Functional Programming in Scheme Name binding, Recursion, Iteration, and Continuations
The Hilbert Curve is a space filling curve that visits every point in a square grid
A hilbert curve of order 5 which is traversed repeatedly to emphasize the maze.
The view enforced on you through this picture is an iterative one: We traverse the
curve one edge after the other. Needless to tell, this gives a very confusing and
complicated understanding of the curve. Below, we will explain the curve in recursive
terms. It turns out that this will be key to understanding the curve. Relative to the Scheme program shown later, this curve is produced by the call (hilbert 5 'up) .
The path taken by a Hilbert Curve appears as a sequence - or a certain iteration - of up, down, left, and right.