Jaime Villate pisze:
> 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.
Page about your packages ( there was examples and docs, now there is no
link )
Hi
Here is last version.
It works only up to 5 iteration ,
http://fraktal.republika.pl/images/lemniscates5.png
because 6 curve is not precise ( on my computer ).
http://fraktal.republika.pl/images/lemniscates6.png
I use png file because svg gives me only black color.
=================== code =============================
load(implicit_plot); /* package by Andrej Vodopivec */
c: x+%i*y;
ER:2; /* Escape Radius = bailout value it should be >=2 */
f[n](c) := if n=1 then c else (f[n-1](c)^2 + c);
ip_grid:[100,100];
ip_grid_in:[15,15];
my_preamble: "set zeroaxis; set title 'Boundaries of level sets of
escape time of Mandelbrot set'; set xlabel 'Re(c)'; set ylabel 'Im(c)'";
implicit_plot(makelist(abs(ev(f[n](c)))=ER,n,1,6),
[x,-2.5,2.5],[y,-2.5,2.5],[gnuplot_preamble,
my_preamble],[gnuplot_term,"png size 1000,1000"],[gnuplot_out_file,
"lemniscates6.png"]);
==========================================
Can it be done better ?
Adam