Mandelbrot set: Power Play (by Kevin Holmes)

In this page, I'm glad to host a Java applet made by Kevin Holmes.

As we have seen in the Mandelbrot set page, the iteration formula that produces the Mandelbrot set is:

Z_n = Z_n-1² + C

Let's consider a more general formula:

Z_n = Z_n-1^k + C

What happens if we use this formula instead of the first one? Obviously, a picture made with k=2 is the classic Mandelbrot set. Different values of k produce different fractal sets.

Click here to see some sample pictures that show the shape of the Mandelbrot set for different values of k.

By smoothly varying the value of k, it is possible to obtain an animation that shows how the shape of the Mandelbrot set is affected by this parameter. Power Play allows you to try out this process by yourself.

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