The time evolution equations of a simplified isolated ideal gas, the ``tetrahedral'' gas, are derived. The dynamical behavior of the López-Ruiz-Mancini-Calbet complexity [R. López-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in this system. In general, it is shown that the complexity remains within the bounds of minimum and maximum complexity. We find that there are certain restrictions when the isolated ``tetrahedral'' gas evolves towards equilibrium. In addition to the well-known increase in entropy, the quantity called disequilibrium decreases monotonically with time. Furthermore, the trajectories of the system in phase space approach the maximum complexity path as it evolves toward equilibrium.