A plane set X admits an inscribed polygon P, if every vertex of a polygon similar to P lies in X. It is still not known whether every Jordan curve admits an inscribed square. In 1977 H.Vaughan proved that every homeomorphic copy of $S^1$ in $ \mathbb{R}^2$ admits at least one inscribed rectangle. In this talk, we present an algorithm implemented in Python that helps us visualize Vaughan’s function, and we classify locally connected plane continua that inscribe rectangles.