Cantor is a 2-dimensional Cantor set, 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 1s in their base 3 representation (e.g. 0.02202 would be in the set), repeatedly excluding the middle third of both coordinates.

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Applets Gallery / Cantor / created Sunday, 5 July 1998
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Copyright © Greg Egan, 1998. All rights reserved.