Mathematics · Study 057
Dragon Curve
Fold a paper strip in half over and over, open every crease to 90 degrees, and you get the Heighway dragon. Watch it unfold to 8,192 segments.
What you're looking at
Each stage takes the whole curve so far, makes a copy, and swings the copy a quarter turn about the end point. The animation shows that swing. The red half is the newest copy. The curve never crosses itself, though it touches at corners, and the finished dragon tiles the plane with copies of itself.
The idea behind it
NASA physicist John Heighway found the curve in 1966 by folding paper, and Martin Gardner made it famous in Scientific American. The sequence of left and right turns can be read from the binary digits of the segment number, which is how it is generated here.
Try this
Watch it unfold from 4 segments to 8,192, then begin again.
