FractalEscape is a simple, escape-time fractal generator.

To compile it, just run make.  You will need libpng installed.

Running it without options will print usage information.

Some notes about the model it uses will help make sense of the options.

For this program, each 'fractal' is a 12 parameter polynomial.  Those 12
parameters are represented as a string of 12 characters, each of which
encodes a number.  This string can be specified using the -f/--fractal
option, or can be generated randomly (more on that below).

The fractal is rendered by estimating escape times for points in a
rectangular grid.  This grid is determined by the -s/--size and -c/--coords
options, which specify the pixel size of the output and the real number
coordinates of the rectangle.  FractalEscape will happily accept output
dimensions of a different aspect ratio from the real coordinates.

The output can be tweaked in two major ways.  First is a scaling option
-m/--maxval.  This will rescale the range of escape time values to fit into
a predefined range of output values.

The other major tweak is oversampling (a.k.a. anti-aliasing).  Activating
the -O/--osfact (that's a capital letter O) option will cause a grid of NxN
values to be computed and averaged for each output pixel.  A value of 2 or 3
vastly improves the visual quality of the output.  Larger values do not have
much benefit.

Output is saved as PNG images, by default named based on the 12 character
string defining the fractal (so that you can easily regenerate a fractal
with different tweak parameters later on).  If generating only a single
fractal (i.e. using the -f/--fractal option), you can specify the filename
with the -o/--output option.  If generating multiple fractals (random mode),
that option will instead specify what directory to save all the images into.

Random generation of fractals is activated with the -r/--random option. This
can optionally take a number of fractals to generate.  If not specified, it
will generate fractals until it receives an interrupt (Ctrl-C), at which
time it will clean up and exit gracefully, trying hard not to leave broken,
half written images in its wake.

The process of generating random fractals goes like this:

- While not enough images have yet been generated ...
  - While not enough candidates for the next image have been analyzed ...
    - Pick a random set of values for the 12 parameters
    - Check the escape time at the 0,0 pixel
    - If it doesn't look boring (doesn't escape too fast) ...
      - Compute a thumbnail (1/10th width & height, no oversampling) version
        of the fractal, passing it through a statistics collector.
      - Compute an 'interestingness' score
      - Save the parameters and score
  - Generate at full resolution the best candidate we found

Currently "enough" candidates is 100, "enough" images is determined by the
--random option as described above.

The 'interestingness' qualification at step 3 works off the rough
observation that fractals that have too little or too much going on (all the
same value, or white noise) are uninteresting.  The scoring for this works
something like this:

1) Mark the most common pixel values as likey background
2) Figure out how many of the next most common pixel values it takes to
   consume 2/3rds of the image.  Positively score values in what I
   empircally determined to be a 'good' range, negatively score values
   outside that.
3) Weight the score based on the fraction of the image area that was marked
   as likely background -- the greater the portion of the image that is
   taken up by background, the more boring the image is.

Cheers,
	-- Matthew "Cheetah" Gabeler-Lee
	   [email protected]