samm.c

/* 
   c program: console, 1-file
   samm.c
   
   algorithms:
   - escape time
   - DEM/M = distance estimation
   - SAC/M = SAM/M 
   
   samm = Stripe Average Method  =  
   Stripe Average coloring = sac 
   with :
   - skipping first (i_skip+1) points from average
   - linear interpolation 
   
   https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/stripeAC
   
  
   
   --------------------------------
   1. draws Mandelbrot set for complex quadratic polynomial 
   Fc(z)=z*z +c
   using samm = Stripe Average Method/Coloring  
   -------------------------------         
   2. technique 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)
   -----
   it is example  for : 
   https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set
 
   -------------
   compile : 

 
 
   gcc samm.c -lm -Wall 
 
 
   ./a.out
   
   convert samm.ppm -resize 800x800 samm.png

   -------- git --------
   
   
   cd existing_folder
   git init
   git remote add origin git@gitlab.com:adammajewski/mandelbrot_wiki_ACh.git
   git add samm.c
   git commit -m "samm + linear interpolation "
   git push -u origin master



 
 
 
*/
#include <stdio.h>
#include <math.h>
#include <complex.h> // https://stackoverflow.com/questions/6418807/how-to-work-with-complex-numbers-in-c
#include <omp.h> //OpenM 
 

#define M_PI        3.14159265358979323846    /* pi */
 
/* screen ( integer) coordinate */
int iX,iY;
const int iXmax = 8000; 
const int iYmax = 8000;

/* world ( double) coordinate = parameter plane*/
double Cx,Cy;

// c = -0.355298979690605  +1.178016112830515 i    period = 0
// c = 0.213487557597331  +0.604701020309395 i    period = 0
const double CxMin=-2.25;
const double CxMax=0.75;
const double CyMin=1.5;
const double CyMax= -1.5;
/* */
double PixelWidth; //=(CxMax-CxMin)/iXmax;
double PixelHeight; // =(CyMax-CyMin)/iYmax;

/* color component ( R or G or B) is coded from 0 to 255 */
/* it is 24 bit color RGB file */
const int MaxColorComponentValue=255; 
FILE * fp;
char *filename="samm.ppm"; // https://commons.wikimedia.org/wiki/File:Mandelbrot_set_-_Stripe_Average_Coloring.png
char *comment="# ";/* comment should start with # */
        
static unsigned char color[3]; // 24-bit rgb color

unsigned char s = 7; // stripe density

const int IterationMax=2500; //  N in wiki 
int i_skip = 2; // exclude (i_skip+1) elements from average

/* bail-out value for the bailout test for exaping points
   radius of circle centered ad the origin, exterior of such circle is a target set  */
const double EscapeRadius=1000000; // = ER big !!!!
double lnER; // ln(ER)
        
        
        
        
double complex give_c(int iX, int iY){
  double Cx,Cy;
  Cy=CyMax - iY*PixelHeight; // reverse Y axis
  Cx=CxMin + iX*PixelWidth;
   
  return Cx+Cy*I;
 
 
}
 


// the addend function
// input : complex number z
// output : double number t 
double Give_t(double complex z){

  return 0.5+0.5*sin(s*carg(z));

}

/*
  input :
  - complex number
  - intege
  output = average or other estimators, like distance or interior
 
*/
double Give_Arg(double complex C , int iMax)
{
  int i=0; // iteration 
   
   
  double complex Z= 0.0; // initial value for iteration Z0
  double A = 0.0; // A(n)
  double prevA = 0.0; // A(n-1)
  double R; // =radius = cabs(Z)
  double d; // smooth iteration count
  double complex dC = 0; // derivative
  double de; // = 2 * z * log(cabs(z)) / dc;
   
    
  // iteration = computing the orbit
  for(i=0;i<iMax;i++)
    { 
    
      dC = 2 * Z * dC + 1; 
      Z=Z*Z+C; // https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/qpolynomials
      
      if (i>i_skip) A += Give_t(Z); // 
      
      R = cabs(Z);
      if(R > EscapeRadius) break; // exterior of M set
   
      prevA = A; // save value for interpolation
        
    } // for(i=0
   
   
  if (i == iMax) 
    A = -1.0; // interior 
  else { // exterior
    de = 2 * R * log(R) / cabs(dC);
    if (de < PixelWidth) A = FP_ZERO; //  boundary
    else {
      // computing interpolated average
      A /= (i - i_skip) ; // A(n)
      prevA /= (i - i_skip - 1) ; // A(n-1) 
      // smooth iteration count
      d = i + 1 + log(lnER/log(R))/M_LN2;
      d = d - (int)d; // only fractional part = interpolation coefficient
      // linear interpolation
      A = d*A + (1.0-d)*prevA;
     }   
  }
    
  return A;  
}
 

/* 
 
 input = complex number
 output 
  - color array as Formal parameters
  - int = return code
*/
int compute_color(complex double c, unsigned char color[3]){
 
  double arg;
  unsigned char b;
   
  // compute 
  arg = Give_Arg( c, IterationMax);
     
  // 
  if (arg < 0.0)
     /*  interior of Mandelbrot set = inside_color =  */
      b = 0;                          
    
  else // exterior and boundary
     {      
       if (arg == FP_ZERO) b= 255; // boundary     
          else b = (unsigned char) (255 - 255*arg ); // exterior
     };
    
 // gray gradient
 color[0]= b;  /* Red*/
 color[1]= b;  /* Green */ 
 color[2]= b;  /* Blue */
 
 
  return 0;
}
 
 
 
void setup(){
 
  //
  PixelWidth=(CxMax-CxMin)/iXmax;
  PixelHeight=(CyMax-CyMin)/iYmax;
  
  lnER = log(EscapeRadius); // ln(ER) 
        
         
  /*create new file,give it a name and open it in binary mode  */
  fp= fopen(filename,"wb"); /* b -  binary mode */
  /*write ASCII header to the file*/
  fprintf(fp,"P6\n %s\n %d\n %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue);
 
}
 



void info(){

  double distortion;
  // widt/height
  double PixelsAspectRatio = (double)iXmax/iYmax;  // https://en.wikipedia.org/wiki/Aspect_ratio_(image) 
  double WorldAspectRatio = (CxMax-CxMin)/(CyMax-CyMin);
  printf("PixelsAspectRatio = %.16f \n", PixelsAspectRatio );
  printf("WorldAspectRatio = %.16f \n", WorldAspectRatio );
  distortion = PixelsAspectRatio - WorldAspectRatio;
  printf("distortion = %.16f ( it should be zero !)\n", distortion );
  printf("\n");
  printf("bailut value = Escape Radius = %.0f \n", EscapeRadius);
  printf("IterationMax = %d \n", IterationMax);
  printf("i_skip = %d = number of skipped elements ( including t0 )= %d \n", i_skip, i_skip+1);

  // file  
  printf("file %s saved. It is called .... in  A Cheritat wiki\n", filename);

}
 



 
void close(){
 
  fclose(fp);
  info(); 

}
 
 
 
 
 
// ************************************* main ************************* 
int main()
{
        
  complex double c;
        
        
 
  setup();      
        
        
  printf(" render = compute and write image data bytes to the file \n");
 //#pragma omp parallel for schedule(static) private(iY, iX, c, color)
  for(iY=0;iY<iYmax;iY++)
    for(iX=0;iX<iXmax;iX++)
      { // compute pixel coordinate        
	c = give_c(iX, iY);  
	/* compute  pixel color (24 bit = 3 bytes) */
	compute_color(c,color);         
	/*write color to the file*/
	fwrite(color,1,3,fp);
      }
        
  
  
  close();
  
         
  return 0;
}