The Sierpinski Carpet is a 2-dimensional extension of the Cantor Set in which repeatedly segments are divided in three and the central portion discarded (see diagram at right). The Sierpinski carpet, unlike the Cantor set, does not give a discrete set – the coloured portion is all joined together. However, the complement of white squares is fractal in nature, and definitely discrete. This set might be defined by a rule of the form: ‘take a (central) square and surround it by 8 squares a third the size. Do this repeatedly. ’
