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Old 10-27-2006, 08:32 AM   #162
Windu Chi
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Originally Posted by Ray Jones


Nope, chaotic equations behave just like normal equations, in fact they're basically just iterated equations. Thus, given the same variables, they give the same results after the same number of iterations, so we are able to display those fancey fractals (Feigenbaum, Mandelbrot, etc) But, due to the fact of iteration, the smallest possible variation in one variable can have an immense effect on the result, which again can dissapear right with the next iteration.
You are talking of the butterfly effect.
Originally Posted by Ray Jones
The calculation of chaos is totally exact, but *only* if you know every single variable of a chaotic system and its exact value. Of course we're not (yet) able to get all those information to calculate a big chaotic system of "real life" like weather. What we are able to do is, we can take a limited set of variables which are known to influence a system the most and use these for an approximate calculation of what might happen. Provided that we found the proper equations already, of course.
You must mean Algebraic equations are the exact ones.
I guess I ment to say partial differential equations and nonlinear partial differential equations.
Navier-Stokes equation for example have few or no exact solutions in close-form.
Which I mean:at least one solution can be expressed by approximation in terms of a bounded number of certain elementary math functions; no infinite series, limits of a algebraic sequences, and no continued fractions.
It's a type of a nolinear partial differential equation.
The solutions to theses types equations are n-dimensional and also you have to deal with the six degrees of freedom in angle.
When the calculation is bound to 3 spacial dimensions.
You can only calculate evolution size of the chaotic mess with stochastic differential equations.
They are more extremely sensitive to initial conditions,
at the start of the numerical iterated process.
Then the Algebraic ones.

Last edited by windu6; 10-27-2006 at 09:01 AM.
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