Generalized Cantor Sets and Their Hausdorff Dimensions

To construct a generalized Cantor set iteratively, remove from the interval [0,1] a specified middle portion of every subinterval at each stage of the construction. This Demonstration runs up to 10 iterations of the Cantor set for five different middle interval variations. For each set, select "show dimension" to give the Hausdorff (or fractal) dimension . This is defined by , where for middle halves, middle thirds, middle fourths, middle fifths and middle sevenths, respectively.

The original Cantor set was defined for and therefore had .