Question: What happens to Julia sets as c leaves the Mandelbrot set?Answer: The filled Julia sets shatter as c crosses the boundary of the Mandelbrot set. |
Click on an arrow (not stem) to see an animation of the behavior of the filled Julia sets as c travels along the path shown. You must have a QuickTime player to view the animation. Click here to download a QuickTime player for Macs or PCs. Have patience while these animations are being loaded. They average around 650K per animation.
More explanation: It is a fact that the filled Julia sets for x^{2} + c assume one of only two possible shapes. Either the filled Julia set is
The Java applet below allows you to make your own movie. Simply click on a point in or near the Mandelbrot set and click Add current E. This gives you your starting c-value. Then click on a second c-value in the Mandelbrot set and again click Add current E. This determines a path along which c will move. Click Animate to compute the resulting animation. Then click Animate again to view the movie.
Please note that your browser must be Java-enabled in order to use this applet. All recent versions of Netsapce or Internet Explorer are Java-enabled.
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