lemniscates



Andrej Vodopivec pisze:
> On Fri, Mar 14, 2008 at 6:05 PM, Adam Majewski <adammaj1 at o2.pl> wrote:
>> Jaime Villate pisze:
>>  Your code is working perfectly and is so short. Great. Thx.
>>  But ...  now I see that I have given wrong conditions. (:-|
>>  I intended to draw:
>>  http://mathworld.wolfram.com/images/eps-gif/MandelbrotLemniscates_700.gif
>>
>>  So I have change: removed z (it is allways 0 )
>>  and now it is OK ( Your solution showed me the way ).
>>  Here is the code:
>>
>>  ======================
>>  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"]);
> 
> implicit_plot ignores nticks. To make the curves smoother increase the
> density of the grid with ip_grid and ip_grid_in:
> 
> ip_grid_in:[15,15]$
> implicit_plot(...)
> 
> 
That's it. Thx.

===========================
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);
/* sets the grid for the first sampling in implicit plots. */
ip_grid:[100,100];
/* sets the grid for the second sampling in implicit plots. */
ip_grid_in:[15,15];
implicit_plot(makelist(abs(ev(f[n](c)))=ER,n,1,4), 
[x,-3,3],[y,-3,3],[gnuplot_preamble, "set zeroaxis"]);
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