A seed particle is placed in the middle of the red circle. Then, a new
particle is started at a random position on the circle. For every time
step, it does a random move one step in any of four (von
Neumann neighbourhood) or eight (Moore neighbourhood) possible directions.
If at the new position there is a neighbouring cell (4/8 neighbours
considered), the particle stays there. Otherwise, it does the next step.
Particles which leave the circle are eliminated.
The right hand side of the graphic shows the fractal dimension d
calculated from the picture by taking into account circles of increasing
radius R around the center and counting the number of particles
N within each circle. Because N~Rd, the slope
of the double-logarithmic plot gives d. Note that d converges
to about 1.7 as the picture gets finished.
Last modified: Sun Jun 23 10:43:25 CEST 2002