dragon curve

The dragon curve can tile the plane in many ways.

Many self-similarities can be seen in the Heighway dragon curve.

In spite of its strange aspect, the Heighway dragon curve has simple dimensions.

The dragon curve is another unusual example.

If each fold is then opened out to create right angled corner, the resulting shape approaches the dragon curve fractal.

The dragon curve drawn using an L-system.

Regular paperfolding sequence (for example, the Dragon curve)

It is a fractal object similar in its construction to the dragon curve and the Hilbert curve.

Research topics have included Ducci sequences (also known as the n-numbers game), dragon curves, arithmetrees, and tropical algebraic geometry.

A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.

This pattern in turn suggests the following method of creating models of iterations of the Heighway dragon curve by folding a strip of paper.

Indeed, when plotting a sufficiently high number of roots of the Littlewood polynomials, structures similar to the dragon curve appear at points close to these coordinates.

The twindragon (also known as the Davis-Knuth dragon) can be constructed by placing two Heighway dragon curves back-to-back.

Tracing an iteration of the Heighway dragon curve from one end to the other, one encounters a series of 90 degree turns, some to the right and some to the left.

In mathematics the regular paperfolding sequence, also known as the dragon curve sequence, is an infinite automatic sequence of 0s and 1s defined as the limit of the following process: