A dragon curve, also known as a
Heighway dragon, is a non self intersection space filling curve. It has a
fractal dimension of 2 and is able to tile the plane.

Demo - 9th iteration

This is the curve generated by repeatedly folding a paper in half. Each
iteration of the curve can be built from the previous. We can describe the curve
in terms of $R$ and $L$, where a $R$ represents turning to the right and drawing
a segment, and a $L$ represents turning to the left and drawing a segement. The
pattern can be described as follows:

Start with a $R$.

For each iteration, append an $R$ to the previous iteration, then add on the
previous iteration reversed and with $L$s and $R$s swapped.

The first few iterations would be:

$R$

$R$$R$$L$

$R$$R$$L$$R$$R$$L$$L$

$R$$R$$L$$R$$R$$L$$L$$R$$R$$R$$L$$L$$R$$L$$L$

The demo above shows the 9th iteration of the dragon curve.