This paper investigates the development of cellular structures created by the propagation of a detonation wave in a gaseous mixture. Two dimensional reactive Euler equations with an idealized one-step Arrhenius type reaction model are solved using the PPM scheme coupled with the exact Riemann solver. The numerical flow solver simulates the evolution process of regular cellular structures of a weakly unstable detonation wave. The cellular structures are generated by two-dimensional sinusoidal perturbations imposed on a ZND detonation wave. The initial sinusoidal perturbation wavelengths are predicted from linear stability analysis. The objective of these calculations is to examine the validity of the linear stability analysis predictions on the final cell sizes of a weakly unstable detonation. We found that for a given mixture, there is not just a single detonation cell size related to the wavelength with maximum growth rate. Instead, depending on the initial perturbation wavelength, the cellular dynamics reaches a final equilibrium state with the corresponding final cell size that belongs to a specific band of unstable wavelengths predicted by the linear stability analysis. Indeed, it is not the magnitude of the perturbation growth rate, but the magnitude of its rate of change with respect to the wavelength that predicts the domain of this specific band and corresponding final cell sizes.