A recursive algorithm for the generation of space-filling curves

Space-filling curves have intrigued both artists and mathematicians for a long time. They bridge the gap between aesthetic forms and mathematical geometry. To enable construction by computer, an efficient recursive algorithm for the generation of space-filling curves is given. The algorithm is elegant, short and considerably easier to implement than previous recursive and non-recursive algorithms, and can be efficiently coded in all programming languages that have integer operations. The algorithmic technique is shown applied to the generation of the Hilbert and a form of the meandering Peano curve. This coding technique could be successfully applied to the generation of other regular space-filling curves.