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Images from the movie.

Lasse Rempe from the University of Liverpool studies dynamical systems. A dynamical system is:

… a physical setting together with rules for how the setting changes or evolves from one moment of time to the next.

One basic goal of the mathematical theory of dynamical systems is to determine or characterize the long-term behavior of the system. (From okstate.edu)

Fractals are one example of a dynamical system. You start with a function that involves complex numbers, and you feed in a number. You feed in the result of the first step to get a second number. And so on.

Another example of a dynamical system is differential equations. If you cannot find an algebraic solution for a differential equation, you can use a numerical technique which is quite like what we did for fractals — enter a number into the equation and get a result, then enter the result into the “system” again to get another result, and so on.

This week’s movie shows some nice art that results from the study of such dynamical systems.

The movie’s over on BBC.com – they don’t allow an embed:

The art of mathematics

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