Dragon curve

Anakha Bhuvanesh
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As the name indicated it comes from its resemblance to a certain mythical creature. Dragon curves are non intersecting recursive curves. It is a member of fractal curves. Its shape is commonly generated from repeatedly folding a strip of paper in half. To construct the curve, represent the left turn with 1 and the right turn with 0. Besides dragon curves, there are other types of curves that are generated differently. It is also named as “The Harter-Heighway Dragon”, “The Jurassic Park Fractal”. It is the youngest fractal, first expressed in the mid-sixties. It is an example of a space-filling curve. It has fractal dimension 2. It is a 2D object. 2001 is considered as the Dragon curve year. A dragon curve is made by folding a piece of paper several times in the same direction and then bent vertically. Even though it touches, it does not intersect. With the increase in number of folds, it becomes more complex. Apart from Dragon curves there are other curves which are generated differently.

Properties of Dragon curve

Dragon curves are made of using one line. It can split the plane. The speciality of this line is such that it never goes over itself. If you take a paper and fold it into half again and again, then unfold it we will get a dragon curve. If the solutions of a polynomial is taken with coefficients in a particular range and plot it on a complex plane, we can find dragon curves.

Heighway dragon


The Heighway dragon is named by William Harter. It was discovered by John Heighway in 1966. The pattern is composed of geometrically similar components spiraling around two curves (0,0) and (1,0). Its boundary is a fractal with dimension 1.523627. It can also be used to tile the plane. A line segment is replaced with two segments at 450 to construct the Heighway dragon curve.



Two Heighway dragons are placed side by side to create a twindragon. i.e. one is rotated by 1800. Its boundary has the same dimension 1.523627 as that of heighway dragon.



Terdragon curves are first introduced in a paper on dragon curves written by Davis and Knuth in 1970. Rather than bisecting the paper at each step, the terdragon trisects it at each step, similar to the Heighway dragon.

Golden Dragon

The name Golden Dragon arises due to its similarity dimension with the golden ratio. Golden dragons are constructed similarly to Heighway dragons, but they use different scaling factors and angles.


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