Properties The space filled by the curve is called the Gosper island. The first few iterations of it are shown below: The Gosper Island can tile the plane. In fact, seven copies of the Gosper island can be joined to form a shape that is similar, but scaled up by a factor of in all dimensions. As can be seen from the diagram below, performing this operation with an intermediate iteration of the island leads to a scaled-up version of the next iteration. Repeating this process indefinitely produces a tessellation of the plane. The curve itself can likewise be extended to an infinite curve filling the whole plane. See also List of fractals by Hausdorff dimension M.C. Escher References External links NEW GOSPER SPACE FILLING CURVES FRACTAL DE GOSPER (in French) Gosper Island at Wolfram MathWorld Flowsnake by R. William Gosper Fractal curves