Functional Programming in Scheme Name binding, Recursion, Iteration, and Continuations
Building Hilbert Curves of order 4
In the same way we made a Hilbert Curve of order 3, we will here see how a Hilbert Curve of order 4 is made.
This is the final development along these lines in this material.
A Hilbert Curve of order 4 is composed of four Hilbert Curves of order 3 connected by three connector lines.
In the starting point we have a Hilbert Curve of order 3, 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 3 are
connected by three connector lines. This makes up a Hilbert Curve of order 4. Relative to the Scheme program shown later, this curve is produced by the call (hilbert 4 'up) .