view the histogram of the logarithm of the mass of the cluster as a function of
the logarithm of the distance from the seed.
Press Start to watch the snowflake grow.
Press Stop to start all over again.
Press Step to watch the snowflake grow on particle at a time.
Programming DLA:
In the following algorithm, R is the maximum distance that any particle is from the first particle, known as the seed.
Each particle occupies one screen pixel in the drawing. Starting with a seed particle in the center of an awt Panel, a new particle is released at a randomly chosen angle a distance R+2 pixels away from seed and it performs a random walk. This particle sticks to the cluster if it lands next to a pixel that is already occupied by a particle. If the random walker ever gets more than 2*R +1 pixels away from the seed particle, the particle is replaced with a new random particle. The process is repeated after the walker sticks or is lost.
Color coding the sites: The first 100 particles are blue, the second 100 are orange, the third 100 are green, the f fourth 100 are red and the remaining ones are blue.
Making the algorithm more efficient: larger steps are taken if the walker is far from the cluster. If the distance of the random walker from the seed, r, is larger than larger than R, walker takes larger steps. The step size is r-R-1 rounded to the nearest integer.
Estimating the fractal dimension of the DLA cluster: the logarithm of the mass of the cluster as a function of the logarithm of the distance from the seed is plotted. Suppose that the cluster were to completely fill the page. Then this log-log plot would have a slope of 2 since the mass is proportional to the area and hence is related to the square of the radius.
area= P r2
To view documentation for this program click on the following link: Documentation
Homeward Bound, oh I wish I was. .
- Simon and Garfunkel