#### Dragon Curve

The Dragon curve is a two-dimensional fractal, also known as Jurassic Park dragon.
It can easily be created with a piece of paper:
1. Fold it $$n$$-times in the same direction.
2. Unfold the paper. Every fold is either a hill or a valley.
3. Twist every fold to make it a $$90^\circ$$ corner. If it´s a hill, twist it to the right, if it´s a valley, twist it to the left.
You can see a visualization of this process below.

###### Formula
The formula for this calculation looks like this:
$$A=\{\text{"L"},\text{"R"}\}, w\in A$$
$$w_1=\text{"R"}$$
$$w_{n+1}=w_n\left[1:|w_n|\right]\cdot \text{"R"}\cdot w_n\left[1:\frac{|w_n|}{2}\right]\cdot \text{"L"}\cdot w_n\left[1+\frac{|w_n|}{2}:|w_n|\right]$$
$$w$$ resembles a word, $$w[i:j]$$ is a substring of $$w$$ with chars from position $$i$$ to position $$j$$.
You can see that the function recursively determines the folding directions.
The calculated word is then translated into a line with one corner for each char of the word. The line makes a left turn when a char is equal to $$\text{"L"}$$ and a right turn when it´s equal to $$\text{"R"}$$. The outcome is visualized below.