Initially the heat bath is empty, so aggregation events happen more readily than evaporation. The heat bath quickly reaches a steady state, meaning the system now has a well defined temperature, and that the net number of aggregation and evaporation events are equal. The system evolves so as to maximize the entropy. In the analogous two dimensional dynamics we observe this system evolve from a small block of randomness in a uniform background to a completely random and disordered state. In contrast, in three dimensions the system evolves from a small cube of randomness to a stable dynamical structure with long range order resembling a square pyramid embedded in fluctuating spherical shells.
Discrete systems have a finite, but extremely large, number of distinct microscopic states.
In general, reversible systems visit almost all of the states before cycling back to the initial state, thus the stable structure generated by the SAME model will persist for longer than we could ever possibly observe it. We would also like to analyze the macroscopic dynamics of physics-like discrete systems using the language of physics. This would require the formulation of the least action principle and the Euler-Lagrange equations for discrete systems. By studying simple models we hope to gain insights useful for dealing with this more general issue. Understanding the mechanisms of pattern formation has obvious significance.