File:Julia IIM 6 circle.png
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[edit]DescriptionJulia IIM 6 circle.png |
English: Modified binary decomposition of dynamical plane for fc(z)=z*z |
Source | Own work |
Author | Adam majewski |
Other versions |
|
C src code
[edit]/*
c console program
1. draws Julia setfor Fc(z)=z*z +c using :
IIM
colors exterior of Julia set using modified decomposition
dynamic 1D array for 24-bit color values
-------------------------------
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 manual creating graphic can't be simpler
------------------
Adam Majewski fraktal.republika.pl
======================
Linux console :
save as n.c
to compile :
gcc n.c -lm -Wall -march=native
to run :
./a.out
Conversion to png is made with convert from ImageMagic
convert j.ppm -resize 2000x2000 j.png
*/
#include <stdio.h>
#include <stdlib.h> /* for ISO C Random Number Functions */
#include <math.h>
/* gives sign of number */
double sign(double d)
{
if (d<0)
{return -1.0;}
else {return 1.0;};
};
/*
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
*/
int main()
{ const double Cx=0.0,Cy=0.0;
/* screen coordinate = coordinate of pixels */
int iX, iY,
iXmin=0, iXmax=10000,
iYmin=0, iYmax=10000,
iWidth=iXmax-iXmin+1,
iHeight=iYmax-iYmin+1,
/* 3D data : X , Y, color */
/* number of bytes = number of pixels of image * number of bytes of color */
iLength=iWidth*iHeight*3,/* 3 bytes of color */
index; /* of array */
/* int iXinc, iYinc,iIncMax=12; */
/* world ( double) coordinate = parameter plane*/
const double ZxMin=-1.5;
const double ZxMax=1.5;
const double ZyMin=-1.5;
const double ZyMax=1.5;
/* */
double PixelWidth=(ZxMax-ZxMin)/iWidth;
double PixelHeight=(ZyMax-ZyMin)/iHeight;
double Zx, Zy, /* Z=Zx+Zy*i */
Z0x, Z0y, /* Z0 = Z0x + Z0y*i */
Zx2, Zy2, /* Zx2=Zx*Zx; Zy2=Zy*Zy */
NewZx, NewZy,
DeltaX, DeltaY,
SqrtDeltaX, SqrtDeltaY,
AlphaX, AlphaY,
BetaX,BetaY, /* repelling fixed point Beta */
AbsLambdaA,AbsLambdaB;
/* */
int Iteration,
IterationMax=6 , /*for modified loop */
iTemp;
/* bail-out value , radius of circle ; */
// const int EscapeRadius=100;
// int ER2=EscapeRadius*EscapeRadius;
//double AR=PixelWidth; /* minimal distance from attractor = Attractor Radius */
// AR2=AR*AR;
//d,dX,dY; /* distance from attractor : d=sqrt(dx*dx+dy*dy) */
/* PPM file */
FILE * fp;
char *filename="j.ppm";
char *comment="# this is julia set for c= ";/* comment should start with # */
const int MaxColorComponentValue=255;/* color component ( R or G or B) is coded from 0 to 255 */
/* dynamic 1D array for 24-bit color values */
unsigned char *array;
/* --------- find repelling fixed point ---------------------------------*/
/* Delta=1-4*c */
DeltaX=1-4*Cx;
DeltaY=-4*Cy;
/* SqrtDelta = sqrt(Delta) */
/* sqrt of complex number algorithm from Peitgen, Jurgens, Saupe: Fractals for the classroom */
if (DeltaX>0)
{
SqrtDeltaX=sqrt((DeltaX+sqrt(DeltaX*DeltaX+DeltaY*DeltaY))/2);
SqrtDeltaY=DeltaY/(2*SqrtDeltaX); }
else /* DeltaX <= 0 */
{
if (DeltaX<0)
{
SqrtDeltaY=sign(DeltaY)*sqrt((-DeltaX+sqrt(DeltaX*DeltaX+DeltaY*DeltaY))/2);
SqrtDeltaX=DeltaY/(2*SqrtDeltaY);
}
else /* DeltaX=0 */
{
SqrtDeltaX=sqrt(fabs(DeltaY)/2);
if (SqrtDeltaX>0) SqrtDeltaY=DeltaY/(2*SqrtDeltaX);
else SqrtDeltaY=0;
}
};
/* Beta=(1-sqrt(delta))/2 */
BetaX=0.5+SqrtDeltaX/2;
BetaY=SqrtDeltaY/2;
/* Alpha=(1+sqrt(delta))/2 */
AlphaX=0.5-SqrtDeltaX/2;
AlphaY=-SqrtDeltaY/2;
AbsLambdaA=2*sqrt(AlphaX*AlphaX+AlphaY*AlphaY);
AbsLambdaB=2*sqrt(BetaX*BetaX+BetaY*BetaY);
printf(" Cx= %f\n",Cx);
printf(" Cy= %f\n",Cy);
printf(" Beta= %f , %f\n",BetaX,BetaY);
//printf(" BetaY= %f\n",BetaY);
printf(" Alpha= %f, %f\n",AlphaX,AlphaY);
//printf(" AlphaY= %f\n",AlphaY);
printf(" abs(Lambda (Alpha))= %f\n",AbsLambdaA);
printf(" abs(lambda(Beta))= %f\n",AbsLambdaB);
/* -----------------------------------------------------------------*/
array = malloc( iLength * sizeof(unsigned char) );
if (array == NULL)
{
fprintf(stderr,"Could not allocate memory");
getchar();
return 1;
}
else
{
/* fill the data array with white points */
for(index=0;index<iLength-1;++index) array[index]=255;
/* ---------------------------------------------------------------*/
for(iY=0;iY<iYmax;++iY)
{
Z0y=ZyMin + iY*PixelHeight; /* reverse Y axis */
if (fabs(Z0y)<PixelHeight/2) Z0y=0.0; /* */
for(iX=0;iX<iXmax;++iX)
{ /* initial value of orbit Z0 */
Z0x=ZxMin + iX*PixelWidth;
/* Z = Z0 */
Zx=Z0x;
Zy=Z0y;
Zx2=Zx*Zx;
Zy2=Zy*Zy;
/*----------- modified loop without checking of abs(zn) -------------*/
for (Iteration=0;Iteration<IterationMax;Iteration++)
{
Zy=2*Zx*Zy + Cy;
Zx=Zx2-Zy2 +Cx;
Zx2=Zx*Zx;
Zy2=Zy*Zy;
};
iTemp=((iYmax-iY-1)*iXmax+iX)*3;
/* --------------- compute pixel color (24 bit = 3 bajts) */
/* exterior of Filled-in Julia set */
/* binary decomposition */
if (Zy>0 )
{
array[iTemp]=255; /* Red*/
array[iTemp+1]=255; /* Green */
array[iTemp+2]=255;/* Blue */
}
if (Zy<0 )
{
array[iTemp]=0; /* Red*/
array[iTemp+1]=0; /* Green */
array[iTemp+2]=0;/* Blue */
};
/* ------------------- check the orientation of Z-plane by marking first quadrant of cartesian plane ----- */
// if (Z0x>0 && Z0y>0) array[((iYmax-iY-1)*iXmax+iX)*3]=255-array[((iYmax-iY-1)*iXmax+iX)*3];
}
}
/*-------------------- draw julia set using IIM/J ------------------------------------------*/
/* initial value of orbit Z=Z0 is repelling fixed point */
Zy=BetaY;
Zx=BetaX;
for (Iteration=0;Iteration<10000000;Iteration++)
{
/* Zn*Zn=Z(n+1)-c */
Zx=Zx-Cx;
Zy=Zy-Cy;
/* sqrt of complex number algorithm from Peitgen, Jurgens, Saupe: Fractals for the classroom */
if (Zx>0)
{
NewZx=sqrt((Zx+sqrt(Zx*Zx+Zy*Zy))/2);
NewZy=Zy/(2*NewZx);
}
else /* ZX <= 0 */
{
if (Zx<0)
{
NewZy=sign(Zy)*sqrt((-Zx+sqrt(Zx*Zx+Zy*Zy))/2);
NewZx=Zy/(2*NewZy);
}
else /* Zx=0 */
{
NewZx=sqrt(fabs(Zy)/2);
if (NewZx>0) NewZy=Zy/(2*NewZx);
else NewZy=0;
}
};
if (rand()<(RAND_MAX/2))
{
Zx=NewZx;
Zy=NewZy;
}
else {Zx=-NewZx;
Zy=-NewZy; }
/* translate from world to screen coordinate */
// iX=(Zx-ZxMin)/PixelWidth;
// iY=(ZyMax-Zy)/PixelHeight; /* reverse Y axis */
iX=(Zx-ZxMin)/PixelWidth;
iY=(Zy-ZyMin)/PixelHeight; /* */
/* plot pixel = boundary of Filled-in Julia set = Julia set*/
iTemp=((iYmax-iY-1)*iXmax+iX)*3;
array[iTemp]=255; /* Red*/
array[iTemp+1]=0; /* Green */
array[iTemp+2]=0;/* Blue */
};
/* --------------------- write the whole data array to ppm file in one step ----------------------------------------- */
/*create new file,give it a name and open it in binary mode */
fp= fopen(filename,"wb"); /* b - binary mode */
if (fp == NULL){ fprintf(stderr,"file error"); }
else
{
/*write ASCII header to the file*/
fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue);
/*write image data bytes to the file*/
fwrite(array,iLength ,1,fp);
fclose(fp);
fprintf(stderr,"file %s saved\n",filename);
//getchar();
}
free(array);
return 0;
} /* if (array .. else ... */
}
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[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
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.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 17:09, 11 May 2011 | 2,000 × 2,000 (695 KB) | Soul windsurfer (talk | contribs) | I have made 10 000 x 10 000 image and resized with image magic : convert big.png -resize 2000x2000 m.png. It has better quality now | |
16:37, 11 May 2011 | 1,000 × 1,000 (59 KB) | Soul windsurfer (talk | contribs) | {{Information |Description ={{en|1=Modified binary decomposition of dynamical plane for fc(z)=z*z }} |Source ={{own}} |Author =Adam majewski |Date = |Permission = |other_versions = }} |
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