
Lorenz 1.2
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What is this?

This program shows you the behavior of a differential equation called Lorenz.
It is famous for its chaotic behavior.

Each trail of line represents one solution of the differential equation over time.
You can see that all solutions eventually fall into two eddies. ( Push mouse button to reset all solutions)
These eddies are called 'strange attractors'.

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Lorenz Equation and how to solve it

The Lorenz equation is given as simple as follows:

	v0(t) = 10 * ( x1(t) - x0(t) );
	v1(t) = 28 * x0(t) - x1(t) - x0(t) * x2(t);
	v2(t) = - 8/3 * x2(t) + x0(t) * x1(t);

where x0(t), x1(t), x2(t) are the function of three dimensional position.
And v0(t), v1(t), v2(t) are the velocity (or, derivative function) of x0(t), x1(t), x2(t) respectively.

In order to solve x(t), you have to numerically integrate the above equations.
There are many methods to integrate numerically. Among them, I used Euler's method.
Euler's method is as follows.

x(t + dt) = x(t) + v(t) * dt;

where dt indicates very short period of time.
By calculating the above equations repeatedly for x0, x1, x2, you can obtain x0(t). x1(t), x2(t)
Euler's method is very simple but not quite precise. 
Usually, other methods such as Runge-Kutta is used to get better solution.

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Changes

The first release( no version num) -> 1.1
 
	Fixed a bug that Lorenz can't quit correctly
	More movement in "Auto" mode
	Added shortcut key for menu items
	Colorful mode is added
	Mouse click resets all points to random position
	Screensaver module is provided though it's very sluggish
	And many more tiny changes that I can't remember

1.1 -> 1.2
	Fixed a bug when zoomed ( no more zoomabale)
	'Trace single solution' menu is added.
	No more flickering in blanker addon and got faster ( I hope)

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About the author

This is my second program for Be. (The first one is "hello world!" :) )
Actually, it's a port from Mac that I wrote a few years ago.
I wrote this program solely to learn programming for Be OS.

Contact me at:

Hiroki Mori
mori@sainet.or.jp
http://www.sainet.or.jp/~mori

Any comments or questions are welcome.
