A weakly universal cellular automaton in the heptagrid

TL;DR

This paper constructs a weakly universal cellular automaton on the heptagrid tessellation, demonstrating its properties and limitations within this specific non-rotation-invariant, planar setting.

Contribution

It introduces a weakly universal cellular automaton in the heptagrid tessellation, highlighting the constraints and uniqueness of such automata in this geometric context.

Findings

Constructed a weakly universal cellular automaton in the heptagrid

Proved the non-improvability of this result for tessellations p,3

Demonstrated the automaton's non-rotation invariance and planarity

Abstract

In this paper, we construct a weakly universal cellular automaton in the heptagrid, the tessellation $\{7,3\}$ which is not rotation invariant but which is truly planar. This result, under these conditions, cannot be improved for the tessellations $\{p,3\}$.