Henon Attractor
The Henon Attractor is an interesting iterated fractal. It consists of two X and Y equations
that produce a fractal made up of strands. As the image on the left shows, two main strands, that
form a rough arc, are the main part of the fractal. As you can also see, identical, yet smaller, strands are
inside the first two. If you were to zoom in on most parts of the fractal, you could easily
see the fractal is identical on every level. Each strand visible contains an infinite amount of
smaller counterparts within. This trait is called self-similarity at all levels. Many
other fractals, such as Julia and Mandelbrot Sets, exhibit this trait.
This fractal is probably the easiest fractal of all featured on this web site to create. It's two
equations are quite simple. No variables other than X and Y are used! The equations are :
xn = yn-1 + 1 - (1.4 * sqr(xn-1))
yn = 0.3 * xn-1
Please note that the SQR function in the first equation represent the Square function. Most
computer language use SQR to square numbers. Once these equations are iterated, the Henon Attractor
is produced.
The Turbo Pascal program used to generate the image on this page can be downloaded. The ZIP file
includes source code and a DOS compiled executable. You'll need at least 1 MB of video RAM to run
this.
Also, a Java applet is online that will generate the Henon Attractor on your computer.