File:Julia IIM 1.jpg
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Captions
DescriptionJulia IIM 1.jpg | Julia set for c=i . Fc(z)=z*z + c. Made using IIM |
Date | |
Source | Own work |
Author | Adam majewski |
Permission (Reusing this file) |
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
|
Summary
[edit]Julia set for c=i . Fc(z)=z*z + c. Made using IIM with random choose of one of two roots.
Compare with
[edit]-
3d-image
-
modified decomposition and IIM/J
-
LSM/J B&W
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LSM/J with colour
C source
[edit]It is a console C program ( one file) It can be compiled under :
- windows ( gcc thru 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. Use file viewer to see it.
C console program which writes an image to PPM file. It is ( probably) multiplatform.
#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;};
};
/* ----------------------*/
int main()
{
const double Cx=0.0,Cy=1.0;
/* screen coordinate = coordinate of pixels */
int iX, iY,
iXmin=0, iXmax=2000,
iYmin=0, iYmax=2000,
iWidth=iXmax-iXmin+1,
iHeight=iYmax-iYmin+1,
/* 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;
/* world ( double) coordinate = parameter plane*/
const double ZxMin=-2.5;
const double ZxMax=2.5;
const double ZyMin=-2.5;
const double ZyMax=2.5;
/* */
double PixelWidth=(ZxMax-ZxMin)/iWidth;
double PixelHeight=(ZyMax-ZyMin)/iHeight;
double Zx, Zy, /* Z=Zx+Zy*i */
NewZx, NewZy,
DeltaX, DeltaY,
SqrtDeltaX, SqrtDeltaY,
AlphaX, AlphaY,
BetaX,BetaY; /* repelling fixed point Beta */
/* */
int Iteration,
IterationMax=100000000;
/* PPM file */
FILE * fp;
char *filename="julia1.ppm";
char *comment="# this is julia set for c=i ";/* 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;
printf(" Cx= %f\n",Cx);
printf(" Cy= %f\n",Cy);
printf(" Beta= %f\n",BetaX);
printf(" BetaY= %f\n",BetaY);
printf(" AlphaX= %f\n",AlphaX);
printf(" AlphaY= %f\n",AlphaY);
/* initial value of orbit Z=Z0 is repelling fixed point */
Zy=BetaY; /* */
Zx=BetaX;
/*-------------------------------------------------------------------*/
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 (Iteration=0;Iteration<IterationMax;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=(Zy-ZyMin)/PixelHeight; /* */
/* plot pixel */
array[((iYmax-iY-1)*iXmax+iX)*3]=0;
array[((iYmax-iY-1)*iXmax+iX)*3+1]=0;
array[((iYmax-iY-1)*iXmax+iX)*3+2]=0;
};
/* 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 saved");
getchar();
}
free(array);
return 0;
} /* if (array .. else ... */
}
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:44, 11 January 2008 | 2,000 × 2,000 (95 KB) | Soul windsurfer (talk | contribs) | {{Information |Description=Julia set for c=i . Fc(z)=z*z + c. Made using IIM |Source=self-made |Date=2008.01.11 |Author= Adam majewski |Permission={{cc-by-3.0}} |other_versions= }} |
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