If you allow cropping, you can always do this.<p>Suppose the tiles are T1, ..., Tn. The &quot;self-tiling&quot; property means you can tile each Tk with smaller copies of T1, ..., Tn. Or, equivalently, you can tile a larger copy of each Tk with copies of T1, ..., Tn.<p>So: pick one of the tiles. Tile it with smaller copies of the tiles. Tile each of those with still-smaller copies. Tile each of <i>those</i> with still-smaller copies. Etc.<p>Now pick a region in the original tile that&#x27;s the same shape as the thing you&#x27;re trying to cover. This process covers (the whole original tile, and hence in particular) that region with finer and finer copies of the tiles.