Chaos theory facts for kids
Very small changes in the starting position of a chaotic system make a big difference after a while. This is why even large computers cannot tell the weather for more than a few days in the future. Even if the weather was perfectly measured, a small change or error will make the prediction completely wrong. Since even a butterfly can make enough wind to change weather, a chaotic system is sometimes called the "butterfly effect". No computer knows enough to tell how the small wind will change the weather.
Some systems (like weather) might appear random at first look, but chaos theory says that these kinds of systems or patterns may not be. If people pay close enough attention to what is really going on, they might notice the chaotic patterns.
The main idea of chaos theory is that a minor difference at the start of a process can make a major change in it as time progresses. Quantum chaos theory is a new idea in the study of chaos theory. It deals with quantum physics.
As an example, take a pendulum that is attached at some point, and swings freely. Connecting a second pendulum to the first will make the system completely different. It is very hard to start in exactly the same position again - a change in starting position so small that it cannot even be seen can quickly cause the pendulum swing to become different from what it was before.
A very important part to the study of chaos theory is the study of mathematics functions that are known as fractals. Fractal functions work like chaotic systems: a small change in the starting values can change the value of the function in ways that look random. Due to the fact that they are mathematical, they are easy to study.
Images for kids
Lorenz equations used to generate plots for the y variable. The initial conditions for x and z were kept the same but those for y were changed between 1.001, 1.0001 and 1.00001. The values for \rho, \sigma and \beta were 45.92, 16 and 4 respectively. As can be seen from the graph, even the slightest difference in initial values causes significant changes after about 12 seconds of evolution in the three cases. This is an example of sensitive dependence on initial conditions.
The Lorenz attractor displays chaotic behavior. These two plots demonstrate sensitive dependence on initial conditions within the region of phase space occupied by the attractor.
A conus textile shell, similar in appearance to Rule 30, a cellular automaton with chaotic behaviour.
The red cars and blue cars take turns to move; the red ones only move upwards, and the blue ones move rightwards. Every time, all the cars of the same colour try to move one step if there is no car in front of it. Here, the model has self-organized in a somewhat geometric pattern where there are some traffic jams and some areas where cars can move at top speed.
Chaos theory Facts for Kids. Kiddle Encyclopedia.