Chaos Theory Mathematics For Kids

What is the Butterfly Effect?

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Looking for a simple way to explain the butterfly effect (chaos theory) to children?

Here is a simple definition, and a hands on real-life example for your kids to try.

Chaos theory is the study of how even simple systems can display complex behaviour. These systems can seem straightforward - but are very sensitive to initial starting conditions and this can cause seemingly 'random' effects.

Take the example of running a marble down a tilted board filled with obstacles. The marble will take a path down the board, hitting certain of the obstacles on the way down. If you drop the marble a second time, it is likely to take a different path. Even if you try to get the marble to take the same path, tiny variations in where you start the marble will cause it to behave differently on the route down.

If you apply this reasoning to even bigger systems, like the weather, then you can see that small events at the start of the system (like the flap of a butterfly's wings in Brazil), could lead to big differences later in the system - like a tornado in Texas.

Would you like to see an example?

Below is a spreadsheet with 2 columns of calculations. For the purpose of looking at chaos theory, these are our 'systems'.

Both columns are using exactly the same calculation with the exact same starting point of .4 (point 4). The graph is only showing one line because both columns are graphing in the same spots. (You may prefer to click to view the spreadsheet in full screen mode).

Now, click on the red box and change the starting point of the second column to .399999999. So we have the same calculation, but have slightly changed the starting point of column two. Click elsewhere on the spreadsheet to recalculate the second column.

You will see the graph now shows that the two systems (calculations) appear to follow along the same lines for a while, then diverge dramatically. The tiny variation at the begining of the system - has caused a big change further along in the process. Try different numbers as a starting point - what does .400001 do to the systems?

If the variation in a simple system like the spreadsheet can appear so dramatic - imagine what a small variation at the start would do in a complex system.

This is pretty much what the study of chaos theory mathematics investigates. OK - there is more to it (feedback loops and topological mixing)! But you have got the basics! If you would like to learn more then try :

Fractals for the Classroom .