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The platform of this toy is divided into six areas describing six different situations in a game of football: scoring a goal, a penalty kick, a corner, a foul, a throw-in and off-side. There is a magnet hidden under each area and there is also one in the ball. The bottom pole of the ball and the top poles of the platform are of the same sign. The ball avoids stopping above any of the areas. The movements of the ball over the magnets is absolutely chaotic. Sometimes you get the impression that the ball is going to stop above one of the areas, and that it is suddenly attracted to another area. Theoretically, it cannot be foreseen where the ball is going to stop. Even a small change of the initial ball position leads to a different result, which is a characteristic feature of the chaotic movement. |
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This is also the case with a real football match. You never know what the score is going to be before the final whistle. The theory of chaos has been employed in many scientific fields, the examples being forecasting the weather or prediction the Stock Exchange quotations. |
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The movement of the magnetic pendulum depends on many factors, like the friction (it can be enhanced if the pendulum is submerged in a liquid), the gravity force (which changes the relative direction if the vertical positioning of the pendulum changes), the attracting or repelling force of magnets (different magnets have slightly different strengths and configurations so they never act with exactly the same force). Let us paint single "gates" with different colours and check in many runs where the pendulum stops, if launched from "exactly" the same position. Then change the initial position and start again. You will get a nice picture. |
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The picture here is the "flag" picture of the research into chaos. It is called Lorenz's attractor or butterfly effect, as it resembles a real butterfly. The line never returns to its previous track and trajectories are separate. Both pictures belong to the class called "fractals", as they are composed of smaller fractions resembling the whole picture. An example of fractals is the common cauliflower, as it is composed of smaller flowers, being copies of the whole one. |