In this chapter, we aim to explore the existence of computationally universal cellular automata constructed on the face-centered cubic lattice, which is one of the arrangements with the highest density in sphere packing. Initially, we derive a rule set inspired by the framework of excitable media, characterized by possessing at least three distinct states and considered a promising foundation for achieving universal computation. Within this rule set, we identify four distinct types of propagating patterns, namely type-I through type-IV gliders. Furthermore, we make modifications to the rule set to enable the emergence of nine different types of stationary patterns while preserving the presence of type-I through type-IV gliders. By conducting collision experiments between a stationary pattern and a propagating pattern, we observe that certain arrangements allow the stationary pattern to act as an “eater” for the propagating pattern. Specifically, collisions involving type-I gliders give rise to type-II or type-IV gliders, while collisions between type-II gliders lead to changes in their direction or the creation of a novel glider referred to as a type-V glider. The results suggest that the iterative application of the reciprocal procedures, namely pattern discovery and rule modification, is promising to achieve universal computation, although computational universality of the obtained rule set has not been proved yet.