**
Chaos Filez
**

Web site and contents by Lloyd Garrick

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The *Lorenz Twins* program plots 2 Lorenz graphs (violet and yellow) simultaneously on top of each other. You can slightly alter the initial
parameters of one of them and see a demonstration of the famous "butterfly effect". You can enter any numbers you want and get all sorts of crazy
graphs, but the three default parameters are 10, 28, and 2.667 (don't ask me why).
In the left graph, the third parameter was set to 2.66701, a difference of only 0.000375% ! The twins start out together and after a while begin to diverge
and go their separate ways, as seen in the lower right of the image.

In the right image, the first parameter was set to 10.01, a difference of 0.1%. Here too the twins start out together and later diverge as can be seen near
the lower center of the image.

At any time you can save the graphs to disk as BMP file. You can also make *much* smaller changes in the initial parameters and get similar effects,
although it takes longer to see. Way cool! No wonder they can't predict weather accurately even a day in advance, at least not in Colorado!

__The following three programs run in DOS.__

These two plot the Lorenz and Rossler attractors respectively, with user input parameters. However, they also plot an audio graph as well. That means *sound* !
You can *hear* the Chaos as well as see it ! A rather strange and unique idea. Try them !

- Lorenz Attractor
- Rossler Attractor

This program (primitive but informing) will tell you just how big your pet fractal is. If you are doing deep zooms (any fractal program, doesn't have to be
FRACTINT), and you know the magnification factor of the zoom image, you can determine the size of the original fractal.

- Fractal Dimension

For example, if you zoom into the Mandelbrot to a magnification of 2e+26, the original Mandelbrot is about ten billion (1e+10) light-years across - about
the size of the known observable Universe.

The *Mandelbrot Benchmark* program draws a default Mandelbrot. When done, the system bell sounds and a message box appears
with a number. And that is the number of seconds it took to do. You see here it takes 141 seconds on my P4-2GHz Dell (which just got totally hosed by a power spike). And it takes 96 seconds on my brand spiffy-new Gateway 3.0GHz DualCore; I would have expected a better improvement ...
You can use this to test system performance, the effect of hardware upgrades, or comparing systems. This is a Win32 benchmark, and will not necessarily
tell you anything about DOS performance, like when using FRACTINT.

This *Strange Attractors* program (SAX25) graphs an infinite number of these images, some examples shown below. It is a Multi-function Grapher/Plotter for Strange Attractors.
You can input parameters or let the program pick random numbers. Images can be saved in full size BMP format. A number of other cute mathematical tricks
and functions also, as well as an autorun "screensaver" mode. This is the current version of my "flagship" program, which initiated my fractal websites
and the UFVP. To my knowledge, this is the only program out there that does these things specifically.

Actually, they are not "images" until you stop the
program amd save them. These graphs are dynamic - constantly growing and changing - forever.
A knockoff of the SAX25 program, *Hypnotica* sits in your quick-launch tray and when fired up fills the screen with an infinite
variety of graphs like above; you never see the same one twice - not in a zillion years. No controls or user input, just launch, watch and be mesmerized. A psychedelic toy ... for those *altered states*.

The *Butterfly* program plots 2 Strange Attractors (red and green) simultaneously on top of each other. Similar to the Lorenz Twins program above, you can slightly alter the initial
parameters of one of them and see another graphical demonstration of the famous "chaos", or "butterfly effect". The red and green of the two graphs are easily seen, and where the pixels overlap you see yellow. This is another variation
of the SAX25 program; the graphs are full screen size, it may be difficult to see in these small pictures here. Amazing differences are seen for very small changes in input parameters, a true demonstration of the
"butterfly effect".

Other than the 3 DOS programs listed above, all of these are coded in VisualBASIC 6.0. They should run on any current system with 32 bit Windows. In the possible but unlikely event you do not have the VB support files installed,
fetch them *here*. Perfectly safe I assure you, it is 100% Microsoft ...

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