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|Karl J. Runge|
|The idea behind "mandelstep" is that by letting you select starting positions and looking at a handful of iteration "trajectories" or "orbits," you can begin to understand more about the different regions of the Mandelbrot set - not just whether a point is inside the set, but what sort of "dance" it does to be a member. Soon you'll be using your intuition about what sort of "dance" a point will do before you run the actual iteration. It's a puzzle. Click on a point; to see why your point is in (or not in) the set, click on "Run" to start the iterations. If the resulting "orbit" does not go to infinity your starting point is in the Mandelbrot set; otherwise it is not (and the color assigned to it on the background image indicates in some sense how "far away" it is from the set). The different regions of the fractal correspond to different kinds of stable, closed orbits.|
|Levels:||High School (9-12), College|
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