Functional Programming in Scheme Name binding, Recursion, Iteration, and Continuations
Building Hilbert Curves of order 1
Here we will study the recursive composition of the most simple Hilbert Curve.
A Hilbert Curve of order 1 is composed of four Hilbert Curves of order 0 connected by three connector lines.
A Hilbert Curve of order 0 is empty
In the starting point we have a Hilbert Curve of order 0 - that is nothing. It is empty.
For illustrative purpose, the empty Hilbert Curve of order 0 is shown as a small circle.
We see how four instances (which in the starting point are overlapping in the middle of the picture)
are moved to the four corners. Finally the four Curves of order 0 are
connected by three connector lines. This makes up a Hilbert Curve of order 1. Relative to the Scheme program shown later, this curve can be produced by the call (hilbert 1 'up) .
