Mandelbrot Magic

Virtual Julia Sets

Now that you are familiar with some of the shapes of the Julia Sets, you should recognize the shape in the panel below. While it closely resembles a Julia Set from the Seahorse Valley, it is actually part of the Mandelbrot Set! <Ctrl>-click to zoom out from this "Virtual Julia Set" to discover where it occurs in the Mandelbrot Set.

Click mouse to Zoom In <Ctrl>-Click mouse to Zoom Out Add <Shift> to Zoom faster

Zoom into the points labeled A,B, and C in the panel above to explore the virtual Julia Sets surrounding a Mandelbrot replica. Notice how the virtual Julia Set resembles an actual Julia Set from the corresponding point in the entire Mandelbrot Set. And yet it is just assembled from parts of the Mandelbrot Set organized in the shape of a Julia Set.

The closer you explore to the edge of the replica Mandelbrot Set, the more the virtual Julia Sets will resemble the real ones.