From: "Jay Hill"<jrhill@nosc.mil>
To: fractal-art@aros.net
Message-ID: <88256564.0008F1A8.01@NOTESGW.NOSC.MIL>
Date: Thu, 4 Dec 1997 17:48:36 -0800
Subject: Re: F.O.T.D., 03-12 (Omnichaos)
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Hi Jim,
When you use the critical point you, it would appear,
get the classic MSet like objects, the Julia sets are
connected and you don't get the images we are
used to seeing from you.  :-)

Here is a short C++ code for computing the critical
points for the Contest formula:

f = z^3 + c(1 + z - z^2)
f' = 3z^2 + c(1-2z)

f'=0 has roots

z0 = (c +- sqrt(c^2 - 3c))/3

// CRITICAL.CPP
// Computes critical points of
//z := z^3 + c*(1+z-z^2)
// by Jay Hill, 1997
#include <complex.h>
#include <stdio.h>
#include <math.h>

void main(int argc, char **argv)
{
  double x=-1, y=0;
  if (argc > 1) x = atof(argv[1]);
  if (argc > 2) y = atof(argv[2]);
 complex c(x,y);
 cout << "c:" << c <<"\n";
 complex z=(c+sqrt(c*(c-3)))/3;
// complex f=(3*z-2*c)*z+c;
 cout << "z:" <<z <<"\n";
}
Usage:
CRITICAL [real part] [imaginary part]

And here is a sample, the splotch near the top of the contest object.
It is centered at -0.559898 + 0.779713i so its z0 = 0.334535 -0.081554i.

distorted          { ; distorted Midget in the Fractint Contest space
                    ; by Jay Hill, 1997
  reset=1960 type=formula formulafile=contest4.frm
  formulaname=contest4 center-mag=-0.559898/0.779713/19.99743
  params=0.334535/-0.081554 maxiter=256
  colors=000000<26>FUsGWvHWv<42>wilxjkxjkxjk<\
  143>xvdywcxwc<30>0WG9g69g6
  savename=distort1
  }
frm:contest4  {; Kerry Mitchell
      ; slightly optimized version of Contest formula
         z=p1, c=pixel:
         z2=sqr(z), z=z*z2+c*(1+z-z2), |z| <= 4
         }

Jay
PS  Jim, and anyone else, don't forget to post your contest entries to the
Fractint list!