A proof of Ollinger's conjecture: undecidability of tiling the plane with a set of $8$ polyominoes

Abstract

We give a proof of Ollinger's conjecture that the problem of tiling the plane with translated copies of a set of $8$ polyominoes is undecidable. The techniques employed in our proof include a different orientation for simulating the Wang tiles in polyomino and a new method for encoding the colors of Wang tiles.

References in corpus (2)

• A chiral aperiodic monotile
• An aperiodic monotile

Cited by in corpus (3)

• Undecidability of Translational Tiling of the 3-dimensional Space with a Set of 6 Polycubes
• Undecidability of Translational Tiling of the 4-dimensional Space with a Set of 4 Polyhypercubes
• Undecidability of tiling the plane with a fixed number of Wang bars