Intrinsic universality of Tile Automata in dimensions other than two

Determine whether the Tile Automata model is intrinsically universal in one dimension and in three or higher dimensions, specifically whether there exists a finite rule set for Tile Automata that can intrinsically simulate all Tile Automata systems in 1D and in 3D or higher.

Background

This work establishes intrinsic universality for the seeded Tile Automata model in 2D under a non-committal simulation definition, using supertiles and a universal rule set. The construction inherently relies on two-dimensional supertiles and single-tile attachment dynamics.

The authors explicitly highlight that extending these IU results beyond 2D is unresolved. In particular, it remains unknown whether analogous IU constructions exist for 1D Tile Automata or for 3D and higher dimensions, especially given that their current supertile-based approach is inherently two-dimensional.