There are many more aspects of this problem to investigate. One of these is the average distance along a dendrite between branches. As stated earlier, this is very important to phase separation in crystallizing systems. Active walker models should be particularly effective for this type of study, since one can follow the path of individual walkers. The roll of diffusion in the bulk fluid must also be investigated further. It may be possible to update the landscape by solving the diffusion equations periodically after a given number of growth attempts. A more rigorous investigation of the real time versus simulation time is also important.
Another important point of study is the interaction between multiple walkers or walkers and impermeable boundaries. It is likely that a depletion region would develop as the edges of clusters approach. The active walker model could be used to study the form of this depletion region as well as the relative length of time to bridge it. This is important for both crystallization and conduction problems in dendrites. It appears that active walkers can play an important role in the study of large scale structures in crystal growth.