Cantor dust is a fractal that can be constructed using string rewriting beginning with a cell [0] and iterating the rules

Let be the number of black boxes, the length of a side of a box, and the fractional area of black boxes after the th iteration, then

			(2)
			(3)
			(4)
			(5)

The number of black squares after , 1, 2, ... iterations is therefore 1, 4, 16, 64, 256, 1024, 4096, 16384, ... (Sloane's A000302). The capacity dimension is therefore

			(6)
			(7)
			(8)
			(9)