Friday, January 25, 2008

Friday Fractal: NLVM Mandelbrot and Julia Sets Applet

The National Library of Virtual Manipulatives at Utah State University has a Mandelbrot and Julia Sets applet that is your first resource for playing with fractal images. Instead of making my own fractal image this week, I have skitched some images for you to peruse and perhaps use in your classes. We have no time to do this in our regular classes but they would be a fun introduction for children in an after school program or math club.

Be sure to read the instructions and the Parents and Teachers files (I have closed the sidebars with these files on these skitches).

The first skitch above shows the Mandelbrot set. There is only one Mandelbrot set. You can zoom into a portion of the image by dragging your mouse over the section you are interested in. It appears in the right hand window. You can then drag in the right hand window to further zoom in and it will appear in the left. Students will observe that the entire Mandelbrot set is reproduced again and again as you zoom in further and further.

Although there is only one Mandelbrot set, there are an infinite number of Julia sets. Julia sets are fractals: there is one Julia set for every point on the Mandelbrot set. Select the Julia Sets option and you will see a Julia set in the left hand window. You can zoom in on this fractal by dragging your cusor over the image. The zoomed image will appear on the right. You can also move the cursor on the coordinate plane that appears so that you can see what happens to the set in the different areas of the plane.

Above you see a zoomed image of a Julia set.

On the last option, you can explore the relationship between the Mandelbrot set and Julia sets. You will see the Mandelbrot set on the left. Shift-click on an area in which you are interested and the Julia set for the point that you selected will appear on the right. You can zoom with your cursor on either window.

I hope that you explore and enjoy this applet. It can help you understand the images that I make and you can begin to make your own with third party software.

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