The Julia Sets

The Julia Set is an interesting slice. By viewing the A and B axes on the screen, with C and D axes at zero we can generate a fascinating 2D object: a perfectly circular fractal disc, one that has no edge, no matter how far you zoom down to look at it. The Julia Sets you've seen in books and magazines are actually slices across all four dimensions: A and B axes are shown on the screen, at non-zero values along the C and D axes.

Now, where do we get those C and D axis values? Why, from a picture of the Mandelbrot Set itself. You simply point the cross-hair at any point on the Mandelbrot Set, I'll pick up the C and D axis values, and generate a picture.

This is the map of the Mandelbrot Set from which you choose your Julia Set:

This Julia Set is at the white cross...

...on the Mandelbrot Set seen below.

If you want to generate picture of closely related Julia Sets, you can check a box for FracRove to remember the present position. After you have generated and saved the picture you can use the nudge controls to reposition the cross-hair to the position you want.

 

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