0. PURPOSE
----------
   In this directory, you will find a collection of programs intended at
 the generation of fractal sets for quadratic homogeneous maps in two variables.

1. INSTALLATION
---------------
   Prerequirements: since this software generates PNG files, you will need an
 installation of the PNG library, which (in unix-like systems) usually means to
 have at least two files: "png.h", and "libpng.a".

   The programs are developed in C language, standard C99.

   To generate the executables, simply copy all the files in this folder to a
 single folder and run "make".


2. USAGE
--------
   Since the generation depends on the region for which one is willing to
 generate the fractal, there is a number of different programs, each one having
 its own set of input arguments.

   We will explain the usage based on the first, general program, fractal. When
 typed with no arguments, the programs responds:

Usage: fractal <output base filename> <itermax> <xi> <eta> <side_length> <offset x> <offset y>

 Each argument means the following:
 <output base filename>: name for the output graphic file
 <itermax>:      maximum number of iterations before declaring a point inside the
                 fractal set
  <xi>:          value for the first invariant
  <eta>:         value for the second invariant
  <side_length>: side length in the complex plane for the intended fractal
  <offset x>:    x coordinate for the middle point of the figure in the complex
                 plane
  <offset y>:    y coordinate for the middle point of the figure in the complex
                 plane

   So the users picks a pair of invariants (xi,eta) and the zone s/he wants to
 depict. The latter is achieved by selected the center point of the figure and
 the side length of the figure. The longest the side-length, the smallest the
 figure, normally.

   This first program generates the fractal sets for the $\Delta^+$ and
 $\Delta^-$ zones.

   The same idea runs for the rest of the programs, which generate fractals for
 the rest of the zones.

fractalalpha
------------
   Generation of fractals for the X axis (except the origin).

fractal_l
---------
   Generation of fractals for the "linear" zone, $C^+$ and $C^-$.

fractal_00
----------
   Generation of fractals in the origin (0,0) of the complex plane.


  The rest of the programs simply take into account "special" cases.

fractal_esp1: For the case $F^+_c$ when $c = 0$.
fractal_esp2: For the case $F^-_c$ when $c = 0$.
fractal_esp3: For the case $G^_c$ when $c = 0$.
fractal_esp5: For the case $F^+_{00}$.
fractal_esp6: For the case $F^-_{00}$.
fractal_esp7: For the case $F^+_{bc}$ when $c=\pm 2b$.

ReadPNGHdr
---------
   This program extracts the info associated to each PNG file that consists of
 several fields: values for xi, eta, offset-x, offset-y, side-length, generation
 date, and maximum number of iterations.