Tuning complexity on randomly occupied lattices

Using diversity of cluster size (mass) as a measurement of structural complexity on randomly occupied lattices, we describe a tuning effect in complexity by parameters L, size of the lattice, and p, probability of occupation. We also show the behavior of the number of fragments (clusters) in relation to the probability of occupation p. Another kind of pattern used to define diversity was the form (shape) of the cluster. A behavior similar to the cluster size diversity was observed. Showing that diversity as a measurement of complexity has an inherent subjective constraint. Scaling relations between the variables measured show some aspects of the complexity of the system and can give more insights into the tuning effect observed.