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Functional Programming in Scheme
Name binding, Recursion, Iteration, and Continuations
Building Hilbert Curves of order 2

Here will study the recursive composition of Hilbert Curves in additional details.

A Hilbert Curve of order 2 is composed of four Hilbert Curves of order 1 connected by three connector lines.

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In the starting point we have a Hilbert Curve of order 1, as constructed above. We see how four instances (which in the starting point are overlapping in the middle of the picture) are moved to the four corners. Two of them are rotated. Finally the four Curves of order 1 are connected by three connector lines. This makes up a Hilbert Curve of order 2. Relative to the Scheme program shown later, this curve is produced by the call (hilbert 2 'up) .