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Introduction Chaos is unpredictable behavior arising in a realistic system because of great sensitivity to beginning circumstances Chaos arises in active systems If two very close starting points diverge even a tiny bit their future behavior is eventually unpredictable Every change in the system will compound with time so very slight changes in the starting point can lead to enormously different outcomes Also because of the extreme disorder predicting the future path of the system is practically impossible The behavior is too sensitive to the conditions so therefore it is always changing Chaotic behavior although appearing random arises from a very hard basis and it is very sensitive to any disturbances The system the above paragraph is referring to can be anything A set of equations is a system as well as weather patterns All systems display chaotic properties For example weather forecasts are never totally accurate Even if the forecast is for the week or a day it may be totally wrong This is due to minor disturbances in airflow Each disturbance may be minor but the changes will increase and add up in time Soon the weather will be far different than what was expected These same chaotic traits apply to math Certain sets of equations for example can be repeated many times creating images called fractals Often fractal equations consist of only an X and Y variable and a few constants Once the equations are repeated many times and the results are plotted on a computer screen incredibly complex images can be produced These pictures called fractals exhibit all of the chaotic traits They are very sensitive to small changes they are unpredictable and they appear chaotic even though they were created using very straightforward non-chaotic equations Now that brings us to chaos theory Chaos theory is a critical part of science mathematics art and computing It proves that the way to express an unpredictable
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