The random packing of regularly and irregularly shaped particles has been studied extensively. Within this paper, packing is studied from the perspective of digitized particles. These digitized particles are developed for and used in cellular automata systems, which are employed for the simple mathematical idealizations of complex systems in physics, chemistry and engineering [S. Wolfram, Rev. Mod. Phys. 55, 601-644 (1983)]. In the present paper, the random packing of digitized particles is studied using the packing routines available in the cellular automata cement hydration model by D.P. Bentz [A Three-dimensional Cement Hydration and Microstructure Program. I. Hydration Rate, Heat of Hydration, and Chemical Shrinkage (National Institute of Standards and Technology, 1995)] and a modified version of the Lubachevsky and Stillinger algorithm [B. D. Lubachevsky and F. H. Stillinger, Journal of Statistical Physics 60, 561-583 (1990)]. It is shown that the packing of digitized particles is comparable to spheres, when taking into account the specific properties of digitized particles.