Step 1: Understanding the Concept: Instead of comparing every cell of each candidate tile to the strip, focus only on the edges where one copy of the tile meets the next copy in the repeating strip. If a tile is the true generator, the right edge of one copy must line up seamlessly with the left edge of the next copy, exactly as seen in the strip, with no broken or duplicated cell at the seam.
Step 2: Key Formula or Approach: For each candidate ($P$, $Q$, $R$, $S$), note the column of cells along its left edge and the column along its right edge. Scan the strip at every point where a seam should occur, spaced at the tile's width, and check whether the strip's cells at that seam match the candidate's edge columns.
Step 3: Detailed Explanation: Checking $P$: the edge columns do not reproduce the seam pattern seen at more than one location in the strip, a break appears where the strip's black run continues but $P$'s edge would break it. Checking $R$ and $S$: similarly, at least one seam location in the strip shows a cell pattern that does not match what tiling $R$ or $S$ would produce there. Checking $Q$: at every seam location along the strip, $Q$'s left and right edge columns reproduce the strip's cells exactly, with the black and white runs continuing smoothly across each junction. Since a correct generating tile must satisfy the seam condition at every junction in the strip, not just one, and only $Q$ does this consistently, $Q$ is the tile that generates the figure.
Step 4: Final Answer: The pattern used to generate the figure is $Q$. \[ \boxed{Q} \]
