Generalized Cantor Sets and Their Hausdorff Dimensions

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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 .


Contributed by: Erin K. Kline and Matthew A. Morena (August 2022)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.