Adam Majewski pisze:
> 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
If it can't be done better ( no answers )
then thx very much for help. (:-)
The result with explanantion is on:
http://commons.wikimedia.org/wiki/Image:Lemniscates5.png
Adam