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Miloslav Ciz 2025-03-20 21:16:10 +01:00
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chaos.md
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@ -6,7 +6,7 @@ Perhaps the most important point is that a chaotic system is difficult to predic
Examples of chaotic systems are the double pendulum, weather (which is why it is so difficult to predict it), dice roll, [rule 30](rule_30.md) cellular automaton, [logistic map](logistic_map.md), [Baker's map](bakers_map.md), gravitational interaction of [N bodies](n_body.md) or [Lorenz differential equations](lorenz_system.md). [Langton's ant](langtons_ant.md) sometimes behaves chaotically. Another example may be e.g. a billiard table with multiple balls: if we hit one of the balls with enough strength, it'll shoot and bounce off of walls and other balls, setting them into motion and so on until all balls come to stop in a specific position. If we hit the ball with exactly the same strength but from an angle differing just by 1 degree, the final position would probably end up being completely different. Despite the system being deterministic (governed by exact and predictable laws of motion, neglecting things like quantum physics) a slight difference in input causes a great different in output.
A simple example of a chaotic equation is also the function *sin(1/x)* for *x* near 0 where it oscillates so quickly that just a tiny shift along the *x* axis drastically changes the result. See how unpredictable results a variant of the function can give:
Another simple example of a chaotic equation is also demonstrated by the [function](function.md) *sin(1/x)* for *x* near 0 where it oscillates so quickly that just a tiny shift along the *x* axis drastically changes the result. See how unpredictable results a variant of the function can give:
| *x* | *1000 * sin(10^9 / x)* |
|-------|------------------------|
@ -107,3 +107,8 @@ It outputs the following:
```
Vertical axis is the *r* parameter, i.e. the population growth speed. Horizontal axis shows stable population size after 1000 generations, starting with different initial population sizes. We can see that up until about *r = 3* the stable population size always stabilizes at around the same size, which gradually increases with *r*. However then the line splits and after around *r = 3.56* the stable population sizes are quite spread out and unpredictable, greatly depending on the initial population size. Pure CHAOS!
## See Also
- [randomness](randomness.md)
- [pseudorandomness](pseudorandomness.md)