Dragon Curves

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:

1. Start with a $R$.
2. 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:

1. $R$
2. $R$ $R$ $L$
3. $R$ $R$ $L$ $R$ $R$ $L$ $L$
4. $R$ $R$ $L$ $R$ $R$ $L$ $L$ $R$ $R$ $R$ $L$ $L$ $R$ $L$ $L$

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