How to generate a Julia Set picture

Every point on the complex plane in and around the Mandelbrot Set will generate a different Julia Set.

1. Click the Explore Slice button on the Control Panel then the Julia Sets option button. I display a map of the Mandelbrot Set.

2. There's a magnified viewbox at the right-hand side of the dialog box. (If the cross-hair doesn't move, click on the New place button.)
3. Click on the position for which you want a Julia Set then Do this one. (If you want to come back and generate an adjacent Julia Set, click Remember this place. You can use the nudge buttons to move the cross-hair.
4. I will generate the Julia Set for that point. There are thousands of Julia sets to explore from that map, thousands more if you enter coordinates in between the map ones. That should keep most of us busy for a few lifetimes.

There is an interesting relationship between Julia Sets. You can find this by producing pictures of four or so adjacent points. My map will give three digits significance, but some Julia Sets flip over suddenly to give quite different pictures for adjacent points. You can enter the coordinates in between the map ones.

For example, in the Dragon Fields, around (R=+0.346, I=+0.075), Julia Sets change dramatically point to point. Try (R=+0.356, I=+0.075) as the second Set. You'll need the in-between Sets at (R=+0.347 to +0.355, I=+0.075) to watch the Julia Sets break up into islands of fractal dust. Try it, you'll see what I mean.

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