From Math Images
|Harter-Heighway Dragon Curve (3D- twist)|
The curve itself is fairly simple, with 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.
The Harter-Heighway Dragon is created by iteration of the curve described above. The curve can be repeated infinitely, so that 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
Perimeter<span class="_togglegroup _toggle_initshow _toggle _toggler toggle-visible" style="di [...]
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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).
Future Directions for this Page
An animation for the showing the fractal being drawn gradually through increasing iterations
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