The fractal ``frog'' (Q1760538)

The author constructs a self-similar fractal curve \({\mathfrak F}\) satisfying the following conditions: it is a quasi-conformal Jordan arc; it is not AC-removable, i.e., there exists a non-trivial function which is continuous in a domain \(D\supset {\mathfrak F}\) and holomorphic in \(D\setminus{\mathfrak F}\) but non-holomorphic on \({\mathfrak F}\); it is not diffeomorphic to the von Koch snowflake. The author builds this curve by means of the Sierpiński gasket and call it the fractal frog. Its Hausdorff dimension equals to \(\log_{4}{6}\).