Tiling with Similar Polyominoes

Tiling with Similar Polyominoes, by Michael Reid
Journal of Recreational Mathematics 31 (2002-2003), no. 1, pp. 15-24.
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The problem of tiling a region, or the whole plane, using congruent copies of a single polyomino has been well studied. Karl Scherer has introduced the problem of using similar copies of a single polyomino. He also considers other shapes besides polyominoes in his privately published book, A Puzzling Journey To The Reptiles And Related Animals. We consider two tiling problems, using similar copies of a single polyomino, tiling a rectangle, and tiling a larger copy of the original shape. We also suggest several directions for further investigation.
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Updated January 8, 2008.