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Want to be a virtual gardener? In this simulation experiment, we are going to use the concept of diffusion limited aggregation to grow fractal plants. When you first run
the Java applet on the graphic screen you only see emptiness and a brown horizontal line drawn across the bottom of the graphic screen. This is the 'bedding ground' (750 pixels long) for plants to grow on. The concept is
similar to that of original WS cluster. In this case it is a straight line instead of a single seed.
The graphic screen is our virtual garden where the plants are to grow. The idea is to create a 'moving particle' and allows it to wonder in random directions until it is found adjacent to any particles or the ground. Since the smallest unit in the graphic screen is a
pixel, the size of the moving particle is the pixel itself and is allowed to move only in any four directions as shown below:
The particle does not allow to move diagonally and the numbers (0.25) indicate the probability of moving in each direction. Since there is only a total of four allowable directions, each has a probability of 0.25 (1/4) to move in that direction. In other words, the particle once created is allow
to wonder in random.
Diagram below illustrates several possible outcomes to the moving particls. Initially a moving particle is created randomly anywhere along a certain distance from the maximum height of plants (if there isn't any plant, the ground will be the reference height). In the Fractal applet, this distance is set to 40 pixels. This
distance, outlined below as an imaginary line, is called the launch boundary.
If the particle is found to wander too far away from the ground it is then destroyed and new particle will be created, again anywhere along the launch boundary. This sets a boundary within which the particle can exist and is called the limit boundary. In the Fractal applet this is
set as a distance of 20 pixels from the launch boundary. Note that setting these boundaries too large will allow greater amount of space for particles to wander and hence takes longer time to grow plants.
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