unsigned char ComputeColor_Fatou (complex double z, int IterMax)
{

  int i;			// number of iteration
  for (i = 0; i < IterMax; ++i)
    {
      z = f(z);
      if (IsEscaping(z)) // escaping = exterior
	{
	  uExterior += 1;
	  return iColorOfExterior;
	}			 

	
	if (IsAttracting3(z)) // 
	{
	  uInterior3 += 1;
	  return iColorOfInterior3;
	}			 


	if (IsAttracting105(z)) //
	{
	  uInterior105 += 1;
	  return iColorOfInterior105;
	}			 
    }

  //
  uUnknown += 1;
  return iColorOfUnknown;
}

/*

  Adam Majewski
  adammaj1 aaattt o2 dot pl  // o like oxygen not 0 like zero 
  
  
  
"Almost failed"

Cubic set z^3+A*z+c with two cycles of length 3 and 105 at L20 in about 20h computed.

c=(-5947392-3850240*i) * 2^-25
A=(-17343094-31007487*i) * 2^-25

-----------

 gcc l.c -lm -Wall -march=native -fopenmp
a@zalman:~/Dokumenty/almost$ ./a.out
setup start
 end of setup 
compute Fatou image 
File 15000_100000.pgm saved . Comment = name = iWidth+IterMax	 f(z) = z^6+A*z+c where A= 15000.0000000000000000 ; -0.9240951240062714 	 c =-0.1772460937500000 ; -0.1147460937500000 
 allways free memory (deallocate )  to avoid memory leaks 
Numerical approximation of Julia set for fc(z)= z^3+A*z+c 
parameter c = ( -0.1772460937500000 ; -0.1147460937500000 ) 
parameter A = ( -0.5168644785881042 ; -0.9240951240062714 ) 
Image Width = 3.000000 in world coordinate
PixelWidth = 0.0002000133342223 
Maximal number of iterations = iterMax = 100000 
ratio of image  = 1.000000 ; it should be 1.000 ...
gcc version: 9.3.0
__STDC__ = 1
__STDC_VERSION__ = 201710
c dialect = C18
a@zalman:~/Dokumenty/almost$ convert 15000_100000.pgm -resize 2000x2000 15.png

  
  ==============================================
  
  
  Structure of a program or how to analyze the program 
  
  
  ============== Image X ========================
  
  DrawImageOfX -> DrawPointOfX -> ComputeColorOfX 
  
  first 2 functions are identical for every X
  check only last function =  ComputeColorOfX
  which computes color of one pixel !
  
  

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

  
  ---------------------------------
  indent d.c 
  default is gnu style 
  -------------------



  c console progam 
  
	export  OMP_DISPLAY_ENV="TRUE"	
  	gcc d.c -lm -Wall -march=native -fopenmp
  	time ./a.out > b.txt


  gcc l.c -lm -Wall -march=native -fopenmp


  time ./a.out

  time ./a.out >i.txt
  time ./a.out >e.txt
  
  
  
  
  
  
  convert -limit memory 1000mb -limit disk 1gb dd30010000_20_3_0.90.pgm -resize 2000x2000 10.png

  
  =======================
  # gnuplot "i.plt"
set terminal svg enhanced background rgb 'white'
set xlabel "re(z)"
set ylabel "DLD"
set title "Relation between z and DLD in the interior of Julia set for c = -1"
set output "interior.svg"
plot "i.txt" with lines

  ----------------------
  d0 - db  = 5.0000000000000000 - 4.5389870050569598 = 0.4610129949430402
 allways free memory (deallocate )  to avoid memory leaks 
Numerical approximation of Julia set for fc(z)= z^2 + c 
parameter c = ( -1.0000000000000000 ; 0.0000000000000000 ) 
Image Width = 4.000000 in world coordinate
PixelWidth = 0.004004 
Maximal number of iterations = iterMax = 1000 
ratio of image  = 1.000000 ; it should be 1.000 ...
gcc version: 7.5.0
  
  
*/

#include <stdio.h>
#include <stdlib.h>		// malloc
#include <string.h>		// strcat
#include <math.h>		// M_PI; needs -lm also
#include <complex.h>
#include <omp.h>		// OpenMP
#include <limits.h>		// Maximum value for an unsigned long long int



// https://sourceforge.net/p/predef/wiki/Standards/

#if defined(__STDC__)
#define PREDEF_STANDARD_C_1989
#if defined(__STDC_VERSION__)
#if (__STDC_VERSION__ >= 199409L)
#define PREDEF_STANDARD_C_1994
#endif
#if (__STDC_VERSION__ >= 199901L)
#define PREDEF_STANDARD_C_1999
#endif
#endif
#endif




/* --------------------------------- global variables and consts ------------------------------------------------------------ */



// virtual 2D array and integer ( screen) coordinate
// Indexes of array starts from 0 not 1 
//unsigned int ix, iy; // var
static unsigned int ixMin = 0;	// Indexes of array starts from 0 not 1
static unsigned int ixMax;	//
static unsigned int iWidth;	// horizontal dimension of array

static unsigned int iyMin = 0;	// Indexes of array starts from 0 not 1
static unsigned int iyMax;	//

static unsigned int iHeight = 15000;	//  
// The size of array has to be a positive constant integer 
static unsigned long long int iSize;	// = iWidth*iHeight; 

// memmory 1D array 
unsigned char *data;
//unsigned char *edge;
//unsigned char *edge2;

// unsigned int i; // var = index of 1D array
//static unsigned int iMin = 0; // Indexes of array starts from 0 not 1
static unsigned int iMax;	// = i2Dsize-1  = 
// The size of array has to be a positive constant integer 
// unsigned int i1Dsize ; // = i2Dsize  = (iMax -iMin + 1) =  ;  1D array with the same size as 2D array



// zoom to part of period
static const double ZxMin = -1.5; //0.6;	//-0.05;
static const double ZxMax = 1.5;	//0.75;
static const double ZyMin = -1.5;	//-0.1;
static const double ZyMax = 1.5;	//0.7;
static double PixelWidth;	// =(ZxMax-ZxMin)/ixMax;
static double PixelHeight;	// =(ZyMax-ZyMin)/iyMax;
static double ratio;


// complex numbers of parametr plane 
//https://fractalforums.org/fractal-mathematics-and-new-theories/28/julia-sets-true-shape-and-escape-time/2725/msg22791#msg22791
/*

c=(-5947392-3850240*i) * 2^-25
A=(-17343094-31007487*i) * 2^-25

*/
double complex c = - 0.11474609375*I -0.17724609375;
	// parameter of function fc(z)=z^6 +A*x+ c  = (15728640-19136512*i) * (2^-25)
                   

double complex  A=  - 0.9240951240062714 *I - 0.5168644785881043;

complex double f(complex double z) {

	return  z*z*z +A*z+ c;		// complex iteration z^6+A*z+c
	}





/*
ER = pow(10,ERe);
   AR = pow(10,-ARe);
 */
 
int ARe_3 = 2; 
double AR_3 ; //= 1e-15;			// increase ARe until black ( unknown) points disapear 
double AR2_3;

int ARe_105 = 2; 
double AR_105 ; //= 1e-15;			// increase ARe until black ( unknown) points disapear 
double AR2_105;



double ER;			//= 1e60;
double ER2;			//ER2 = ER*ER
double AR2;			//AR2 = AR*AR

complex double z3  = 0.5900999663884065+0.2837738661170331*I;
complex double z105 = -0.5147160557032144-0.2946889400739363*I; //
//-0.3861355806430767 -0.3080847982463079*I;


/*
[-0.1570883645161246,-0.5331333747802431],
[-0.4586468403362385,0.4180413342397985],
[0.5900999663884065,0.2837738661170331]]


period 105 
*/

int IterMax = 100000;




/* colors = shades of gray from 0 to 255 */
unsigned char iColorOfExterior = 250;
unsigned char iColorOfInterior3 = 100;
unsigned char iColorOfInterior105 = 30;
unsigned char iColorOfBoundary = 0;
unsigned char iColorOfUnknown = 20;

// pixel counters
unsigned long long int uUnknown = 0;
unsigned long long int uInterior3 = 0;
unsigned long long int uInterior105 = 0;
unsigned long long int uExterior = 0;



/* ------------------------------------------ functions -------------------------------------------------------------*/





//------------------complex numbers -----------------------------------------------------





// from screen to world coordinate ; linear mapping
// uses global cons
double
GiveZx (int ix)
{
  return (ZxMin + ix * PixelWidth);
}

// uses globaal cons
double
GiveZy (int iy)
{
  return (ZyMax - iy * PixelHeight);
}				// reverse y axis


complex double
GiveZ (int ix, int iy)
{
  double Zx = GiveZx (ix);
  double Zy = GiveZy (iy);

  return Zx + Zy * I;


}




double cabs2(complex double z){

	return creal(z)*creal(z)+cimag(z)*cimag(z);


}




// ****************** DYNAMICS = trap tests ( target sets) ****************************


/* -----------  array functions = drawing -------------- */

/* 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 * iWidth;
}



unsigned int Give_i_from_z(complex double z){

	unsigned int ix = (creal(z)-ZxMin)/PixelWidth;
	unsigned int iy = (ZyMax - cimag(z))/PixelHeight;
	return Give_i(ix,iy);
}

// ***********************************************************************************************
// ********************** edge detection usung Sobel filter ***************************************
// ***************************************************************************************************

// from Source to Destination
int
ComputeBoundaries (unsigned char S[], unsigned char D[])
{

  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;
  // boundaries are in D  array ( global var )

  // clear D array
  memset (D, iColorOfExterior, iSize * sizeof (*D));	// for heap-allocated arrays, where N is the number of elements = FillArrayWithColor(D , iColorOfExterior);

  // printf(" find boundaries in S array using  Sobel filter\n");   
#pragma omp parallel for schedule(dynamic) private(i,iY,iX,Gv,Gh,G) shared(iyMax,ixMax)
  for (iY = 1; iY < iyMax - 1; ++iY)
    {
      for (iX = 1; iX < ixMax - 1; ++iX)
	{
	  Gv =
	    S[Give_i (iX - 1, iY + 1)] + 2 * S[Give_i (iX, iY + 1)] +
	    S[Give_i (iX - 1, iY + 1)] - S[Give_i (iX - 1, iY - 1)] -
	    2 * S[Give_i (iX - 1, iY)] - S[Give_i (iX + 1, iY - 1)];
	  Gh =
	    S[Give_i (iX + 1, iY + 1)] + 2 * S[Give_i (iX + 1, iY)] +
	    S[Give_i (iX - 1, iY - 1)] - S[Give_i (iX + 1, iY - 1)] -
	    2 * S[Give_i (iX - 1, iY)] - S[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)
	    {
	      D[i] = 255;
	    }			/* background */
	  else
	    {
	      D[i] = 0;
	    }			/* boundary */
	}
    }



  return 0;
}



// copy from Source to Destination
int
CopyBoundaries (unsigned char S[], unsigned char D[])
{

  unsigned int iX, iY;		/* indices of 2D virtual array (image) = integer coordinate */
  unsigned int i;		/* index of 1D array  */


  //printf("copy boundaries from S array to D array \n");
  for (iY = 1; iY < iyMax - 1; ++iY)
    for (iX = 1; iX < ixMax - 1; ++iX)
      {
	i = Give_i (iX, iY);
	if (S[i] == 0)
	  D[i] = 0;
      }



  return 0;
}



int IsEscaping(complex double z){

	if (cabs2 (z) > ER2) return 1;
	return 0;
}


int IsAttracting3(complex double z){

	if (cabs2 (z - z3) < AR2_3) return 1;
	return 0;
}





int IsAttracting105(complex double z){

	if (cabs2 (z - z105) < AR2_105) return 1;
	return 0;
}






// find basin and it's color using simple test ( bailout ) for escaping to infinity 

unsigned char
ComputeColor_Fatou (complex double z, int IterMax)
{

  int i;			// number of iteration
  for (i = 0; i < IterMax; ++i)
    {




      z = f(z);
      if (IsEscaping(z)) // escaping = exterior
	{
	  uExterior += 1;
	  return iColorOfExterior;
	}			 

	
	if (IsAttracting3(z)) // 
	{
	  uInterior3 += 1;
	  return iColorOfInterior3;
	}			 


	if (IsAttracting105(z)) //
	{
	  uInterior105 += 1;
	  return iColorOfInterior105;
	}			 





    }

  //
  uUnknown += 1;
  return iColorOfUnknown;


}





// plots raster point (ix,iy) 
int
DrawFatouPoint (unsigned char A[], int ix, int iy, int IterMax)
{
  int i;			/* index of 1D array */
  unsigned char iColor = 0;
  complex double z;


  i = Give_i (ix, iy);		/* compute index of 1D array from indices of 2D array */
  z = GiveZ (ix, iy);
  iColor = ComputeColor_Fatou (z, IterMax);
  A[i] = iColor;		// interior

  return 0;
}




// fill array 
// uses global var :  ...
// scanning complex plane 
int
DrawFatouImage (unsigned char A[], int IterMax)
{
  unsigned int ix, iy;		// pixel coordinate 

  fprintf (stderr, "compute Fatou image \n");
  // for all pixels of image 
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax, uUnknown, uInterior3, uInterior105, uExterior)
  for (iy = iyMin; iy <= iyMax; ++iy)
    {
      fprintf (stderr," %d from %d \r", iy, iyMax);	//info 
      for (ix = ixMin; ix <= ixMax; ++ix)
	DrawFatouPoint (A, ix, iy, IterMax);	//  
    }

  return 0;
}


//=========





// plots raster point (ix,iy) 
int MarkTrapPoint (unsigned char A[], int ix, int iy)
{
  int i;			/* index of 1D array */
  
  complex double z;


  i = Give_i (ix, iy);		/* compute index of 1D array from indices of 2D array */
  z = GiveZ (ix, iy);
  if (IsAttracting3(z))   A[i] = 255 - A[i];		// inversion
  
  if (IsAttracting105(z))   A[i] = 255 - A[i];		// inversion

  return 0;
}



// fill array 
// uses global var :  ...
// scanning complex plane 
int MarkTraps (unsigned char A[])
{
  unsigned int ix, iy;		// pixel coordinate 

  fprintf (stderr, "Mark traps\n");
  // for all pixels of image 
#pragma omp parallel for schedule(dynamic) private(ix,iy) shared(A, ixMax , iyMax, uUnknown, uInterior3, uInterior105, uExterior)
  for (iy = iyMin; iy <= iyMax; ++iy)
    {
      fprintf (stderr," %d from %d \r", iy, iyMax);	//info 
      for (ix = ixMin; ix <= ixMax; ++ix)
	MarkTrapPoint (A, ix, iy);	//  
    }

  return 0;
}


//======================================================================================



int IsInside (int x, int y, int xcenter, int ycenter, int r){

	
	double dx = x- xcenter;
	double dy = y - ycenter;
	double d = sqrt(dx*dx+dy*dy);
	if (d<r) 
		return 1;
	return 0;
	  

} 

int PlotPoint(complex double z, unsigned char A[]){

	
	unsigned int ix_seed = (creal(z)-ZxMin)/PixelWidth;
	unsigned int iy_seed = (ZyMax - cimag(z))/PixelHeight;
	unsigned int i;
	
	
	 /* mark seed point by big pixel */
  	int iSide =3.0*iWidth/2000.0 ; /* half of width or height of big pixel */
  	int iY;
  	int iX;
  	for(iY=iy_seed-iSide;iY<=iy_seed+iSide;++iY){ 
    		for(iX=ix_seed-iSide;iX<=ix_seed+iSide;++iX){ 
    			if (IsInside(iX, iY, ix_seed, iy_seed, iSide)) {
      			i= Give_i(iX,iY); /* index of _data array */
      			A[i]= 255;}}}
	
	
	return 0;
	
}


// fill array 
// uses global var :  ...
// scanning complex plane 
int MarkAttractors (unsigned char A[])
{
  
	int iter;
	
	complex double z;
  	fprintf (stderr, "mark attractors \n");
  
  	// period 3 cycle
  	z = z3;
  	PlotPoint(z, A);
	for (iter = 0; iter < 3; ++iter)
    		{ z  = f(z);
    		  PlotPoint(z, A);	
    		 
      				}
      	// period 105			
      	z = z105;
  	PlotPoint(z, A);
	for (iter = 0; iter < 105; ++iter)
    		{ z  = f(z);
    		  PlotPoint(z, A);	
    		 
      				}

  return 0;
}


//======================================================================================










// *******************************************************************************************
// ********************************** save A array to pgm file ****************************
// *********************************************************************************************

int
SaveArray2PGMFile (unsigned char B[], int ia, int ib,  int ic, int id,  int ie, char *comment)
{

  FILE *fp;
  const unsigned int MaxColorComponentValue = 255;	/* color component is coded from 0 to 255 ;  it is 8 bit color file */
  char name[100];		/* name of file */
  snprintf (name, sizeof name, "%d_%d_%d_%d_%d", ia, ib, ic ,id,ie);	/*  */
  char *filename = strcat (name, ".pgm");
  char long_comment[200];
  sprintf (long_comment, "%s\t f(z) = z^6+A*z+c where A= %.16f ; %.16f \t c =%.16f ; %.16f", comment, creal(A),cimag(A), creal(c), cimag(c));





  // save image array 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", long_comment, iWidth, iHeight, MaxColorComponentValue);	// write header to the file
  fwrite (B, iSize, 1, fp);	// write array with image data bytes to the file in one step 
  fclose (fp);

  // info 
  printf ("File %s saved ", filename);
  if (long_comment == NULL || strlen (long_comment) == 0)
    printf ("\n");
  else
    printf (". Comment = %s \n", long_comment);

  return 0;
}




int
PrintCInfo ()
{

  printf ("gcc version: %d.%d.%d\n", __GNUC__, __GNUC_MINOR__, __GNUC_PATCHLEVEL__);	// https://stackoverflow.com/questions/20389193/how-do-i-check-my-gcc-c-compiler-version-for-my-eclipse
  // OpenMP version is displayed in the console : export  OMP_DISPLAY_ENV="TRUE"

  printf ("__STDC__ = %d\n", __STDC__);
  printf ("__STDC_VERSION__ = %ld\n", __STDC_VERSION__);
  printf ("c dialect = ");
  switch (__STDC_VERSION__)
    {				// the format YYYYMM 
    case 199409L:
      printf ("C94\n");
      break;
    case 199901L:
      printf ("C99\n");
      break;
    case 201112L:
      printf ("C11\n");
      break;
    case 201710L:
      printf ("C18\n");
      break;
      //default : /* Optional */

    }

  return 0;
}


int
PrintProgramInfo ()
{


  // display info messages
  printf ("Numerical approximation of Julia set for fc(z)= z^3+A*z+c \n");
  //printf ("iPeriodParent = %d \n", iPeriodParent);
  //printf ("iPeriodOfChild  = %d \n", iPeriodChild);
  printf ("parameter c = ( %.16f ; %.16f ) \n", creal (c), cimag (c));
  printf ("parameter A = ( %.16f ; %.16f ) \n", creal (A), cimag (A));

  printf ("Image Width = %f in world coordinate\n", ZxMax - ZxMin);
  printf ("PixelWidth = %.16f \n", PixelWidth);
  printf ("AR_3 = %.16f \n", AR_3);
  printf ("ER = %.16f \n", ER);
   


  //printf("pixel counters\n");
  //printf ("uUnknown = %llu\n", uUnknown);
  //printf ("uExterior = %llu\n", uExterior);
  //printf ("uInterior = %llu\n", uInterior);
  //printf ("Sum of pixels  = %llu\n", uInterior+uExterior + uUnknown);
  //printf ("all pixels of the array = iSize = %llu\n", iSize);


  // image corners in world coordinate
  // center and radius
  // center and zoom
  // GradientRepetition
  printf ("Maximal number of iterations = iterMax = %d \n", IterMax);
  printf ("ratio of image  = %f ; it should be 1.000 ...\n", ratio);
  
  
  
  printf ("pixel counters\n");
  printf ("uUnknown = %llu\n", uUnknown);
  printf ("uExterior = %llu\n", uExterior);
  printf ("uInterior3 = %llu\n", uInterior3);
  printf ("uInterior105 = %llu\n", uInterior105);
  printf ("Sum of pixels  = %llu\n", uInterior3 + uInterior105 + uExterior + uUnknown);
  printf ("all pixels of the array = iSize = %llu\n", iSize);
  printf ("Maximum value for an unsigned long long int = ULLONG_MAX = %llu\n",
	  ULLONG_MAX);

  //




  return 0;
}






// *****************************************************************************
//;;;;;;;;;;;;;;;;;;;;;;  setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
// **************************************************************************************

int
setup ()
{

  fprintf (stdout, "setup start\n");






  /* 2D array ranges */

  iWidth = iHeight;
  iSize = iWidth * iHeight;	// size = number of points in array 
  // iy
  iyMax = iHeight - 1;		// Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
  //ix

  ixMax = iWidth - 1;

  /* 1D array ranges */
  // i1Dsize = i2Dsize; // 1D array with the same size as 2D array
  iMax = iSize - 1;		// Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].

  /* Pixel sizes */
  PixelWidth = (ZxMax - ZxMin) / ixMax;	//  ixMax = (iWidth-1)  step between pixels in world coordinate 
  PixelHeight = (ZyMax - ZyMin) / iyMax;
  ratio = ((ZxMax - ZxMin) / (ZyMax - ZyMin)) / ((double) iWidth / (double) iHeight);	// it should be 1.000 ...

  // minimal radius of circla containing all the Julia set
  ER = 2.0; 
  ER2 = ER*ER;
  
  // radius of maximal circle which is inside component
  AR_3 = 7.0*pow (10, -ARe_3);
  AR2_3 = AR_3*AR_3;
  
  AR_105 = 2.5*pow (10, -ARe_105); // adjust the radius : 
  AR2_105 = AR_105*AR_105;


  /* create dynamic 1D arrays for colors ( shades of gray ) */
  data = malloc (iSize * sizeof (unsigned char));


  if (data == NULL)
    {
      fprintf (stderr, " Could not allocate memory");
      return 1;
    }





 


  fprintf (stdout, " end of setup \n");

  return 0;

}				// ;;;;;;;;;;;;;;;;;;;;;;;;; end of the setup ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;




int
end ()
{


  fprintf (stdout, " allways free memory (deallocate )  to avoid memory leaks \n");	// https://en.wikipedia.org/wiki/C_dynamic_memory_allocation
  free (data);


  PrintProgramInfo ();
  PrintCInfo ();
  return 0;

}

// ********************************************************************************************************************
/* -----------------------------------------  main   -------------------------------------------------------------*/
// ********************************************************************************************************************

int
main ()
{
  setup ();


  DrawFatouImage (data, IterMax);	// first find Fatou
  SaveArray2PGMFile (data, iWidth, IterMax, ARe_3, ARe_105, 1,"name = iWidth_IterMax_ARe_ ARe_3_ARe_105_1");
  
  MarkTraps(data );
  SaveArray2PGMFile (data, iWidth, IterMax, ARe_3,  ARe_105,2,"name = iWidth_IterMax+1_ARe ARe_3_ARe_105_1");

  MarkAttractors(data);
  SaveArray2PGMFile (data, iWidth, IterMax, ARe_3,  ARe_105,3,"name = iWidth_IterMax+1_ARe ARe_3_ARe_105_1");
  
  end ();

  return 0;
}