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November 2010

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Fixing m to be a power of 2; setting k and l to be zero; and looping i and j over the range [1,m], we get an integer f(i,j,k,l,m) for each pair (i,j).

Drawing a point on the j-th row of the i-th line when f(i,j,0,0,m) is zero and leaving it blank when it is not yields the Hilbert space-filling curve, which is a fractal.We received two interesting answers. The first was from John Tromp, who sent us a magnificent C program that generates this curve and has its shape:

The second was from Tim Tran, who switched the order, fixed i and j, and looped with k and l, producing a fractal-like construct:


If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com