Question concerning Julia/Mandelbrot set software

2017-12-14 05:23:47

Hey guys I'm studying the Mandelbrot set, specifically this Julia set $Q(z) = z^2 - 1 $ and I'm trying to find NONREAL points that become eventually fixed at the fixed points (pre image). I was wondering if there is a software that can iterate backward from a point on a Julia/Mandelbrot set so I can find these points graphically!

The fixed points are $\dfrac{1 \pm \sqrt{5}}{2}$. The inverse images of these that are not fixed points are $\dfrac{-1 \mp \sqrt{5}}{2}$. The inverse images of

$\dfrac{-1-\sqrt{5}}{2}$ are $\pm \frac{i}{2} \sqrt{2 \sqrt{5}-2}$.

As for software: any of the standard mathematical software systems should do fine. Maple, Mathematica, Matlab, Sage, ...

  • The fixed points are $\dfrac{1 \pm \sqrt{5}}{2}$. The inverse images of these that are not fixed points are $\dfrac{-1 \mp \sqrt{5}}{2}$. The inverse images of

    $\dfrac{-1-\sqrt{5}}{2}$ are $\pm \frac{i}{2} \sqrt{2 \sqrt{5}-2}$.

    As for software: any of the standard mathematical software systems should do fine. Maple, Mathematica, Matlab, Sage, ...

    2017-12-14 07:25:38