File:Julia IIM 6 basilica.png
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Summary[edit]
| Description |
English: Modified binary decomposition of dynamical plane for fc(z)=z*z -1
|
| Date | |
| Source | Own work |
| Author | Adam majewski |
Compare with[edit]
- Examples of two-tile subdivision rules see figure 6 on page 116 from : EXPANDING THURSTON MAPS by MARIO BONK AND DANIEL MEYER[1]
C src code[edit]
Code was formatted with Emacs
/*
c console program
1. draws Julia setfor Fc(z)=z*z +c using :
IIM/J
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 e.c -lm -Wall
to run :
./a.out
*/
#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=-1.0,Cy=0.0;
/* screen coordinate = coordinate of pixels */
int iX, iY,
iXmin=0, iXmax=1000,
iYmin=0, iYmax=1000,
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=-1.7;
const double ZxMax=1.7;
const double ZyMin=-1.7;
const double ZyMax=1.7;
/* */
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;
/* PPM file */
FILE * fp;
char *filename="6_basilica_.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 */
}
else
{
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);
}
free(array);
return 0;
} /* if (array .. else ... */
}
Licensing[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. | |
|
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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. |
You may select the license of your choice.
Rererences[edit]
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 15:31, 19 December 2012 | | 1,000 × 1,000 (49 KB) | Adam majewski (talk | contribs) | changed coordinate to 1.7 to remove artifacts |
| 15:07, 11 May 2011 |  | 1,000 × 1,000 (47 KB) | Adam majewski (talk | contribs) | {{Information |Description ={{en|1=Modified decomposition of dynamical plane for fc(z)=z*z -1}} |Source ={{own}} |Author =Adam majewski |Date = |Permission = |other_versions = }} |
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