I will begin by recalling how I met the late Nikola Buric and how our friendship developed in a short time. Motivated by quite different interests in the transition between quantum and classical mechanics, at first, we both were studying possibilities for a theory of quantum-classical hybrid systems, which became the focus of our discussions. - This has recently led me to explore cellular automata (CA) which, quite surprisingly, show well known features of quantum mechanics (QM). Such as a linear updating rule resembling a discretized form of the Schroedinger equation together with its conservation laws. In particular, a whole class of natural Hamiltonian CA, which are based entirely on integer-valued variables and couplings and derived from an action principle, can be mapped reversibly to continuum models with the help of sampling theory [Shannon's Theorem]. This results in "deformed" quantum mechanical models with a finite discreteness scale l, which for l-> 0 reproduce the familiar continuum limit. Such CA can form multipartite systems consistently with the tensor product structures of many-body QM, while maintaining linearity. Interestingly, discreteness necessitates a many-time formulation reminding of relativistic dynamics. We conclude that the superposition principle is fully operative already on the level of such primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement and might offer a primitive understanding of the Born rule. - Time permitting, I will relate these findings to the Cellular Automaton Interptetation of QM, recently proposed by G. 't Hooft.
