Mandelbrot and Julia: A surprising relationship

My students's honours projects revealed a surprising relation between Mandelbrot and Julia sets, illustrated in the video. As is well known, each point on the Mandelbrot set generates a corresponding Julia set, and moving the point on Mandelbrot causes the corresponding Julia to vary in a characteristic way. Also as is well known, the Mandelbrot set contains reduced images of itself, and similarly the Julia set contains reduced images of itself. Here is what surprised me: moving a point about the reduced Mandelbrot set causes the reduced Julia set to vary, in exactly the same characteristic style as moving a point about the full Mandelbrot causes the full Julia to vary. This only becomes apparent when using a real-time interactive application such as Mandelbrot Maps. Is this fact well known? (I've spotted at least one other YouTube video illustrating the fact, so I'm not the only one to discover it.)

The video above was produced by my student, Alasdair Corbett, whose version of Mandelbrot Maps for Android phones and tablets is available from Google Play (formerly Android Market). Alasdair is using the Google Play rating system as part of the evaluation for his honours project, and I encourage you to download the app and rate it. (Not to mention that it's great fun to use.) We believe Alasdair's project is the only Android app that permits real-time interaction showing the relation between Mandelbrot and Julia.

If you don't have an Android device available, you can see the same effect using Iain Parris and Edward Mallia's web app. (But it's not as much fun without a touch screen!)

That Mandelbrot Maps apps is wonderful. It's so fast! In what language was it programmed?
mandelbrot adds the start value at each iteration, while julia set will be added (generally) with a constant.

so they are almost the samething.
This fact seems obvious to me, if you look at a flag and wave it about; what you see changes. If you make a tiny flag and look at it with a microscope and wave it about, you get the same effect, it's just a case of scale.
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