A Proof of Ollinger's Conjecture: Undecidability of Tiling the Plane with a Set of 8 Polyominoes.

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.