On Fri, 2008-03-14 at 18:05 +0100, Adam Majewski wrote:
> load(implicit_plot);
> c: x+%i*y;
> ER:2; /* Escape Radius = bailout value */
> f[n](c) := if n=1 then c else (f[n-1](c)^2 + c);
> implicit_plot(makelist(abs(ev(f[n](c)))=ER,n,1,5),
> [x,-3,3],[y,-3,3],[nticks, 1000000],
> [gnuplot_preamble, "set zeroaxis"]);
> ===========================
> I have make big number for nticks but it didn't make lines more smooth.
> Can it be done better ? ( As in Mathemathica )
Andrej has already answered (you just have to be patient because it
takes a long time to get that nice plot). I do not know how to make the
x and y scale equal in gnuplot, but if you use openmath it will be done
by default (as well as showing the axes):
ip_grid_in:[10,10]$
implicit_plot(makelist(abs(ev(f[n](c)))=ER,n,1,4),[x,-3,3],[y,-3,3],[plot_format,openmath]);
I still have to make some changes to make implicit_plot accept the new
options in plot2d, such as [legend,false].
> There is another question :
> What if ER <2 ?
>
> I allways thought that it tends to boundary of Mandelbrot set
> from inside :
> http://mathworld.wolfram.com/PearCurve.html
> http://en.wikipedia.org/wiki/Polynomial_lemniscate
> http://www.2dcurves.com/higher/higherm.html
> Is it true ?
Yes. Look for instance at the L3 lemniscate:
implicit_plot(makelist(abs(ev(f[3](c)))=n/2,n,1,4),[x,-3,3],[y,-3,3],[plot_format,openmath]);
> Curves for ER<2 are diffrent from those for ER>=2 .
> Is it an error on below page ?
> http://www.2dcurves.com/higher/higherm.html
I think in that page the should use 2 rather than 1, to define the equipotential curves. That's
why their pear curve looks like a light bulb and not a pear.
> ( some www help pages from your page are lost ? )
Oh really, please tell me the URL and I'll fix it.
Cheers,
Jaime