Title: Magnetic Mandelbrot
Post by: Kalles Fraktaler on July 31, 2014, 10:12:59 PM
I want to do the Magnetic Mandelbrot 1 fractal and eventually find the perturbation method for it. However I only get almost all orbits trapped, i.e. an almost only black picture, no matter how high I set the maximum iteration. But it has some expected shapes. What am I doing wrong? Is there a different bailout criteria? (http://www.icd.com/tsd/fractals/beginner/equation2.gif) std::complex<double> Z(Zr,Zi), C(m_pX[x],m_pY[y]), _1(1,0), _2(2,0);
std::complex<double> T = (Z*Z) + (C-_1);
std::complex<double> N = Z*_2 + (C-_2);
std::complex<double> K = T/N;
Z = K*K;
Zr = Z.real();
Zi = Z.imag();
Title: Re: Magnetic Mandelbrot
Post by: cKleinhuis on August 01, 2014, 11:35:17 AM
yes there is, in the ultrafractal formula definition bailout criteria is:
|z| < @bailout && |z - 1| > @lowerbailout
lowerbailout defaults to "0.0005"
but i checked it, this part of the bailout is not so siginificantly influencing the image, at least i did not end with an image like yours when removing that part!
Title: Re: Magnetic Mandelbrot
Post by: Roquen on August 01, 2014, 03:11:12 PM
Is this what you expect: http://glsl.heroku.com/e#18816.0
Title: Re: Magnetic Mandelbrot
Post by: 3dickulus on August 06, 2014, 04:45:46 AM
Or this ? /***************************************************************************
qtfmag.cpp - description
-------------------
begin : Wed Sep 5 2001
copyright : (C) 2001 by 3Dickulus.
email : ***@****.net
***************************************************************************/
/***************************************************************************
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
***************************************************************************/
#include "qtfpainter.h"
/**********************************************************
*
* Magnetic funcs
*/
void QtfPainter::mag0func( double r, double i)
{
uint count = 0;
double p;
double q;
double a;
double b;
double mag;
double dr = divergence*0.33333;
while ( count++ < maxiter)
{
a = r * r - i * i + 3;
p = (r + r);
b = p * i;
p += 2;
q = i; q += i;
mag = (p * p + q * q);
r = (a * p + b * q) / mag;
i = (p * b - a * q) / mag;
a = r * r - i * i;
i = dr * r * i;
r = a;
if ( (fabs(r-1) + fabs(i)) < 0.0001)
{
count |= 16;
break;
}
if ( fabs(a) > 10000) break;
}
coltmp = (count >= maxiter) ? 0 : ( count % maxcol + 2 );
return;
}
void QtfPainter::mag1func( double r, double i)
{
uint count = 0;
double p;
double q;
double a;
double b;
double dr = divergence*0.33333;
double mag,magr,magi;
magr = r + 1;
magi = i;
r = 0;
i = 0;
while ( count++ < maxiter)
{
a = r * r - i * i + magr - 1;
p = b = (r + r);
p += magr; p -= 2;
b *= i; b += magi;
q = i; q += i; q += magi;
mag = (p * p + q * q);
r = (a * p + b * q) / mag;
i = (p * b - a * q) / mag;
a = r * r - i * i;
i = dr * r * i;
r = a;
if ( (fabs(r-1) + fabs(i)) < 0.0001)
{
count |= 16;
break;
}
if ( fabs(a) > 10000) break;
}
coltmp = (count >= maxiter) ? 0 : ( count % maxcol + 2 );
return;
}
void QtfPainter::mag2func( double r, double i)
{
uint count = 0;
double p;
double q;
double a;
double b;
double mag;
double dr = divergence*0.33333;
while ( count++ < maxiter)
{
a = r * r - i * i + 9;
b = 2 * r * i;
p = a * r - b * i + 6;
q = a * i + b * r;
a = 3 * (r * r - i * i) + (6 * r) + 7;
b = 3 * (r * i + r * i) + (6 * i);
mag = a * a + b * b;
r = (p * a + q * b)/mag;
i = (a * q - p * b)/mag;
mag = r * r - i * i;
i = dr * r * i;
r = mag;
if ( (fabs(r-1) + fabs(i)) < 0.0001)
{
count |= 16;
break;
}
if ( fabs(a) > 10000) break;
}
coltmp = (count >= maxiter) ? 0 : ( count % maxcol + 2 );
return;
}
void QtfPainter::mag3func( double r, double i)
{
uint count = 0;
double p = r + 1;
double q = i;
double a;
double b;
double dr = divergence*0.33333;
double re, im;
double ren, imn;
double ret, imt;
double mag,magr,magi;
re = (p - 1) * (p - 2) - q * q;
im = q * (2 * p - 3);
magr = p * p - q * q - 3 * p + 3;
magi = 2 * p * q - 3 * q;
r = 0;
i = 0;
while ( count++ < maxiter)
{
ren = r * r - i * i;
imn = 2 * r * i;
a = ren + 3 * (p - 1);
b = imn + 3 * q;
ret = a * r - b * i + re;
imt = a * i + b * r + im;
a = 3 * ren + 3 * ((p - 2) * r - q * i) + magr;
b = 3 * imn + 3 * (q * r + (p - 2) * i) + magi;
mag = a * a + b * b;
r = (ret * a + imt * b) / mag;
i = (a * imt - ret * b) / mag;
a = r * r - i * i;
i = dr * r * i;
r = a;
if ( (fabs(r-1) + fabs(i)) < 0.0001)
{
count |= 16;
break;
}
if ( fabs(a) > 10000) break;
}
coltmp = (count >= maxiter) ? 0 : ( count % maxcol + 2 );
return;
}
EDIT: image 1x generated by mag0func image 1q generated by mag1func the other 2 funcs are variants of these two
|