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	Chaos and Strange Attractors as Art ?

Note :

A complete understanding of the material in the following sections, is not
necessary for using either, the Chaos Engine ( program file SA18TC.EXE )
and working artistically with the many stores images, or the Screen Saver (
SA18.SCR ). The Binary Data file
( SA18LIB.BIN ) is the required information Library where 88 bytes are used
to store the unique generating, locating and scaling information for each
of the many stored images.
This document and all files described herein are contained in the
self-extracting file SA18.EXE .


Introduction and Background :

The Chaos Engine as an art medium, has evolved from a study of a unique
form of mathematically defined systems of chaos. Each state of these
systems is defined by a point on the XY coordinate plane. Subsequent states
or points, are mapped via application of an 18 element, rank 3 tensor of
coefficients, specific to each unique system. Tensor elements are ordered
coefficients, additively applied to every possible product combination of
the current X and Y state coordinates in powers 0, 1 and 2, thus defining
each subsequent system state. It was discovered that if the 18 tensor
elements were chosen at random from the approximate interval from 1 to +1,
then about one in every several hundred so defined systems would exhibit
behavior that was stable or bounded, non-degenerative and non-periodic.
This weakly chaotic behavior would result in evolving points for each
subsequent state of the system, defining a progressive image where
locations in the image were clearly attractive of most systems states (
i.e.  the  system, though fundamentally chaotic in nature, nevertheless
"prefers" certain states of attraction ). Visually, it was observed that
these strange attractors tended to have pleasing and interesting qualities
especially if the spectral colors are used to indicate orbital
accelerations in various image areas, and a corresponding new art form was
born.

A computer was assigned the task of developing a library of images by the
random process selection of sets of tensor coefficient elements and
applying a series of tests to reject systems that lacked the desired weak
chaotic behavior. Each acceptable system was stored as the 18 tensor
elements together with scaling and locating dimensional parameters,
requiring 88 bytes for each image in the library file of images. The unique
tensor elements can be thought of as a kind of mathematical "genetic code"
for the corresponding "creature" strange attractor image. The Chaos Engine
enables the artist to view the 18 tensor elements while the image is
evolving, and allows for the dynamic "tweaking" of any selected element and
the observed effect on the dynamic image. Given even the crude precision of
the chaos engine tweaking tools, there still is likely to be more than 10
E+50 different "viable" possible images!

About the Colors :

The color assigned to pixel points representing each system state, is keyed
to the normalized acceleration at that point in the progressive development
of the strange attractor. It is the magnitude of the change in vector
displacements, between the vector of the preceding point to the current
point, and the vector from the current point to the subsequent point. In a
qualitative sense, it is the magnitude of the "jerk" felt at each point if
one was "riding" the points around the developing image. Normal Spectral
colors are used form Blue representing the minimal accelerations through
Cyan, Green, Yellow and Red representing maximum accelerations. Excursions
beyond either extreme are represented by a progression to Magenta. The
program samples the early progression of system states to define a mean and
standard deviation of accelerations. Normalized scaling from full Magenta
beyond the Blue up to full Magenta beyond the Red is indicative of from -2
to +2 standard deviations.

System and Program Information :

For either the Chaos Engine or the Screen Saver, using the highest screen
image resolution that will permit a color depth of at least 64K (16 bit )
and will display the developing images in a reasonable time, will produce
the best viewing. Allow each image to develop sufficiently to fully
appreciate the fine details and colors [ allow images to finish and go to
subsequent images in the Screen Saver ] . For the Chaos Engine, the program
file ( SA18TC.EXE ), the Library Image file ( SA18LIB.BIN ), and the
required Run-Time Module file ( VBRUN300.DLL ), should be placed in the
same directory or folder location. Start the program ( SA18T.EXE ) in
Windows by any of the usual methods , e.g. - double click ( SA18T.EXE ) in
file manager for Windows 3.1 or in the Explorer for Windows 95, using the
Run command, or permanently installing the program icons (recommended). The
Screen Saver file ( SA18.SCR ) together with ( SA18LIB.BIN ) and (
VBRUN300.DLL ) should be placed in C:\Windows\System to function as a
screen saver in the usual manner.
[ A copy of ( SA18LIB.BIN ) must be placed in C:\Windows\System since the
Screen Saver will "look" for it at this location.]

Using the Chaos Engine :

On starting the Chaos Engine an image is selected at random from the
library and displayed using spectral colors ranging from Magenta/Blue to
Red/Magenta, for tranquilly and violently chaotic regions of the strange
attractor respectively.

The sizing and positioning buttons [Bigger], [Smaller], [Taller], [Wider],
[Up], [Down], [Left], [Right] all do what they say when clicked. Left and
Right Clicking are for Large and Small adjustments respectively. [Taller] /
[Wider] change the aspect ratio of the image without changing the overall
size. All of these controls do nothing to the character of the images.

Images are selected from the library using the vertical scroll slider and
the selected image number is indicated above the top end of the slider.

Any of the 18 Tensor Elements displayed at the top may be selected for
"tweaking" by left clicking the number. The selected parameter will appear
in a different color than the rest. The parameter will be rounded off to
six decimal places when tweaked up or down using the [Add] or [Sub.]
buttons respectively. Six levels of additive or subtractive adjustments are
possible according to the following table :

	Action		Added or Subtracted Amount

	Left Click		0.1
	Right Click		0.01
	Shift - Left Click	0.001
	Shift - Right Click	0.0001
	Ctrl - Left Click	0.00001
	Ctrl - Right Click	0.000001

Immediately on tweaking a parameter, the image clears and redraws using the
altered parameter, allowing the artist to observe the effect on the image.
On occasion, the tweaked parameter will render the system unstable or
unbounded and the green "OK" indicator will intermittently or continuously
change to a red "OUT !". At this point the artist can recover to the
previous stable state by reversing the offending action using the [Add] or
[Sub.] buttons appropriately. In any case, clicking the image number will
return all parameters to the library values and is therefore a sure way to
recover.

An altered image can be stored by replacing the starting image in the
library by holding both the Ctrl and Shift keys while clicking [Save].
Stable images can be redisplayed by clicking the "OK" indicator. Exit the
program by clicking [Exit]

Using the Screen Saver :

The Screen Saver should function in the usual way except that the "N" key
will cause an immediate change to another image and the "H" key will cause
an image to "hold" after complete development until the "N" key is pressed.
A "beep" will sound when the "H" key is pressed and at one minute intervals
while an image is holding. The "S" key will display the image number of the
total number of images.

Note that some Windows systems "refuse" to recognize SA18.SCR . In Windows
v3.1, this problem can always be corrected by editing the [windows] section
of WIN.INI and the [boot] section of SYSTEM.INI respectively as follows :

ScreenSaveActive=1			SCRNSAV.EXE=c:\windows\system\sa18.scr

For stubborn cases there is included a simple executable form of the screen
saver SA18SCR.EXE, but this naturally requires manual launching.

Have Fun !

Steve Giannoni
CasaGiannoni@worldnet.att.net

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