/* 

Adam Majewski
fraktal.republika.pl


 c program:
  1. draws Julia set for z^15-z

  using  escape time 
  aproximates julia set near fixed point z=0 using 14-arm star

compare with :
 http://www.ijon.de/mathe/julia/node6.html

similar image ( 13 petals) but different function and method of drawing
I think that function below image is not the same as used for creating image 
 -------------------------------         
 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





====================

gcc z.c -Wall -lm
time ./a.out

=====================

 memory is OK 
File 10.000000.pgm saved. 
 find boundaries in data array using  Sobel filter
File 20.000000.pgm saved. 
copy boundaries from edge array to data array 
File 30.000000.pgm saved. 

real	0m0.875s
user	0m0.860s
sys	0m0.000s

 
 */
#include <stdio.h>
#include <stdlib.h> // malloc
#include <math.h>
#include <complex.h>
#include <string.h> // strcat
 
  const int iXmax = 1000; 
 const int iYmax = 1000;
 int iSize ; //= iXmax*iYmax; //
// target set for points falling into alfa fixed point
// is a circle around alfa fixed point
// with radius = AR
double AR ; // radius of target set around alfa fixed point in world coordinate AR = PixelWidth*TargetWidth; 
double AR2; // =AR*AR;
double TargetRadiusInPixels; // radius of target set in pixels ; 

int NumberOfPetals=14;

// memmory 1D arrays 
 unsigned char *data;
 unsigned char *edge;
 int i; // index of array
double TwoPi=2.0*M_PI;

/* gives position of 2D point (iX,iY) in 1D array  ; uses also global variable iWidth */
unsigned int Give_i(unsigned int ix, unsigned int iy)
{ return ix + iy*iYmax; }


 
// save data array to pgm file 
int SaveArray2PGMFile( unsigned char data[], double t)
{
 
  FILE * fp;
  const unsigned int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ;  it is 8 bit color file */
  char name [10]; /* name of file */
  sprintf(name,"%f", t); /*  */
  char *filename =strcat(name,".pgm");
  char *comment="# ";/* comment should start with # */
 
  /* save image to the pgm file  */      
  fp= fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode  */
  fprintf(fp,"P5\n %s\n %u %u\n %u\n",comment,iXmax,iYmax,MaxColorComponentValue);  /*write header to the file*/
  fwrite(data,iSize,1,fp);  /*write image data bytes to the file in one step */
  printf("File %s saved. \n", filename);
  fclose(fp);
 
  return 0;
}

double GiveTurn(double complex z)
{
  double argument;
 
  argument = carg(z); //   argument in radians from -pi to pi
  if (argument<0) argument=argument + TwoPi; //   argument in radians from 0 to 2*pi
  return argument/TwoPi ; // argument in turns from 0.0 to 1.0
}



// all points of interior fall into fixed point z=0
// thru 14 petals
unsigned char GiveColorOfInterior(double x, double y)

{
int i;
int iMax=NumberOfPetals; 
double angle;
double  offset = 1.0/(2.0*iMax);


 //  works !!!!!!
  angle=GiveTurn(x+y*I); 
  if (angle< offset  || (1.0-offset)<angle) return 231; // 
for(i=0;i<iMax;++i) if (angle< offset+ (1.0*i)/iMax) return ((unsigned char)(230-i));  

    return 160; // 
      
 
}

int AddBoundaries(unsigned char data[])
{
 
  unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i; /* index of 1D array  */
  /* sobel filter */
  unsigned char G, Gh, Gv; 
 
 
 
 
  printf(" find boundaries in data array using  Sobel filter\n");   

  for(iY=1;iY<iYmax-1;++iY){ 
    for(iX=1;iX<iXmax-1;++iX){ 
      Gv= data[Give_i(iX-1,iY+1)] + 2*data[Give_i(iX,iY+1)] + data[Give_i(iX-1,iY+1)] - data[Give_i(iX-1,iY-1)] - 2*data[Give_i(iX-1,iY)] - data[Give_i(iX+1,iY-1)];
      Gh= data[Give_i(iX+1,iY+1)] + 2*data[Give_i(iX+1,iY)] + data[Give_i(iX-1,iY-1)] - data[Give_i(iX+1,iY-1)] - 2*data[Give_i(iX-1,iY)] - data[Give_i(iX-1,iY-1)];
      G = sqrt(Gh*Gh + Gv*Gv);
      i= Give_i(iX,iY); /* compute index of 1D array from indices of 2D array */
      if (G==0) {edge[i]=245;} /* background */
      else {edge[i]=0;}  /* boundary */
    }
  }
 
    return 0;
}
 
int CopyBoundaries()
{
 
  unsigned int iX,iY; /* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i; /* index of 1D array  */
      

 printf("copy boundaries from edge array to data array \n");
 for(iY=1;iY<iYmax-1;++iY)
    for(iX=1;iX<iXmax-1;++iX)
       {i= Give_i(iX,iY); if (edge[i]==0) data[i]=0;}
 
 
 
  return 0;
}

 int main()
 {
 
  /* screen ( integer) coordinate */
  int iX,iY;
 
  
  iSize = iXmax*iYmax; //
 /* world ( double) coordinate = parameter plane*/
 const double xMin=-1.2;
 const double xMax=1.2;
 const double yMin=-1.2;
 const double yMax=1.2;
 /* */
 double PixelWidth=(xMax-xMin)/iXmax;
 double PixelHeight=(yMax-yMin)/iYmax;
 //
 /* color  is coded from 0 to 255 */
 /* it is 8 bit color file */
 
 unsigned char color;

//

 double x, y, tempx,    /* Z=x+y*i   */
 x0, y0,  /* Z0 = x0 + y0*i */
 x2, y2; /* x2=x*x;  y2=y*y  */
 double x2y2; //, y4, x4, x2my2;
 double x10,y10;
 /*  */
 int Iteration;
 const int IterationMax=2000;

  
 /* bail-out value , radius of circle ;  */
 const int EscapeRadius=2;
 int ER2=EscapeRadius*EscapeRadius;
 TargetRadiusInPixels = 250.0; // = 15.0; // radius of target set in pixels ; Maybe increase to 20 = 1000/50
 AR = PixelWidth*TargetRadiusInPixels; // !!!! important value  ( and precision and time of creation of the pgm image ) 
 AR2= AR*AR;

/* create dynamic 1D arrays for colors ( shades of gray ) */
  data = malloc( iSize * sizeof(unsigned char) );
  edge = malloc( iSize * sizeof(unsigned char) );
  if (edge == NULL || edge == NULL )
    {
      fprintf(stderr," Could not allocate memory\n");
      return 1;
    }
  else fprintf(stderr," memory is OK \n");


 

 /* compute and write image data bytes to the file*/
 for(iY=0;iY<iYmax;++iY)
    {
     y0=yMax - iY*PixelHeight; /* reverse Y  axis */
     if (fabs(y0)<PixelHeight/2) y0=0.0; /*  */  
     printf(" iy = %d from %d\r", iY, iYmax); //info   
     for(iX=0;iX<iXmax;++iX)
       {    /* initial value of orbit Z0 */
        x0=xMin + iX*PixelWidth;
        /* Z = Z0 */
       x=x0;
       y=y0;
            
       x2=x*x;
       y2=y*y;
       x2y2= x2+y2;
      // color=100;
       /* */
       for (Iteration=0;Iteration<IterationMax ;Iteration++)
          { 
             if (x2y2>ER2) { color=245;                      break;}/* exterior of Filled-in Julia set   */
             // check test every 14 iteration 
             if (!(Iteration % NumberOfPetals) && (x2y2<AR2)) { color=GiveColorOfInterior(x,y); break;}/* interior of Filled-in Julia set   */
             // z^15- z
             y10= y2*y2*y2*y2*y2;
             x10= x2*x2*x2*x2*x2;


//(%i3) realpart(z1);
//(%o3) -15*x*y^14        +455*x^3*y^12      -3003*x^5*y^10      +6435*x^7*y^8                  -5005*x^9*y^6                  +1365*x^11*y^4      -105*x^13*y^2      +x^15        -x
tempx = -15.0*x*y10*y2*y2 +455.0*x2*x*y10*y2 -3003.0*x*x2*x2*y10 +6435.0*x*x2*x2*x2*y2*y2*y2*y2 -5005.0*x*x2*x2*x2*x2*y2*y2*y2 +1365.0*x*x10*y2*y2 -105.0*x10*x2*x*y2 +x10*x2*x2*x -x ; 
//(%i4) imagpart(z1);
//(%o4) -y^15        +105*x^2*y^13      -1365*x^4*y^11      +5005*x^6*y^9                  -6435*x^8*y^7                   +3003*x^10*y^5      -455*x^12*y^3    +15*x^14*y-y
y =     -y10*y2*y2*y +105.0*x2*y10*y2*y -1365.0*x2*x2*y10*y +5005.0*x2*x2*x2*y2*y2*y2*y2*y -6435.0*x2*x2*x2*x2*y2*y2*y2*y  +3003.0*x10*y2*y2*y -455.0*x10*x2*y2*y +15*x10*x2*x2*y  -y;

	     x=tempx;
             x2=x*x;
             y2=y*y; 
             x2y2= x2+y2;     
             
          };

    // if (Iteration==IterationMax) color=GiveColorOfInterior(x,y); ;
     i=Give_i(iX,iY);
     data[i]=color;
                         
    
  
  }
 }
SaveArray2PGMFile(data,TargetRadiusInPixels+1.1); 
AddBoundaries(data); 
SaveArray2PGMFile(edge,TargetRadiusInPixels+2.10); 
CopyBoundaries();
SaveArray2PGMFile(data,TargetRadiusInPixels+3.10);  

//
  free(data);
  free(edge);

 return 0;
 }