Space-filling
This project displays space-filling curves. The code was written by Kerry Mitchell for Ultra Fractal, check his paper here. See also this project for 3d space filling curves.
One way to construct space-filling curves is to start from a square, split it into smaller squares and connect their centers with a curve. This process is iterated on the smaller squares to produce, in the limit of an infinite number of iterations, a space-filling curve. For practical and aesthetic reasons, the pictures below display only the result of a finite number of iterations.
The most famous such curve is the Hilbert curve, where each square is split into four smaller squares.
However, splitting each squares into a larger number of smaller squares allows for a larger diversity of curves. Here are some obtained by splitting each square into 16 smaller squares.
Breaking each square into 25 squares...
...or into 36 squares
