From Math Images
|Harter-Heighway Dragon Curve|
Basic DescriptionThis fractal is described by a curve that undergoes a repetitive process (called an iterated process). To begin the process, the curve has a basic segment of a straight line.
Then at each iteration,
- Each line is replaced with two line segments at an angle of 90 degrees (other angles can be used to make fractals that look slightly different).
- Each line is rotated alternatively to the left or to the right of the line it is replacing.
The Harter-Heighway Dragon is created by iteration of the curve process described above, and is thus a type of fractal known as iterated function systems. This process can be repeated infinitely, and the perimeter or length of the dragon is in fact infinite. However, if you look to the image at the right, a 15th iteration of the Harter-Heighway Dragon is already enough to create an impressive fractal.
An interesting property of this curve is that although the corners of the fractal seem to touch at various points, the curve never actually crosses over itself. Also, the curve exhibits self-similarity when iterated infinitely because as you look closer and closer at the curve, the curve continues to look like the larger curve.
A More Mathematical Explanation
- Note: understanding of this explanation requires: *Algebra
Changing the Angle
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About the Creator of this Image
SolKoll is interested in fractals, and created this image using an iterated function system (IFS).
Wikipedia, Wikipedia's Dragon Curve page Cynthia Lanius, Cynthia Lanius' Fractals Unit: A Jurassic Park Fractal
Future Directions for this Page
An animation of the fractal being drawn gradually through increasing iterations (a frame for each individual iteration)
Also, an animation that draws the curve at the 13 or so iteration, but slowly to show that the curve never crosses itself.
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