# [Maxima] lemniscates

Jaime Villate villate at fe.up.pt
Fri Mar 14 08:06:27 CDT 2008

```On Fri, 2008-03-14 at 10:38 +0100, Adam Majewski wrote:
> I would like to draw family of curves:
> z: abs(zn)=r
> where
> r is constant positive number
> c is constant complex number
> zn: f(n,z)

> f[n,z] :=
> if n=0
>    then z
>    else (f[n-1, z]^2 + c);
>
> Can I do it in Maxima ?

Sure. Here is one way to do it (Mario can show you another way of doing
it!).

(%i3) z: x+%i*y\$
(%i4) f[n](z) := if n=0 then z else (f[n-1](z)^2 + c)\$
(%i5) implicit_plot(makelist(abs(ev(f[n](z),c=1))=2,n,0,2), [x,-3,3],
[y,-3,3])\$

I'm very interested in the work you are doing with chaos and fractals.
I've been extremely busy and I have not taught my course on dynamical
systems for more than a year, so my dynamical systems package was
abandoned for over a year.
This semester I'm teaching dynamics again; I started with a physics
introduction and next week I will start lecturing on dynamical systems
and I will have to retake the work with that package.
Please send me any comments or ideas for improvements and I will try to
do something before the new version of Maxima is released.
Best regards,
Jaime

```