Harter-Heighway Dragon
From Math Images
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- | + | Wikipedia, [http://en.wikipedia.org/wiki/Dragon_curve Wikipedia's Dragon Curve page] | |
+ | Cynthia Lanius, [http://math.rice.edu/~lanius/frac/jurra.html Cynthia Lanius' Fractals Unit: A Jurassic Park Fractal] | ||
|ToDo=*An animation for the showing the fractal being drawn gradually through increasing iterations | |ToDo=*An animation for the showing the fractal being drawn gradually through increasing iterations | ||
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Revision as of 14:27, 29 June 2009
- This image is an artistic rendering of the Harter-Heighway Curve (also called the Dragon Curve), which is a fractal. This curve is an iterated function system and is often referred to as the Jurassic Park Curve, because it garnered popularity after being drawn and alluded to in the novel Jurassic Park by Michael Crichton (1990).
Harter-Heighway Dragon Curve (3D- twist) |
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Contents |
Basic Description
This fractal is described by a curve that undergoes an iterated process. To begin the process, the curve starts out as a line as the base segment. Each iteration replaces each line with two line segments at an angle of 90 degrees (other angles can be used to make various looking fractals), with each line being rotated alternatively to the left or to the right of the line it is replacing. To learn more about iterated functions, click here.
The Harter-Heighway Dragon is created by iteration of the curve process described above. This process can be repeated infinitely, and the perimeter 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.
The perimeter of the Harter-Heighway curve increases by with each repetition of the curve.
An interesting property of this curve is that the curve never crosses itself. Also, the curve exhibits self-similarity 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
Properties
Changing the Angle
Teaching Materials
- There are currently no teaching materials for this page. Add teaching materials.
About the Creator of this Image
SolKoll is interested in fractals, and created this image using an iterated function system (IFS).
References
Wikipedia, Wikipedia's Dragon Curve page Cynthia Lanius, Cynthia Lanius' Fractals Unit: A Jurassic Park Fractal
Future Directions for this Page
- An animation for the showing the fractal being drawn gradually through increasing iterations
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