File:Mandelbrot Atom Domains Animation.gif

No higher resolution available.

Mandelbrot_Atom_Domains_Animation.gif ‎(600 × 600 pixels, file size: 1.91 MB, MIME type: image/gif, looped, 50 frames, 25 s)

This is a file from the Wikimedia Commons. The description on its description page there is shown below.
Commons is a freely licensed media file repository. You can help.

Summary

DescriptionMandelbrot Atom Domains Animation.gif	English: Mandelbrot Atom Domains Animation for periods 1-50
Date	15 November 2014
Source	I have made animated gif from images made with program by Claude Heiland-Allen
Author	Adam majewski

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Long description

Algorithm : A period domain, also called "atom domain"^[1]^[2]^[3]

This animated gif is made from ppm files, see bash src code below. Each frame shows one ppm file.

Numbers shows periods of atom domains. Number n means that on the image ther are domains for periods from 1 to n.

Note that :

atom domains are overlapping
atom domain contain :
- component of mandelbrot set with period n ( compare with BOF61^[4])
- exterior of this component
- some other componnets

"Atom domains surround hyperbolic components of the same period, and are generally much larger than the components themselves, which makes them useful for finding components." Claude Cite error: Closing </ref> missing for <ref> tag, modified to show only atom domains.

// http://mathr.co.uk/blog/2014-11-02_practical_interior_distance_rendering.html

// gcc -std=c99 -Wall -Wextra -pedantic -O3 -fopenmp -o mandelbrot mandelbrot.c -lm

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

const double pi = 3.141592653589793;
const double infinity = 1.0 / 0.0;
const double colour_modulus = 5.7581917135421046e-2; // (1.0 + 1.0 / (phi * phi)) / 24.0;
const double escape_radius_2 = 512.0 * 512.0;

static inline double cabs2(complex double z) {
  return creal(z) * creal(z) + cimag(z) * cimag(z);
}

static inline unsigned char *image_new(int width, int height) {
  return malloc(width * height * 3);
}

static inline void image_delete(unsigned char *image) {
  free(image);
}

static inline void image_save_ppm(unsigned char *image, int width, int height, const char *filename) {
  FILE *f = fopen(filename, "wb");
  if (f) {
    fprintf(f, "P6\n%d %d\n255\n", width, height);
    fwrite(image, width * height * 3, 1, f);
    fclose(f);
  } else {
    fprintf(stderr, "ERROR saving `%s'\n", filename);
  }
}

static inline void image_poke(unsigned char *image, int width, int i, int j, int r, int g, int b) {
  int k = (width * j + i) * 3;
  image[k++] = r;
  image[k++] = g;
  image[k  ] = b;
}

static inline void colour_hsv_to_rgb(double h, double s, double v, double *r, double *g, double *b) {
  double i, f, p, q, t;
  if (s == 0) { *r = *g = *b = v; } else {
    h = 6 * (h - floor(h));
    int ii = i = floor(h);
    f = h - i;
    p = v * (1 - s);
    q = v * (1 - (s * f));
    t = v * (1 - (s * (1 - f)));
    switch(ii) {
    case 0: *r = v; *g = t; *b = p; break;
    case 1: *r = q; *g = v; *b = p; break;
    case 2: *r = p; *g = v; *b = t; break;
    case 3: *r = p; *g = q; *b = v; break;
    case 4: *r = t; *g = p; *b = v; break;
    default:*r = v; *g = p; *b = q; break;
    }
  }
}

static inline void colour_to_bytes(double r, double g, double b, int *r_out, int *g_out, int *b_out) {
  *r_out = fmin(fmax(255 * r, 0), 255);
  *g_out = fmin(fmax(255 * g, 0), 255);
  *b_out = fmin(fmax(255 * b, 0), 255);
}

static inline void colour_mandelbrot(unsigned char *image, int width, int i, int j, int period) {
  double r, g, b;
  colour_hsv_to_rgb(period * colour_modulus, 0.5, 1.0, &r, &g, &b); // changed b from tanh(distance )to 1.0 
  int ir, ig, ib;
  colour_to_bytes(r, g, b, &ir, &ig, &ib);
  image_poke(image, width, i, j, ir, ig, ib);
}

static inline void render(unsigned char *image, int maxiters, int width, int height, complex double center, double radius) {

  double pixel_spacing = radius / (height / 2.0);

   #pragma omp parallel for schedule(dynamic, 1)
    for (int j = 0; j < height; ++j) {
     for (int i = 0; i < width; ++i) {
      double x = i + 0.5 - width / 2.0;
      double y = height / 2.0 - j - 0.5;
      complex double c = center + pixel_spacing * (x + I * y);
      complex double z = 0;
      complex double dc = 0;
      double minimum_z2 = infinity; // atom domain
      int period = 0;

      // iteration 
      for (int n = 1; n <= maxiters; ++n) {
        dc = 2 * z * dc + 1;
        z = z * z + c;
        double z2 = cabs2(z);

        if (z2 < minimum_z2) {
          minimum_z2 = z2;
          period = n;}}

         colour_mandelbrot(image, width, i, j, period);
 
    }
  }
}

int main(int argc, char **argv) {

  if (argc != 8) {

     
    fprintf(stderr,
	    "usage: %s maxiters width height creal cimag radius filename\n example :\n ./mandelbrot  100 1024 1024 -0.75 0 1.5 1.ppm\n now argc = %d \n", argv[0], argc);
    return 1;
  }

  
  int maxiters = atoi(argv[1]);
  int width = atoi(argv[2]);
  int height = atoi(argv[3]);
  complex double center = atof(argv[4]) + I * atof(argv[5]);
  double radius = atof(argv[6]);
  const char *filename = argv[7];
 
  unsigned char *image = image_new(width, height);

  render(image, maxiters, width, height, center, radius);
  image_save_ppm(image, width, height, filename);
  image_delete(image);

  return 0;
}

Bash and Image Magic src code

#!/bin/bash

# script file for BASH 
# which bash
# save this file as g.sh
# chmod +x g.sh
# ./g.sh

# code for creating ppm files using program mandelbrot
for i in $(seq  1 50)
do
  echo  
 ./mandelbrot $i 1024 1024 -0.75 0 1.5 $i.ppm 
done

 
# for all ppm files in this directory
for file in *.ppm ; do
  # b is name of file without extension
  b=$(basename $file .ppm)
  # convert from pgm to gif and add text ( level ) using ImageMagic
  convert $file -pointsize 100 -annotate +10+100 $b ${b}.gif
  echo $file
done
 
# convert gif files to animated gif
convert -resize 600x600 -delay 50  -loop 0 %d.gif[1-50] a600.gif
 
echo OK

References

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	17:16, 26 November 2014	600 × 600 (1.91 MB)	Soul windsurfer	smaller because preview is not working
	16:46, 26 November 2014	800 × 800 (2.91 MB)	Soul windsurfer	smaller
	16:38, 26 November 2014	1,000 × 1,000 (4.01 MB)	Soul windsurfer	changed code, removed distance ( black color)
	20:09, 15 November 2014	600 × 600 (2.46 MB)	Soul windsurfer	User created page with UploadWizard

File usage

The following 3 pages use this file:

[1] Atom Domain by Robert P. Munafo

[2] Practical interior distance rendering by Claude Heiland-Allen

[3] tlab : atom-domains

[4] Bof61 algorithm in wikibooks

[1]

[2]

[3]

[4]

File:Mandelbrot Atom Domains Animation.gif

Contents

Summary

Licensing

Long description

Bash and Image Magic src code

References

Captions

Items portrayed in this file

depicts

creator

some value

copyright status

copyrighted

copyright license

Creative Commons Attribution-ShareAlike 4.0 International

inception

15 November 2014

MIME type

image/gif

File history

File usage