Make-Your-Own Mandelbrot Set
Well, the title is a bit misleading, since the Mandelbrot set is predefined, i.e., you can't change it. But, you can choose the colors you want to view it in, and you can also zoom in on and explore what has been called one of the most intricate and beautiful objects in mathematics.
You also have the option of creating the Julia set for any spot in the Mandelbrot set. To do this, zoom in to the spot you want to generate the Julia set for. Then change the "type of fractal" option to Julia. Now click on the spot on the picture you wish to use. The coordinates of the point you click will be used as the parameter for the Julia set. As is mentioned in the Information on the Mandelbrot set, there is a strong relationship between the Mandelbrot set and the Julia sets. See what you can determine about this relationship by creating Julia sets at various points on the Mandelbrot set. Where do the most interesting ones occur? What happens when you are "inside" the Mandelbrot set as opposed to outside? Do you notice any similarities between the area of the Mandelbrot set that you click in and the Julia set produced?
If you find a fractal you like, share it! Post a message that includes your fractal by scrolling to the bottom of the page after you make your fractal.
To learn more on the Mandelbrot set, go here. To learn more about how fractals are generated, go here.
Please understand that fractals are very computation intensive. Your fractal may take a few
seconds to generate, and it will take longer as you zoom in more (although no longer than 15
seconds, unless the server is really busy). Also understand that the server has only a limited
degree of mathematical accuracy, so once you zoom past a certain critical depth, your image will
start to become pixelated.