The dragon curve is a recursive non-intersecting curve whose name derives from its similarity to a dragon. There are many different types of dragon curves.

### Heighway Dragon

The Heighway Dragon was first investigated by physicists at NASA John Heighway, Bruce Banks and William Harter.

The construction of the Heighway Dragon can be written as a Lindenmayer System with

- Angle 45°
- Axiom FX
*(Initial String)* - String Rewriting rules
- X —> X+YF+
- Y —> −FX-Y

where ‘**F**‘ means ‘draw forward’, ‘**+’** means ‘turn 45° clockwise’, and ‘**−**‘ means ‘turn 45° anticlockwise’. **X** and **Y** do not correspond to any drawing action and are only used to control the evolution of the curve. *This notation will be used for the rest of the post.*

In other words, the Heighway dragon is constructed by replacing a line segment with two segments “*with a right angle and with a rotation of 45° alternatively to the right and to the left*“.

### Twindragon

The twindragon can be constructed by joining two Heighway dragon curves back-to-back, so one is rotated by 180°.

It can also be written an a Lindenmayer system by adding another section in the initial string: FX+FX+.

### Terdragon

The terdragon was first introduced by Davis and Knuth in a paper on dragon curves in 1970. It can be described by the following Lindenmayer system:

- Angle 120°
- Axiom F
*(Initial String)* - String rewriting rules
*F*↦*F+F−F*

### Lévy Dragon

Finally, the Lévy dragon is a curve studied by Paul Lévy as part of a general study of self-similar curves (see Fractals). This was motivated by the work of Helge von Koch and the Koch Curve. It is also known as the Lévy C curve.

Its Lindenmayer system can be described as follows:

- Angle 120°
- Axiom F
*(Initial String)* - String rewriting rules
*F*↦ +*F–F+*

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