  Periodic lattices have been predominantly explored for decades, owing to
their peculiar vibrational behavior. On the other hand, certain types of
aperiodic lattices have enabled new phenomena that may not be otherwise
attainable in periodic ones. In this paper, a new class of aperiodic lattices
inspired by cellular automaton is introduced. Cellular automaton was originally
developed as a machine replication algorithm and it has been intensively
explored in computer science. These algorithms yield structures that are not
necessarily periodic, yet follow well-defined rules that lead to interesting
aperiodic patterns. The concept is utilized here to build elastic lattices
following such rules, and Ulam-Warburton Cellular Automaton (UWCA) is
demonstrated as an example. Resulted UWCA lattices are shown to exhibit unique
dynamical properties, including symmetric eigenfrequency spectra, repeated
natural frequencies of large multiplicity, and the emergence of strongly
localized corner modes. It is envisioned that computer-algorithm-inspired
lattices may unlock new wave phenomena that could outperform existing lattice
designs.
