Fractals/Computer graphic techniques/2D/gfile

         "Any computer-generated picture is a finite collection of pixels." ( A Dudko, M Yampolsky)[1]

Graphic files

One can :

  • directly create graphic file
  • open existing graphic file
  • add/read/remove text information to graphic file

Types of graphic files :

  • images
    • static images
    • moving images
      • video ( ogg file ) - one needs special program ( viewer) to run it
      • animation ( animated gif file without viewer)
  • non-image files

Static imagesEdit

Digital Image Representation

  • raster
  • vector

Dynamic range of the image

  • LDR
    • standard LDR
    • LDR tone mapped from HDR
    • Pseudo-HDR or Exposure Blending or Exposure fusion = Images that have been merged from several exposures without creating an intermediate HDR image and without the use of tone mapping
  • HDR
    • data = Unprocessed HDR = floating point framebuffer ( in OpenGl GL_RGB16F, GL_RGBA16F, GL_RGB32F, or GL_RGBA32F )

Raster filesEdit

PGM image file and C++ program by Ilya Voyager





// create 1D array
 iSize = iWidth*iHeight; // size = number of points in array  
  /* create dynamic 1D arrays for colors ( shades of gray ) */
  data = malloc( iSize * sizeof(unsigned char) );
  if (data == NULL )
      fprintf(stderr," Could not allocate memory\n");
      return 1;

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

SaveArray2PGMFile (unsigned char A[], int a, int b,  int c, 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", a, b, c );	/*  */
  char *filename = strcat (name, ".pgm");
  char long_comment[200];
  sprintf (long_comment, "fc(z)=z*(1+z)*(1+z)*(C-(2C+1)*z+(3+4*C)*z*z/4)  %s", comment);

  // 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
  size_t rSize = fwrite (A, sizeof(A[0]), iSize, fp);	// write whole array with image data bytes to the file in one step 
  fclose (fp);

  // info 
  if ( rSize == iSize) 
  		printf ("File %s saved ", filename);
  		if (long_comment == NULL || strlen (long_comment) == 0)
    		printf ("\n");
  			else { printf (". Comment = %s \n", long_comment); }
  	else {printf("wrote %zu elements out of %llu requested\n", rSize,  iSize);}

  return 0;

// free memory


#the P3 means colors are in ascii, then 3 columns and 2 rows, then 255 for max color, then RGB triplets
3 2
255 0 0
0 255 0
0 0 255
255 255 0
255 255 255
0 0 0

The image (expanded): w:Image:tiny6pixel.png

The above image was expanded without interpolation, using the imagemagick command

convert -sample %6400 tiny6pixel.ppm tiny6pixel.png

The P6 format of the same image will store each color component of each pixel with one byte (thus three bytes per pixel) in the order Red, Green then Blue. The file will be smaller but the color information will not be readable by humans:

#any comment string
3 2

The PPM format is not compressed and thus requires more space and bandwidth than a compressed format would require. For example, the above 192x128 PNG image has a file size of 187 bytes. When converted to a 192x128 PPM image, the file size is 73848 bytes. The PPM format is generally an intermediate format used for image work before converting to a more efficient format, for example the PNG (Portable Network Graphics) format. The PPM format can be converted to PNG without loss of information.

The PPM format is certainly simple to write from scratch. The following Python code makes the above example image. It can be adapted to making useful images by reading or constructing an array of numerical data, and programming a conversion of the data to color triplets.

triplets=[ [255, 0, 0], [0, 255, 0], [0, 0, 255], [255, 255, 0], [255, 255, 255], [0, 0, 0] ]
width=3; height=2
comment='any comment string'
ftype='P6' #use 'P3' for ascii, 'P6' for binary

ppmfile.write("%s\n" % (ftype)) 
ppmfile.write("#%s\n" % comment ) 
ppmfile.write("%d %d\n" % (width, height)) 

if ftype=='P3':
    for red,green,blue in triplets:
        ppmfile.write("%d %d %d\n" % (red,green,blue)) 
elif ftype=='P6': #print 1 byte per color
    for red,green,blue in triplets:
        ppmfile.write("%c%c%c" % (red,green,blue))


Similar code in C :

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#define xor(a, b) (((!a && b)) || (a && !b))

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

   /* Declare the variables */
   FILE* ppmFile;
   int columns, rows, numberOfPixelsInPicture;

   /* Check the input arguments */
   if(argc != 4){
      printf("Usage: %s cols rows fname.ppm\n\n", *argv);
      return 1;

   /* Open the file and write the first 4 lines to it */
   ppmFile = fopen(argv[3], "w");
   columns = atoi(argv[1]);
   rows = atoi(argv[2]);
   numberOfPixelsInPicture = rows * columns;
   fprintf(ppmFile, "P3\n%d\n%d\n255\n", columns, rows);

   int m, n;
   for(m=0;m<rows;m++) {
      for(n=0;n<columns;n++) {
         /* Set the pixels in the bottom left of the picture a green-yellow color */
         if(m>n) {
            fprintf(ppmFile, "%d 255 %d\n", (256*m)/rows, (256*n)/columns);
         } else if(xor((m/10)%2,(n/10)%2)) {
            /* Create a checkerboard pattern in the upper-right of the picture */
            /* Create the blue-red pixels in the checkerboard pattern */
            fprintf(ppmFile, "%d 0 %d\n", (255*m*n)/numberOfPixelsInPicture, 255 -(255*m*n)/numberOfPixelsInPicture);
         } else {
            /* Create the black pixels in the checkerboard pattern */
            fprintf(ppmFile, "0 0 0\n");
      /* Print a blank line between rows */
      fprintf(ppmFile, "\n");

   return 0;

Assembler code

; create a ppmb file by ker2x
: yasm -f elf64 ppmb.asm 
; gcc -o ppmb ppmb.o 
; ./ppmb | hexdump

segment .data
    header:     db  'P6 4 4 255', 0x0a
    headerlen:  equ $-header
    image:      db  255,0,0, 0,255,0, 0,0,255, 255,255,255
    imagelen:   equ $-image

segment .text
global main

    mov eax, 4
    mov ebx, 1
    mov ecx, header
    mov edx, headerlen
    int 0x80
    mov eax, 4
    mov ebx, 1
    mov ecx, image
    mov edx, imagelen
    int 0x80
    mov eax, 4
    int 0x80
    mov eax, 4
    int 0x80
    mov eax, 4
    int 0x80
    ; Call sys_exit(0)
    mov eax, 1
    xor ebx, ebx
    int 0x80

C code

Static array for one color : code in C for creating pgm text file :

#include <stdio.h>

int main(){
  int iX,iY;
  const int iXmax = 300; 
  const int iYmax = 300;
  /* color  is coded from 0 to 255 */
  /* it is 8 bit color RGB file */
  const int MaxColorComponentValue=255; 
  FILE * fp;
  char *filename="m.pgm";
  char *comment="# this is my new text pgm file ";  /* comment should start with # */
  static unsigned char color;
  /*create new file,give it a name and open it in text mode  */
  fp= fopen(filename,"w"); /*  text mode */
  /*write ASCII header to the file*/
  fprintf(fp,"P2\n%s\n%d %d\n%d\n",comment,iXmax,iYmax,MaxColorComponentValue);
  /*write image data bytes to the file*/
      color=150;   /* compute  pixel color (8 bit = 1 byte) */
      fprintf(fp," %d ", color);   /*write color to the file*/
    fprintf(fp," \n ");
  return 0;

To compile it :

gcc m.c

To run it :


Remember that :

  • fwrite is used for binary files
  • fprintf is used for binary and text files

so if you want to use fwrite then you will get binary file ( even if you will open it in text mode ):

C code : Static 2D array for whole image

#include <stdio.h>

int main(){

  int iX,iY;
  const int iXmax = 100; 
  const int iYmax = 100;
  unsigned char data[iYmax][iXmax]; /* 2D array for colors ( shades of gray ) */
  const int MaxColorComponentValue=255; /* color component is coded from 0 to 255 ;  it is 8 bit color file */
  FILE * fp;
  char *filename="n.pgm";
  char *comment="# this is my new binary pgm  file";/* comment should start with # */
  /* fill the data array */
/* write the whole data array to ppm file in one step */      
fp= fopen(filename,"wb"); /*create new file,give it a name and open it in binary mode  */
fprintf(fp,"P5\n %s\n %d %d\n %d\n",comment,iXmax,iYmax,MaxColorComponentValue);  /*write header to the file*/
fwrite(data,sizeof data,1,fp);  /*write image data bytes to the file*/
printf("OK - file %s saved\n", filename);
return 0;

C code : virtual 2D array and dynamic 1D array

Here image is a virtual 2D array, but in program we use 1D array.

Relations between indexes :

i = ix + iy*iWidth; // index of 1D array 
ix = i % iWidth;
iy = (i- ix) / iWidth;

Here is whole program where we only check ranges of array's indexes without using explicit array :

#include <stdio.h>

/* --------- global variables ----------------- */

// 2D array 
// Indexes of array starts from 0 not 1 
unsigned int ix, iy;
unsigned int ixMin = 0;
unsigned int ixMax = 3; //
unsigned int iWidth ; // = (ixMax -ixMin + 1) = 4
unsigned int iyMin = 0;
unsigned int iyMax = 3; //
unsigned int iHeight ; //= (iyMax -iyMin + 1) =  4
// The size of array has to be a positive constant integer 
unsigned int i2Dsize ; // = iWidth*iHeight = 16

// 1D array 
unsigned int i; // index of 1D array
unsigned int iMin = 0;
// Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
unsigned int iMax ; // = i2Dsize-1; // = 15
// The size of array has to be a positive constant integer 
unsigned int i1Dsize ; // = i2Dsize  = (iMax -iMin + 1) = 16 ;  1D array with the same size as 2D array

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

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

/* ---------------------- main ------------------*/
int main()

iWidth = (ixMax -ixMin + 1); // 
iHeight = (iyMax -iyMin + 1); //
i2Dsize = iWidth*iHeight; // number of points in array 
iMax = i2Dsize-1; // Indexes of array starts from 0 not 1 so the highest elements of an array is = array_name[size-1].
i1Dsize = i2Dsize; // 1D array with the same size as 2D array

// first method using 1D index i 
for (i=iMin; i<i1Dsize; ++i) printf(" %d \n", i ); // from 0 to 15

// second method using 1D index i 
for (i=iMin; i<=iMax ;  ++i) printf(" %d \n", i ); // from 0 to 15

// check second method using 1D index i
for (i=iMin; i<=iMax ;  ++i)  // i from 0 to 15
 { ix = i % iWidth;
   iy = ( i- ix) / iWidth; // inversion of f function
   printf(" ix = %d ; iy = %d ; i = %d \n",ix , iy , i );}

// using 2D indexes :  iy and ix
  for(ix=ixMin;ix<=ixMax;++ix) printf(" ix = %d ; iy = %d ; i = %d \n", ix, iy, f(ix,iy) );

return 0;

Lua code for binary B@W PBM file :

-- The Computer Language Shootout
-- contributed by Mike Pall

local width = tonumber(arg and arg[1]) or 100
local height, wscale = width, 2/width
local m, limit2 = 50, 4.0
local write, char = io.write, string.char

write("P4\n", width, " ", height, "\n")

for y=0,height-1 do
  local Ci = 2*y / height - 1
  for xb=0,width-1,8 do
    local bits = 0
    local xbb = xb+7
    for x=xb,xbb < width and xbb or width-1 do
      bits = bits + bits
      local Zr, Zi, Zrq, Ziq = 0.0, 0.0, 0.0, 0.0
      local Cr = x * wscale - 1.5
      for i=1,m do
        local Zri = Zr*Zi
        Zr = Zrq - Ziq + Cr
        Zi = Zri + Zri + Ci
        Zrq = Zr*Zr
        Ziq = Zi*Zi
        if Zrq + Ziq > limit2 then
          bits = bits + 1
    if xbb >= width then
      for x=width,xbb do bits = bits + bits + 1 end

Python code

# -*- coding: utf8 -*-
# code by User:Geek3
# use the PNM format (
# no need for external libraries

import colorsys
from math import *

width, height = 800, 600

# create header
image = open('pnm-example.ppm', 'w')
image.write('P3\n') # color image
image.write('{0} {1}\n'.format(width, height))

def color(ix, iy):
    '''return color for specific position'''
    # create a rainbow ring
    rx = (ix + 0.5 - width / 2.) / 100.
    ry = (iy + 0.5 - height / 2.) / 100.
    angle = pi + atan2(rx, ry)
    amplitude = (rx**2 + ry**2) * exp(1 - (rx**2 + ry**2))
    return colorsys.hsv_to_rgb(angle / (2*pi), amplitude, 1)

for iy in range(height):
    for ix in range(width):
        c = color(ix, iy)
        image.write('{0} {1} {2}'.format(*[int(max(0, min(256*i, 255))) for i in c]))
        if (ix < width - 1):
            image.write(' ')


PFM (Portable FloatMap) is the unofficial floating point Netpbm image format for HDR images[3]

Portable Float Map (PFM) format[5]

  • Analogous to PPM / PGM / PBM
  • binary file
  • No compression
  • There are no comments in these files


  • text header = 3 lines of text. Each of the three lines of text ends with a 1-byte Unix-style carriage return: 0x0a in hex, not the Windows/DOS CR/LF combination.
    • Files begins with type = ASCII characters "PF" or "Pf". PF means it's a color PFM ( 3-channel RGB color imag). Pf means it's a grayscale PFM ( a monochrome single-channel image).
    • next line is resolution : 2 integers = [xres] [yres]" indicates the x and y resolutions of the image
    • last line is contains sigle floating point value: byte_order.
  • data : Three float per pixel ( series of three 4-byte IEEE 754 single precision floating point numbers for each pixel, specified in left to right, bottom to top order )

The text header of a .pfm file takes the following form:

[xres] [yres]

Check file using xxd:

   xxd memorial.pfm|head

output :

00000000: 5046 0a35 3132 2037 3638 0a2d 312e 3030  PF.512 768.-1.00
00000010: 3030 3030 0a00 8020 3c00 001e 3b00 0038  0000... <...;..8


  • PNG color type (

Octave code that creates array ( memory image) and saves it to the file[6]

# octave m-file based on the m-file by Chris King
# an MyImage here is a matrix for 24 bit (3 byte) colors

# load packages
pkg load image; # imwrite
pkg load miscellaneous; # waitbar

# constan values 
nx = 480;
ny = 480;
MyImage = zeros(ny,nx,3); # 2D matrix filled with zeros
Zxmin = -dSide;
Zxmax = dSide;
Zymin = -dSide;
Zymax = dSide;

stepy = (Zymax - Zymin)/(ny - 1);
stepx = (Zxmax - Zxmin)/(nx - 1);

# computations 
waitbar(0,'Please wait...'); # info 
for iy = 1:ny
  Zy = Zymax - iy*stepy; # invert y axis
  for ix= 1:nx
    Zx = Zxmin + ix*stepx;
    if(Zy>0 && Zx>0)  # first quadrant should be in upper right position
  end # for ix
end # for iy
image(MyImage); # display image 
imwrite(MyImage,'s.png' ); # save image to the file



Raw file format:[7]

  • binary file[8], it means tha you cannot open it in the text editor but only in the special program or a hex editor
  • raster file[9]: file "consist of a sequential listing of pixel (data) values, described row by row, beginning with the top row, working left to right. " [10]
  • not compressed
  • the file contains no image formatting information
  • File size depends only on the image dimensions and pixel data format


  • data ( non color data, need processing)
  • static image ( data = color)
    • non photo image = image created by computer
    • photo = image from digital camera.[11] It need demosaicing
  • video,like Y4M

How to use raw filesEdit

  • programs can save the raw iteration data for later colouring or other analysis.[12]
  • stages of raw processing[13][14][15]
  • because the file contains no image formatting information before reading/opening the file one needs informations about:
    • Image dimensions
    • pixel data format
    • Pixel scan order
    • Byte arrangement (little or big endian format)

Library for raw editing:

Example Fractal programs using raw format:

  • SuperFractalThing by K I Martin ( Java, cross-platform )
  • Kalles Fraktaler by Karl Runmo uses kfb map files
    • kf-extras programs for manipulating output from Kalles Fraktaler 2
  • Mandel Machine by Botond Kósa
  • mandelbulber ( m3p file holds only the parameters, while .m3i holds also the raw image )

Photo editors for raw files[16]

Examples of raw Image processing procedures

  • Raw image before processing, Binary image, Outline image, Skeletonized image after preprocessing, Composition image of raw and outline images, Composition image of raw and skeletonized image[17]
  • Image-Processing-Over-Time-of-A-Raw-Fractal by ImageJ
  • Tips for making better images by Paul Bourke
    • do the fractal creation not in 8 bit, but use 16 bit or floating point for each pixel ( pfm file
    • apply antialiasing by supersampling each final pixel ( render a 30,000 pixel version of the image )
    • do all colour external to the fractal creation using gradient maps...allows you to make appearance decisions independent to the creation

pixel data formatEdit

Pixel data can contain information about:

  • color
  • other numerical data like :
    • escape time measured in iterations,
    • distance estimation from DEM algorithm

In PIL ( Python Imaging Library ) pixel color format is defined by modes[18]:

  • 1 (1-bit pixels, black and white, stored with one pixel per byte)
  • L (8-bit pixels, black and white)
  • P (8-bit pixels, mapped to any other mode using a colour palette)
  • RGB (3x8-bit pixels, true colour)
  • RGBA (4x8-bit pixels, true colour with transparency mask)
  • CMYK (4x8-bit pixels, colour separation)
  • YCbCr (3x8-bit pixels, colour video format)
  • I (32-bit signed integer pixels)
  • F (32-bit floating point pixels)
  • LA (L with alpha)
  • RGBX (true colour with padding)
  • RGBa (true colour with premultiplied alpha).





Moving imagesEdit

Animated gifEdit

Convert pgm ( or other ) static files into animated gif using BASH and Image Magic :[20]


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

# for all pgm files in this directory
for file in *.pgm ; do
  # b is name of file without extension
  b=$(basename $file .pgm)
  # convert from pgm to gif and add text ( level ) using ImageMagic
  convert $file -pointsize 100 -annotate +10+100 $b ${b}.gif
  echo $file

# convert gif files to animated gif
convert -delay 100   -loop 0 %d.gif[0-24] a24.gif

echo OK
# end

or another version by ClaudiusMaximus[21]

for i in ??.svg
  rsvg $i ${i%svg}png
  convert ${i%svg}png ${i%svg}gif
gifsicle --delay 4 --loop --optimize ??.gif > out.gif

Don't forget about : 12.5MP limit = 500 x 500 x 50 frames = 600 x 600 x 34 frames = 1000 x 1000 x 12 frames


Steps from pgm to video using Image Magic convert :

  • pgm files to gif files
  • gif files to video

convert -delay 100   -loop 0 %d.gif[0-25] a25.mpg


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

# for all pgm files in this directory
for file in *.pgm ; do
  # b is name of file without extension
  b=$(basename $file .pgm)
  # change file name to integers and count files
  ((i= i+1))
  # convert from pgm to gif and add text ( Cx from name of file ) using ImageMagic
  convert $file -pointsize 50 -annotate +10+100 $b ${i}.gif
  echo $file
echo convert all gif files to one ogv file
ffmpeg2theora %d.gif --framerate 12 --videoquality 9  -o output129.ogv

echo b${i} OK
# end


One can made a video from images. For examp

e creating WebM video files using ffmpeg [22][23]

ffmpeg -i x%08d.png -r 24 tifa.webm

or ffmpeg2theora:[24]

ffmpeg2theora %d.gif --framerate 5 --videoquality 9 -f webm --artist "your name" -o otput.webm

If you use files names containing parameter ( here Cx ), then it would be easy to sort files and make video :

  char name [10]; /* name of file */
  i = sprintf(name,"%2.7f",Cx); /* result (is saved in i) but is not used */
  char *filename =strcat(name,".pgm"); /* new name thru concatenate of  strings  */


  • video file in YUV4Mpeg format
  • raw video before compressing into other formats[25]

Graphic file documentationEdit




Using Image Magic :

  • comment
  • escape [28]

Image Magic one can add comment to png image using mogrify :[29]

mogrify -comment "My test comment" p.png

or using convert :[30]

convert in.png \
        -set 'Copyright' 'CC-BY-SA 4.0' \
        -set 'Title' 'A wonderful day' \
        -set comment 'Photo taken while running' \

To read comment from png :

identify -verbose p.png  | grep -i "comment:"
   comment: My test comment

or :

identify -format "%c" X.ppm


A chunk is a fragment of information which is used in many multimedia formats, such as PNG, IFF, MP3 and AVI. Each chunk contains a header which indicates some parameters (e.g. the type of chunk, comments, size etc.) In the middle there is a variable area containing data which are decoded by the program from the parameters in the header.[31]

Text chunk is one of standard ancillary PNG chunks. Its name is a tEXt.[32]

Standard keywords for PNG text chunks:

   Title            Short (one line) title or caption for image
   Author           Name of image's creator
   Description      Description of image (possibly long)
   Copyright        Copyright notice
   Creation Time    Time of original image creation
   Software         Software used to create the image
   Disclaimer       Legal disclaimer
   Warning          Warning of nature of content
   Source           Device used to create the image
   Comment          Miscellaneous comment; conversion from GIF comment

The ancillary chunks currently known to ImageMagick are bKGD, cHRM, gAMA, iCCP, oFFs, pHYs, sRGB, tEXt, tRNS, vpAg, and zTXt.

Example with convert from Image Magic :

convert in.png -define png:include-chunk=tEXt file.txt out.png

On can use pnmtopng utility :

pnmtopng -text file.txt 1000.pgm > 1000.png

where text file file.txt is :

Title            Short (one line) title or caption for image
Author           Name of image's creator
Description      Description of image (possibly long)
Copyright        Copyright notice
Creation Time    Time of original image creation
Software         Software used to create the image
Disclaimer       Legal disclaimer
Warning          Warning of nature of content
Source           Device used to create the image
Comment          Miscellaneous comment; conversion from GIF comment


separate text fileEdit

Save pgm file and also text file with some description of the image:

// save "A" array to pgm file and info txt file
int SaveArray2PGMFile( unsigned char A[], double k, char* text)
  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  , error Naruszenie ochrony pamięci  */
  snprintf(name, sizeof name, "%f", k); /*  */
  char *filename =strncat(name,".pgm", 4);
  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,iWidth,iHeight,MaxColorComponentValue);  /*write header to the file*/
  fwrite(A,iLength,1,fp);  /*write A array to the file in one step */
  printf("File %s saved. \n", filename);

  // save info text filename
 filename =strcat(name,".txt");
 fp= fopen(filename,"wb");
 fprintf(fp,"This  image shows rectangle part of dynamic plane of discrete complex dynamical system  z(n+1) = fc(zn) \n");
 fprintf(fp," where  fc(z)= z^2 + c \n");
 fprintf(fp,"with numerical approximation of parabolic Julia set \n\n");
 fprintf(fp,"parameter c is a root point between iPeriodParent = %d and iPeriodOfChild  = %d hyperbolic components of Mandelbrot set \n", iPeriodParent , iPeriodChild);
 fprintf(fp,"on the end of the internal ray of parent component of Mandelbrot set with angle = 1/%d in turns \n", iPeriodChild);
 fprintf(fp," c = ( %f ; %f ) \n", Cx, Cy); 
 fprintf(fp," \n");
 fprintf(fp,"critical point z = Zcr= ( %f ; %f )  \n", creal(Zcr), cimag(Zcr)); 
 fprintf(fp,"parabolic alfa fixed point z = ZA = ( %f ; %f )  \n", creal(ZA), cimag(ZA)); 
 fprintf(fp," radius around parabolic fixed point AR =  %.16f ; Pixel width = %.16f   \n", AR, PixelWidth);
 fprintf(fp," iMaxN =  %d ; ARn = %.16f \n",iMaxN, ARn);    // info 
 fprintf(fp," EscapeRadius ER =  %f ; \n", EscapeRadius);
 fprintf(fp," Fatou coordinate U(Zcr) = Ux0 =  %f ; \n", Ux0);
 fprintf(fp," Maxima number of iterations : iMax = %d \n\n", iMax);
 fprintf(fp," Image shows rectangular part of  dynamic plane  with %s\n", text);
 fprintf(fp," from ZxMin = %f to ZxMax = %f\n", ZxMin, ZxMax);
 fprintf(fp," from ZyMin = %f to ZyMax = %f\n\n", ZyMin, ZyMax);
 fprintf(fp," iWidth = %d and iHeight = %d\n", iWidth, iHeight);
 fprintf(fp," distortion = %f ; It should be 1.0 \n", ((ZxMax-ZxMin)/(ZyMax -ZyMin)/(iWidth/iHeight)));
 if (t==0) fprintf(fp," No lost pixels : t = %d ; Parameters iMax and AR are good \n",t);
    else fprintf(fp," Error : there are lost pixels : t > 0 ; you should increase iMax or make bigger AR \n\n"); 
 fprintf(fp," computations made with double type numbers \n\n");
 fprintf(fp,"use (k+AR) for file names where k is a number of file ; range(k) =[0,k] so there are (k+1) png files nad (k+1) text files \n\n");
 fprintf(fp,"made with c console program  \n");

 printf("File %s saved. \n", filename);

  return 0;

Parameter filesEdit


Dot files are text files describing graphs in dot language. Example file :

digraph "BinaryAddingMachine" {
a [shape=circle]
b [shape=circle]
 a -> a [label="1/1",color=red];
 a -> a [label="2/2",color=blue];
 b -> a [label="1/2",color=red];
 b -> b [label="2/1",color=blue];

This file can be coverted to other formats using command line program dot. For example, to svg :

dot -Tsvg -o b.svg

fractint parfilesEdit

"Fractint uses Parameter files[34][35] to save/restore all options and settings,[36] required to recreate particular images. The parameters required to describe an image require very little disk space, especially compared with saving the image itself. " [37]

Most important settigs are :

Example file :

{ ; quite good spirals 
  reset=2000 type=mandel passes=1
  params=0/0 float=y maxiter=1000 inside=0 outside=15

To use it :

  • Save file to fractint main directory.
  • Run fractint.
  • press 2 key
  • press F6 key
  • select file

Reset causes Fractint to reset all calculation related parameters to their default values. Non-calculation parameters such as "printer=", "sound=", and "savename=" are not affected.[38] The reset=1730 in the parameter file shows that it was created with 17.3 version of Fractint.[39]

Viewer for programmersEdit

This program :

  • opens binary ppm ( P6) or pgm ( P5) files
  • it does not opens asci versions of these files.

It can be used to check image by checking output in console as mouse moves. Add your code to Motion function and update Zxmin and Zymin ( world coordinate).

It not works for newest version of OpenGl.

 * image.c
 * read in a PPM or PGM binary image and display it, full size
  Based on code by : 
   Dr. Lori L. Scarlatos
   Stony Brook University
   "I do not have a license for image.c; 
   it was created as an example for my students.
   Please feel free to use it.
   Best regards,
* ----------------------------
* it does not opens asci versions of these files 
* examples files : 

  // gcc v.c -lm -lGLU -lglut -Wall // ? windows 
    gcc v.c -lm -lglut -lGL -lGLU -Wall // ubuntu 
  ./a.out 5.pgm



locate glut.h

#include <GL/freeglut.h>
#include <GL/glut.h>


//#include <Windows.h>
#include <GL/gl.h>
#include <GL/glu.h>
//#include <GL/glut.h> // oryginal glut 
#include <GL/freeglut.h> // freeglut 
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h> /* fabs*/
//#include <malloc.h>

/* Global variables */

#define MAXLINE 80	/* maximum length of a line of text */


3.2 Conventions

In developing the freeglut library, we have taken careful steps to ensure consistency in function operation across the board, 
in such a manner as to maintain compatibility with GLUT's behavior whenever possible. In this section some of the important conventions of FreeGLUT, 
and their compatibility with GLUT, are made explicit.

3.2.1 Window placement and size

There is considerable confusion about the "right thing to do" concerning window size and position. GLUT itself is not consistent between Windows and UNIX/X11; 
since platform independence is a virtue for freeglut, we decided to break with GLUT's behaviour. 
Under UNIX/X11, it is apparently not possible to get the window border sizes in order to subtract them off the window's initial position until some time after the window has been created. 
Therefore we decided on the following behavior, both under Windows and under UNIX/X11:

When you create a window with position (x,y) and size (w,h), the upper left hand corner of the outside of the window (the non-client area) is at (x,y) and the size of the drawable (client) area is (w,h). 
The coordinates taken by glutInitPosition and glutPositionWindow, as well as the coordinates provided by FreeGLUT when it calls the glutPositionFunc callback, specify the top-left of the non-client area of the window.
When you query the size and position of the window using glutGet, FreeGLUT will return the size of the drawable area
--the (w,h) that you specified when you created the window
--and the coordinates of the upper left hand corner of the drawable (client) area
--which is NOT the (x,y) position of the window you specified when you created it.


GLint ImageWidth, ImageHeight;	         /* size of the Image in pixels */
GLint WindowWidth, WindowHeight;	/* size of the window in pixels */
GLint MaxScreenWidth, MaxScreenHeight;	/* size of the screen in pixels */

GLubyte *Picture;	/* Array of colors (GLubyte)  */
int size;

// mouse position as a global variables 
//static float mx=0.0f,my=0.0f ;
int iX, iY; // 
int centerX = 200, centerY = 200;
GLint iYmax,iXmax; // mouse coordinate inside image

unsigned char pixel[3];

// change it manually !!!!!

const double  ZyMin=-1.0;
const double  ZxMin=-2.0;
const double  PixelHeight=0.0020010005002501  ;
const double  PixelWidth=0.0020010005002501  ;

int filetype;
enum {P2, P3, P5, P6};	/* possible file types */

/* gives position of point (iX,iY) in 1D array  ; uses also global variables */
unsigned int f(unsigned int _iX, unsigned int _iY)
{return (_iX + (iYmax-_iY-1)*iXmax );}

* Read from a PPM or PGM (binary) file 
* Output is a array of GLubyte 
void readPPM (char *filename, GLubyte **pic) {

	FILE *fp;
	char line[MAXLINE];
	int i, rowsize;
        // int size; // moved to global var 
        int j ;
	GLubyte *ptr;

/* Read in file type */
  fp = fopen(filename, "r"); /* in Unix rb = r */
  if (fp==NULL) {perror(" perror : " ); printf("Error from fopen : I can't open %s file' ! ", filename); exit(1); }
  else printf("File %s has been opened !\n", filename);
  /* Each file starts with aa two-byte magic number (in ASCII) that explains :
   * - the type of file it is (PBM, PGM, and PPM) 
   * - its encoding (ASCII or binary). 
   * The magic number is a capital P followed by a single digit number. 
  fgets (line, MAXLINE, fp); /* 1st line : Magic Number  */
  switch (line[1])
   case '2':
       filetype = P2; 
       printf("This is PGM text file (P2), but now I do not have procedure for opening it \n");
   case '3' :
      filetype = P3;
      printf("This is PPM text file (P3), but now I do not have procedure for opening it !\n");
   case '5':
       filetype = P5; 
       printf("This is PGM binary file (P5) and I can open it !\n");
   case '6' :
      filetype = P6;
      printf("This is PPM binary file (P6) and I can open it !\n");
   default : 
      printf("Error from readPPM : need binary PPM or binary PGM file as input!\n");
 /* if this is a comment, read next line. Maybe in binary files there is no comment ?*/
/* there maybe more then one line of comment */
 fgets (line, MAXLINE, fp); 
 while  (line[0]=='#') 
  { printf(" comment  = %s \n", line); /* 2nd or more line  starting with # =  comment, print it   */
    fgets (line, MAXLINE, fp); // read next line 

/* Read in width and height, & allocate space */
/* these 2 numbers should be in one line with space between them */
   /* 3nd line: width  and height */
  sscanf(line, "%d %d", &ImageWidth, &ImageHeight);
  printf ("iWidth = %d\n", ImageWidth);
  printf ("iHeight = %d\n",  ImageHeight);

  if (filetype == P5) {
	  size = ImageHeight * ImageWidth; /* greymap: 1 byte per pixel */
	  rowsize = ImageWidth;
  else /* filetype == P6 */ {
	  size = ImageHeight * ImageWidth * 3; /* pixmap: 3 bytes per pixel */
	  rowsize = ImageWidth * 3;
  *pic = (GLubyte *)malloc (size); /* create dynamic array */

/* Read in maximum value (ignore) */
  fgets (line, MAXLINE, fp); /* next  line */
  /*  */
  if (filetype==P5 || filetype==P6){
    /* Read in the pixel array row-by-row: 1st row = top scanline */
    ptr = *pic + (ImageHeight-1) * rowsize;
    for (i = ImageHeight; i > 0; i--) {
          /* For binary File I/O you use fread and fwrite */
	  j = fread((void *)ptr, 1, rowsize, fp); 
	  ptr -= rowsize;
   if (j) printf("File %s has been read !\n", filename);
          else printf(" j Error from readPPM procedure : I can't read %d file !.\n", j);
  else printf("Error from readPPM procedure : I can't read %s file !. It should be P5 or P6 file !\n", filename);
  printf("File %s has been closed !\n", filename);

/* Draw the picture on the screen */

void Draw(void) {
        /* black background of GLUT window */
        glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Clear the background of our window to black
        glClear(GL_COLOR_BUFFER_BIT); //Clear the colour buffer (more buffers later on)
        glLoadIdentity(); // Load the Identity Matrix to reset our drawing locations
        glFlush(); // Flush the OpenGL buffers to the window
        // left lower corner of displayed image 
	glRasterPos2i(-1,-1); // By default, OpenGL assumes a system running from -1 to 1, 
        switch (filetype){
          case P5 : 	/* greymap: use as illumination values */
		glDrawPixels(ImageWidth, ImageHeight, GL_LUMINANCE, GL_UNSIGNED_BYTE, Picture);
                printf("P5 Image has been drawn !\n");
	  case  P6 :
		glDrawPixels(ImageWidth, ImageHeight, GL_RGB, GL_UNSIGNED_BYTE, Picture);
                printf("P6 Image has been drawn !\n");
         default : 
                printf("Error from Draw procedure : There is no image to draw !\n");


// Detecting Mouse Clicks
// x and y specify the location (in window-relative coordinates) of the mouse when
// the event occurred
void MouseClicks (int button, int state, int x, int y)
switch (button)
if (state == GLUT_DOWN)
// do something
// etc., etc.

// mouse motion 
//The x and y callback parameters 
// indicate the  mouse  location 
// in window relative coordinates
// x, y –> coordinates of the mouse relative to upper left corner of window

// setting the mouse position to be relative to the mouse
// position inside the window

void PassiveMouseMotion(int x, int y) {
   //double Zx,Zy;
   //double Ux; 
   //int index;
   //GLubyte Gray;

   // put your code here  ???? 
   iX = x;
   /* invert y axis */
   iY = WindowHeight - y -1 ; //+ (glutGet(GLUT_WINDOW_HEIGHT) - ImageHeight); ///glutGet(GLUT_WINDOW_HEIGHT) - y; // ????

   /* output : prints to console  */
  if ((filetype==P5 || filetype==P6) && -1<iX && iX< ImageWidth  && iY<ImageHeight) // && iY<ImageHeight

     glReadPixels(iX, iY, 1, 1, GL_RGB, GL_UNSIGNED_BYTE, pixel);
   // pixel coordinates of the mouse relative to upper left corner of window
   printf(" pixel iX=%3d / %d ;  iY=%3d  color = %d  \n", iX, MaxScreenWidth,  iY, pixel[1] );

static void Key(unsigned char key, int x, int y)
    switch (key) {
	case 27 : {glutLeaveFullScreen(); break;}/* esc */
        case 'f': {glutFullScreen(); break; }
        case 'q': {printf("Key preseed and exit \n"); exit(1) ;}
        case 'Q': {printf("Key preseed and exit \n"); exit(1) ;}
        case 't': {glutFullScreenToggle(); break; } // GLUT does not include the glutLeaveFullScreen and glutFullScreenToggle functions from freeglut 
	default: return ;

 Resize the picture  ; OpenGL calls this function whenever the window is resized 
 Called when window is resized,  also when window is first created,    before the first call to display().
void Reshape(GLint w, GLint h) {

/* save new screen dimensions */
     WindowWidth = w;
     WindowHeight = h;
    /* the viewport is the rectangular region of the window where the image is drawn */
   // Viewport : A rectangular region in the screen for display  (in screen coordinate system) 
    glViewport(0, 0, ImageWidth-1, ImageHeight-1); // glViewport( 0.f, 0.f, SCREEN_WIDTH, SCREEN_HEIGHT );
    // Define a world window : A rectangular region in the world that is to be displayed (in world coordinate system)
    // By default, OpenGL assumes a system running from -1 to 1, 
    gluOrtho2D(-1, 1, -1, 1); // An orthographic projection is basically a 3D projection that does not have perspective

Initialization: create window 
glutInitWindowSize(600, 600);
void MyInit(int argc, char *argv[]) {
    char filename[MAXLINE];
  /* Read in the file (allocates space for Picture) */
  if (argc < 2) 
	printf ("Enter the name of a binary PPM or PGM file: ");
	scanf("%s", filename);
	readPPM ((char *)filename, &Picture);
    else { readPPM (argv[1], &Picture); }
  glutInit(&argc, argv);

  MaxScreenWidth  = glutGet(GLUT_SCREEN_WIDTH);
  MaxScreenHeight = glutGet(GLUT_SCREEN_HEIGHT);   
  glutInitWindowPosition(-1, 1); // upper  left  corner
  glutInitWindowSize(MaxScreenWidth, MaxScreenHeight ); // full screen of my monitor
  glutInitDisplayMode(GLUT_RGB | GLUT_SINGLE);
  if (glutCreateWindow("OpenGl binary pgm/ppm Image viewer ") == GL_FALSE) 
      {printf("Error from  MyInit , glutCreateWindow\n"); exit(1);}

/* ------------------ Main program ---------------------------------------*/
int main(int argc, char **argv)
    MyInit(argc, argv);
    glutPassiveMotionFunc(PassiveMouseMotion); // mouse move with no key pressed 
    glutReshapeFunc(Reshape); //  move or resize of screen window 
    glutDisplayFunc(Draw); // 
    return 0;

See alsoEdit


  1. Computability of the Feigenbaum Julia set by Artem Dudko, Michael Yampolsky
  2. The Computer Language Benchmarks Game
  3. portable-floatmap-format-io-java by Nayuki
  4. imagemagick : high-dynamic-range
  5. HDR by Josef Pelikán & Alexander Wilkie
  6. Sigel disc in Matlab by Chris King
  7. [:w:Raw image format|Raw image format in wikipedia]
  8. wikipedia: Binary_file
  9. wikipedia: Image_file_formats - Raster_formats
  11. rawpedia - The encyclopedia of RawTherapee, raw shooting and everything raw
  12. Faking distance estimate colouring by Claude Heiland-Allen
  13. cnet: how-to-process-and-edit-raw-files
  14. techradar: how-to-process-raw-images-the-right-way
  15. how-to-post-process-photos-in-the-right-order--cms by by Jackson Couse24 Oct 2016
  16. itsfoss : raw-image-tools-linux
  17. Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method Kyung-Hoe Huh, et al.
  18. imaging module doc: concepts
  19. Gnu Parallel
  20. Moebius transformation animated GIFs by Fritz Mueller
  21. ReCode Project - Topographic Form animated by ClaudiusMaximus
  22. How this video was made by Mukund
  23. mini-fract in Lisp by Yannick Gingras
  24. wikibooks help about converting video : ffmpeg2theora
  25. fileinfo : extension y4m
  26. pngmeta
  27. PNG and exif
  28. Image Magic - escape
  29. Stackoverflow : How to add extra meta data to PNG?
  30. Stackoverflow : Insert a text chunk into a png image
  31. wikipedia : Chunk (information)
  32. PNG (Portable Network Graphics) Specification, Version 1.2 : chunk
  34. A short Introducion to PAR Files by Laurent Chabin
  35. julian haight : filmer instructions
  36. Fractint doc index
  37. Fractint par files by Rupert Russell
  38. fractint Image Calculation Parameters
  39. [Fractint] FOTD 27-07-11 (Bad Moon on the Rise [No Rating])