File:Demj.jpg
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Summary
DescriptionDemj.jpg | Julia set using DEM/J for c=-0.74543+0.11301*i and f(z)=z*z+c. It is the same as Fig 4.15 on page 194 from "The science of fractal images" by Peitgen and Saupe |
Date | |
Source | self-made ( C program ) |
Author | Adam majewski |
Compare with
-
Misiurewicz point
-
c close to −0.74−0.11i
-
c = -0.74543 + 0.11301 i
http://www.mostlymaths.net/2011/06/gift-quadratic-julia-set-for-icelands.html
https://plus.google.com/+OwenMaresh/posts/TPPdrnC56t9
To construct: find the parameter value associated with the frond-tail Misiurewicz point of the period-27 bulb of the n-Mandelbrot set, and make pictures of the Julia sets associated with them. Owen Maresh
C source code
It is a console C program ( one file) It can be compiled under :
- windows ( gcc through Dev-C++ )
- linux and mac using gcc :
gcc main.c -lm
it creates a.out file. Then run it :
./a.out
It creates ppm file in program directory.
Convert to jpg and resize from 2.8 GB ppm file to 331 kB jpg file with Image Magic:
convert g3.ppm -resize 2000x1250 g3.jpg
Use file viewer to see it.
/*
c console program:
1. draws Julia setfor Fc(z)=z*z +c
using DEM/J algorithm ( Distance Esthimation Method for Julia set )
-------------------------------
2. technic of creating ppm file is based on the code of Claudio Rocchini
http://en.wikipedia.org/wiki/Image:Color_complex_plot.jpg
create 24 bit color graphic file , portable pixmap file = PPM
see http://en.wikipedia.org/wiki/Portable_pixmap
to see the file use external application ( graphic viewer)
---------------------------------
I think that creating graphic can't be simpler
comments : Adam Majewski
gcc d.c -lm
it creates a.out file. Then run it :
./a.out
*/
#include <stdio.h>
#include <math.h>
int GiveEscapeTimeJ(double _Zx0, double _Zy0,double C_x, double C_y, int iMax, double _ER2)
{
int i;
double Zx, Zy;
double Zx2, Zy2; /* Zx2=Zx*Zx; Zy2=Zy*Zy */
Zx=_Zx0; /* initial value of orbit */
Zy=_Zy0;
Zx2=Zx*Zx;
Zy2=Zy*Zy;
for (i=0;i<iMax && ((Zx2+Zy2)<_ER2);i++)
{
Zy=2*Zx*Zy + C_y;
Zx=Zx2-Zy2 +C_x;
Zx2=Zx*Zx;
Zy2=Zy*Zy;
};
return i;
}
/*
estimates distance from point c to nearest point in Julia set
for Fc(z)= z*z + c
z(n+1) = Fc(zn)
this function is based on function mndlbrot::dist from mndlbrot.cpp
from program mandel by Wolf Jung (GNU GPL )
http://www.mndynamics.com/indexp.html
Hyunsuk Kim :
For Julia sets, z is the variable and c is a constant. Therefore df[n+1](z)/dz = 2*f[n]*f'[n] -- you don't add 1.
For the Mandelbrot set on the parameter plane, you start at z=0 and c becomes the variable. df[n+1](c)/dc = 2*f[n]*f'[n] + 1.
*/
double jdist(double Zx, double Zy, double Cx, double Cy , int iter_max)
{
int i;
double x = Zx, /* Z = x+y*i */
y = Zy,
/* Zp = xp+yp*1 = 1 */
xp = 1,
yp = 0,
/* temporary */
nz,
nzp,
/* a = abs(z) */
a;
for (i = 1; i <= iter_max; i++)
{ /* first derivative zp = 2*z*zp = xp + yp*i; */
nz = 2*(x*xp - y*yp) ;
yp = 2*(x*yp + y*xp);
xp = nz;
/* z = z*z + c = x+y*i */
nz = x*x - y*y + Cx;
y = 2*x*y + Cy;
x = nz;
/* */
nz = x*x + y*y;
nzp = xp*xp + yp*yp;
if (nzp > 1e60 || nz > 1e60) break;
}
a=sqrt(nz);
/* distance = 2 * |Zn| * log|Zn| / |dZn| */
return 2* a*log(a)/sqrt(nzp);
}
/* ------------------------------------------------------*/
int main(void)
{
const double Cx=-0.74543;
const double Cy=0.11301;
/* screen ( integer) coordinate */
int iX,iY;
const int iXmax = 40000;
const int iYmax = 25000;
/* world ( double) coordinate = parameter plane*/
const double ZxMin=-2.0;
const double ZxMax=2.0;
const double ZyMin=-1.25;
const double ZyMax=1.25;
/* */
double PixelWidth=(ZxMax-ZxMin)/iXmax;
double PixelHeight=(ZyMax-ZyMin)/iYmax;
/* color component ( R or G or B) is coded from 0 to 255 */
/* it is 24 bit color RGB file */
const int MaxColorComponentValue=255;
FILE * fp;
char *filename="g3.ppm";
char *comment="# ";/* comment should start with # */
static unsigned char color[3];
double Zx0, Zy0; /* Z0 = Zx0 + Zy0*i */
/* */
int LastIteration;
const int IterationMax=2000;
/* bail-out value , radius of circle ; */
const int EscapeRadius=400;
int ER2=EscapeRadius*EscapeRadius;
double distanceMax=PixelWidth/5; /*jdist( 0,0,Cx,Cy, IterationMax);*/
/*create new file,give it a name and open it in binary mode */
fp= fopen(filename,"wb"); /* b - binary mode */
/*write ASCII header to the file*/
fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue);
/* compute and write image data bytes to the file*/
for(iY=0;iY<iYmax;++iY)
{
Zy0=ZyMax - iY*PixelHeight; /* reverse Y axis */
if (fabs(Zy0)<PixelHeight/2) Zy0=0.0; /* */
for(iX=0;iX<iXmax;++iX)
{ /* initial value of orbit Z0 */
Zx0=ZxMin + iX*PixelWidth;
LastIteration = GiveEscapeTimeJ(Zx0, Zy0, Cx, Cy, IterationMax, ER2);
/* compute pixel color (24 bit = 3 bytes) */
if (LastIteration==IterationMax)
{ /* interior of Julia set = white */
color[0]=255;
color[1]=255;
color[2]=255;
}
else /* exterior of Filled-in Julia set = */
{ double distance=jdist(Zx0,Zy0,Cx,Cy,IterationMax);
if (distance<distanceMax)
{ /* Julia set = black */
color[0]=0; /* Red*/
color[1]=0; /* Green */
color[2]=0;/* Blue */
}
else
{ /* exterior of Julia set = white */
color[0]=255;
color[1]=255;
color[2]=255;
};
}
/* check the orientation of Z-plane */
/* mark first quadrant of cartesian plane*/
/* if (Z0x>0 && Z0y>0) color[0]=255-color[0]; */
/*write color to the file*/
fwrite(color,1,3,fp);
}
}
fclose(fp);
printf("file %s saved\n", filename);
getchar();
return 0;
}
Licensing
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Items portrayed in this file
depicts
some value
29 February 2008
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 21:45, 26 June 2011 | 2,000 × 1,250 (332 KB) | wikimediacommons>Soul windsurfer | better quality |
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