One- and two-dimensional cellular automata (CA) simulations of neutral "atoms," viewed as "complex" distributions of electron density around a central nucleus, are performed in order to explore CA-based discretized and connectionist approaches to the synthesis and structure-dynamics problems of many-electron systems. A link between CA and the quantum mechanics of atoms is made by taking the Thomas-Fermi theory as an illustrative example. Starting from a nonstationary distribution, the stationary distribution of electron density around a nucleus arises out of a natural stability criterion described through CA rules. © 1996 John Wiley & Sons, Inc.