20200129.mandelbrot-iteration.c

// Draw a graph of argument or modulus of p_n(z)
// where p_0(z) = z and p_{i+1}(z) = p_i(z)^2 + z

// Written by David A. Madore, 2020-01-29.  Public Domain.

#include <stdio.h>
#include <math.h>
#include <complex.h>
#include <assert.h>

#ifndef WIDTH
#define WIDTH 800
#endif

#ifndef HEIGHT
#define HEIGHT 800
#endif

#ifndef NBITER
#define NBITER 8
#endif

#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif

#ifndef SHOW_ABS
#define SHOW_ABS 0 // Set to 1 to produce a plot of modulus rather than arg
#endif

#ifndef DIVIDE
#define DIVIDE 0 // Set to 1 to divide p_n(z) by z^(2^n) on output
#endif

int
main (void)
{
#if SHOW_ABS
  printf ("P2\n%d %d\n255\n", WIDTH, HEIGHT);
#else
  printf ("P3\n%d %d\n255\n", WIDTH, HEIGHT);
#endif
  for ( int i=0 ; i<HEIGHT ; i++ )
    {
      for ( int j=0 ; j<WIDTH ; j++ )
	{
	  double complex c
	    = (((double)j)/(WIDTH-1) * 2 - 1) * 1.3 - 0.75
	    - I * (((double)i)/(HEIGHT-1) * 2 - 1) * 1.3;
	  double complex z = c;
#if DIVIDE
	  double complex u = c;
#endif
	  int iter;
	  for ( iter=0 ; iter<NBITER ; iter++ )
	    {
	      z = z*z + c;
#if DIVIDE
	      u = u*u;
#endif
	    }
	  if ( 1 )
	    {
#if DIVIDE
	      z /= u;
#endif
#if SHOW_ABS
	      double abs = log(cabs(z)) / (M_PI*2);
	      unsigned char gray;
	      double p = abs - floor(abs);
	      if ( p < 0 || p != p )
		p = 0;
	      else if ( p > 1 )
		p = 1;
	      if ( p < 0.5 )
		gray = 255 * (2*p);
	      else
		gray = 255 * (2-2*p);
	      printf (" %d", gray);
#else
	      double arg = carg(z) / (M_PI*2);
	      unsigned char colr, colg, colb;
	      double p = arg*6 + 3;
	      while ( p >= 6 )
		p -= 6;
	      while ( p < 0 )
		p += 6;
	      if ( p < 1 )
		{
		  colr = 0;
		  colg = 255*(1-p);
		  colb = 255;
		}
	      else if ( p < 2 )
		{
		  colr = 255*(p-1);
		  colg = 0;
		  colb = 255;
		}
	      else if ( p < 3 )
		{
		  colr = 255;
		  colg = 0;
		  colb = 255*(3-p);
		}
	      else if ( p < 4 )
		{
		  colr = 255;
		  colg = 255*(p-3);
		  colb = 0;
		}
	      else if ( p < 5 )
		{
		  colr = 255*(5-p);
		  colg = 255;
		  colb = 0;
		}
	      else
		{
		  colr = 0;
		  colg = 255;
		  colb = 255*(p-5);
		}
	      printf ("\t%d %d %d", colr, colg, colb);
#endif
	    }
	}
      printf ("\n");
    }
}

See https://twitter.com/gro_tsen/status/1222911282116014080 for further explanations.