Intrinsic universality of 2D asynchronous cellular automata

Establish whether two-dimensional asynchronous cellular automata admit an intrinsically universal rule set, i.e., determine if there exists a finite-state cellular automaton in 2D with asynchronous updating that can (under the intrinsic universality framework) simulate the dynamics and configurations of any other 2D asynchronous cellular automaton.

Background

The paper studies intrinsic universality (IU) across self-assembly and cellular automata models, and proves IU for seeded Tile Automata under a strong non-committal simulation definition. It further shows IU for a restricted form of asynchronous cellular automata (pairwise ACA with neighborhood size 2).

Despite these advances, the authors note that the general problem of IU for 2D asynchronous cellular automata remains unresolved. Prior work has made progress toward 1D settings, but a comprehensive IU result for the full 2D asynchronous model (without the pairwise restriction) is still lacking.