Diffusion-limited aggregation: A relationship between surface   thermodynamics and crystal morphology
  We have combined the original diffusion-limited aggregation model introduced by Witten and Sander with the surface thermodynamics of the growing solid aggregate. The theory is based on the consideration of the surface chemical potential as a thermodynamic function of the temperature and nearest-neighbor configuration. The Monte Carlo simulations on a two-dimensional square lattice produce the broad range of shapes such as fractal dendritic structures, densely branching patterns, and compact aggregates. The morphology diagram illustrating the relationship between the model parameters and cluster geometry is presented and discussed. 
Vladislav A. Bogoyavlenskiy and Natasha A. Chernova