OEIS A000361: Fractal tilings with holes and positive measure

We unpack the curious link behind sequence A000361: a self-replicating, holey tiling on the Mandelvyn triangle that nonetheless has positive Lebesgue measure. The story weaves a four-reptile tiling, inspired by Paul Lévy’s two-reptile, with counting of filled equilateral triangles along lines on the Mandelvyn triangle. It shows how infinite self-similarity can coexist with nonzero area, connecting number theory to geometric measure theory, and invites reflection on positive-measure fractals and the foundations of measure.

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