Cantor is a 2-dimensional Cantor set (also known as a Sierpinski carpet): a square divided into nine parts with the middle rectangle removed, and the same process applied to the other eight rectangles, *ad infinitum.* The black region is the Cantor set; the gaps are decorated. A version where all the rectangles are identical squares can be described mathematically as the set of (*x*, *y*) such that *x* and *y* lie between 0 and 1 and contain no 1*s* in their base 3 representation; e.g. (0.02202_{3}, 0.20022_{3}) would be in the set.

If you **click or drag** on the applet, the point you select is used as one corner of the middle rectangle, and all further subdivisions remove the same vertical and horizontal fractions of the remaining regions.