The Complex Functions shader provides 99 base functions some of which are
really basic, 1/z, log(z), sin(z) etc.,  while  some are rather arbitrary
combinations of the basic functions. In each case these may be modifed by
selecting one of 16 "function modes", e.g. func(1/z), or by being subject
to function iteration. Most functions remain "interesting" when  iterated
up to 5 or 6 times, some up to 16 or more times.  Additionally, the forms
of the functions or there presentation may be further modified  by  means
of the "Pre" and "Post" modifiers,  domain mapping,  contour control  and
other control parameters.

There are therfore a very large number of  potential  variations  of  the
patterns generated by the shader and it is not practical to present  them
using one scene fore each. For this reason the scenes have been organised
into various series of related scenes in which, in most cases, each scene
cycles through each of the 99 base functions keeping  the  other  control
parameters constant. Exceptions are the series in which the functions are
subject to being iterated and a few scenes where the function id does not
change.

When cycling through the functions each function is displayed for just 15
seconds which, though short, provides adequate time to view each function
when it is presented. Each scene therefore takes almost 25 minutes, 99*15
seconds, to cycle through the full set of functions.  However, by default
VGHD will change scenes every 5 minutes though this can be  increased  to
60 minutes via the full screen settings page of the VGHD program. As many
people will prefer to use the 5 minutes scene duration I have provided  5
variants of those scenes that try to cycle through the set of  functions,
these differ only by starting at function ids 0, 21, 41, 61 and 81.  Five
minutes is adequate to cycle through 20 functions at 15 seconds  each, so
between them the set of 5 scenes cover all 99  functions  even  when  the
scene duration is only five minutes.

For most scenes the above timing provides a compromise between displaying
each function for a reasonable length of time and not taking too long  to
cycle through the full set.  However,  some scenes both cycle through the
set of functions and calculate the function after a number of iterations.
In these cases the combination of function id and iteration level changes
more often - 7 times as often when the maximum iteration level is 6 - and
the images therefore change much more rapidly. The alternative of using a
longer function duration could have been used but would have needed  many
more scenes to cover the same set of examples,  as  a result these scenes
are rather hurried, but you can easily slow them down by editing the .scn
files if you want a more leisurely presentation.

A different,  though related,  aspect  of timing is the duratation of the
transitions between functions or iterations.  The  default for this is to
be instantaneous but most scenes override this by using transition mode 2
and specifying that 20 percent of the function or iteration  duration  is
to be used for transitions.
