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.


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This page maintained by

Noel Giffin,
noel@triumf.ca