3.12 Parameter Explorer/Evolver
Since fractint is such a wonderfully complex program it has more than a
few parameters to tweak and options to select. To the inexperienced
user the choice is bewildering. Even for the experts the chaotic
nature of the mathematical processes involved make it difficult to know
what to change in order to achieve the desired effect.
In order to help with this situation the Fractint parameter evolver has
been developed. It varies those parameters for you and puts the
results on screen as a grid of small images. You can then choose the
one which you like best and regenerate it full screen, or if you don't
like any of the variations, you can try again to see if anything better
turns up!
Enough explanations for now, lets see how easy it is to use:
With the default Mandlebrot set on the screen simply hold down the
'Alt' key and press the '1' key on the top row (DON'T use the numeric
keypad to the right, it won't work). You'll see a screen full of images
generated starting from the middle and spiraling outwards. The perfect
Mandlebrot set will be in the middle and the others will be warped and
distorted by having had the initial value of Z perturbed at random...
but you don't need to know that (which is the whole point really!).
'Alt-1' produces a low level of mutation of the fractal, only 'mild'
parameters are changed, those which have a more subtle effect. For much
wilder variations try pressing 'Alt-7' now. This give the maximum
available mutation with just about everything being twiddled and
fiddled to rather dramatic effect as you should now be seeing.
To select an image for full screen display simply bring up a zoombox by
pressing 'Page-up' once. The center image will now have a white box
around it. Hold down the 'Ctrl' key and use the arrow keys to move this
box around until it's outlining an image you like. Pressing 'B' will
now exit from evolver mode and redraw the selected image full size. If,
rather than exiting from evolver mode, you just press 'enter', then a
whole new set of images is generated, all based around the one you
selected (which is now the middle image of the new set).
From a basic point of view that's it! Just press alt-number to
scramble things when you're out of inspiration, it works for any of the
fractal types in fractint including formulae... easy! (chaotic, but
easy :-) )
As this is a Fractint feature, there is, of course, a lot more to it
than the basics described above...
For a start, there are some handy hotkeys to use, 'F2' and 'F3' are
used to alter the amount of mutation or the amount by which the
selected parameters can be varied. 'F2' halves the amount of mutation,
'F3' doubles it. So if things on-screen are looking a bit samey just
press 'F3' a few times to crank up the mutation level.
Using 'F2' to decrease mutation levels is a way of moving towards a
goal image. Say that a set of images contained one that looked a little
like, maybe, a cats face and you wished to try and get something more
cat like. To achieve this simply select the desired image and press
'F2'. The newly generated images should be more alike, though probably
still quite widely varied. With luck, one of the new images will be
even more cat like. Select this one and press 'F2' again. Continue like
this, selecting the center image again if there are no improvements in
the current generation, until eventually all the images are alike and
you've arrived at your goal (or at least you're probably as close as
it's possible to get with that fractal type).
As you look for more details in the images it is useful to reduce the
number of images per generation, thus producing larger sub images.
Pressing 'F4' will reduce the number of images per side on the grid by
two and pressing 'F5' increments the gridsize similarly.
'F6' will switch between normal random mutation and 'spread' random
mutation. In 'spread' mode the amount of mutation allowed in an image
is varied according to each images position in the grid. Those images
near the center are allowed a lesser degree of freedom of mutation than
those around the outside. This produces a sea of images, stable at the
center with wilder variations around the edges. This mode is best used
with larger gridsizes and becomes completely silly at a gridsize of
three!
'Ctrl-e' brings up the evolver control screen on which you have manual
access to the evolution parameters varied by the hotkeys described
above.
These are:
Gridsize. The number of sub images per side of the
screen. Use
odd numbers only.
Max Mutation The maximum amount by which a parameter may be
varied
Mutation Reduction The Max mutation value is multiplied by this
between
generations. This can be used to automatically goal
seek without having to use the 'F2' key.
Grouting Turns on or off the gap between sub images, at
large
values of gridsize this can reclaim valuable screen
area for display use.
Pressing 'F6' brings up a screen from which you can control what
parameters get varied and in what manner. You'll notice that as well as
the mutation modes 'random' and 'spread' there are other ways of
stirring things around, read on......
As well as randomly mutating parameter values (referred to as 'evolver
mode' or just 'evolving') a chosen set of parameters can be varied
steadily across the screen thus allowing the user to explore what
happens as a parameter is slowly changed ('explorer mode' or
'exploring'). For example, to get acquainted with parameter exploring
and produce a map of the Julia sets, try this:
Start Fractint and set the type to Julia and the resolution higher than
320x200, once the default Julia set has been generated, press 'Ctrl-e'
to bring up the evolver/explorer control panel.
Set evolve mode to yes and then press 'F6' to bring up the screen that
allows you to choose what gets varied.
Now set the first entry (param1) to 'x' and the second (param2) to 'y'.
This tells Fractint to vary param1 (the real part of c) across the
screen and param2 (the imaginary part of c) down the screen. Make sure
all the other parameters are set to 'no' so that nothing else gets
changed to confuse things.
Press 'Return' to go back to the main evolver control screen and you'll
see that a few more items have appeared. These control just how much
the parameters are varied across the screen and what their starting
values should be, leave them as they are but increase gridsz to 15.
Also switch on the parameter zoom box option.
When you exit this control screen with the 'Return' key, you'll see a
grid of Julia sets generated all mapped out onto the imaginary plane,
squint and you'll be able to spot the underlying Mset!
When you press 'Pageup' this time you'll notice that there are two
boxes on screen with a larger box centered around the normal selection
box. 'Ctrl-pageup' or 'Ctrl-pagedown' varies the size of this box
which represents the 'parameter' zoom box. The parameter zoombox
allows you to look at smaller areas of the parameter space in more
detail. To explain this further look at how the Julia sets change
across the screen, around the area of 'seahorse valley' on the
underlying Mset, the Julia sets undergo a sharp change in character.
This area of change can be examined in more detail using parameter
zooming. Make the outer zoombox a few grids across and select an image
in the area of this change with the outer box straddling it. Look at
the images right in the corners of the parm zoombox, when you press
'Enter' and a new generation of images is generated the same images
will be in the corners of the screen with more sub images between them,
allowing a finer look at how the change progresses. In this way, you
can observe the chaotic areas in parameter space with the unique pseudo
four dimensional view offered by the explorer.
In the example shown above, you were just exploring the variation in
two 'real' parameters, i.e. they can take fractional values, and the
idea of being able to create an image half way between two others is
valid. However, many of the parameters in fractint are discrete, i.e.
can be only one of a set of specific values. Examples of discrete
parameters are inside colouring method or decomposition values and the
way in which these are explored is different in that parameter zooming
has no meaning for discrete parameters.
When a discrete parameter is set to vary with x or y it is simply
cycled through all possible values and round again. Words are getting
clumsy so it's time for another example methinks!
First press 'Insert' to restart Fractint and get everything back to its
default values for a fresh start. Set the fractal type to 'fn*fn' this
type requires the user to choose two trig functions and this choice is
made on the 'Z' screen. There are around thirty different functions to
choose from and checking out all the different combinations is a not
inconsiderable task manually. With the explorer, however, it's a piece
of cake!
Set the screen resolution to the highest you can view and press 'Ctrl-
e' to bring up the control panel and enable evolving mode. Set the
gridsize to 29 and leave the parameters at their defaults. Now, press
'F6' to enter 'variable tweak central' and set trig function 1 to 'x'
and trig function 2 to 'y', and all the others to 'no'. Exit the two
screens and you'll see generated all of the different combinations
possible even if they are rather small examples!
To find out what particular combination of trig functions an image is
using, just select the image using the zoombox and bring up the 'z'
screen. You don't have to press 'Enter', simply highlighting the
appropriate image with the ctrl-arrow keys will do.
And that just about sums up the evolver! Much more could be written but
it's better experienced, try writing your formulae with more variable
parameters and trig functions so that their behavior can be
investigated.
Try using it with any fractal type, if in doubt just see what happens!
It should be noted here that some of the fractal types such as the IFS
do not terminate, they run on forever and as such aren't usable with
the evolver as the first sub image would never finish to allow the next
one to generate. These fractal types are detected and you won't be
allowed to start the evolver with these.
There now only remains to mention that you can save image sets and
restore them later to carry on exploring from a different seed image:
's' saves and 'r' restores as in normal fractint operation and the
screenfull is saved as a single gif file.
Have fun! See Evolver Commands (p. 38).