Chaos and Randomness

[Swapnil]

I recently heard that there are two main phenomenons which are discussed in statistics: chaos and randomness. What exactly is the difference between the two?

[HallsofIvy]

I wasn't aware the chaos was discussed in statistics! Chaos involves deterministic (i.e. non-random) phenomena that are so complex the results can LOOK random but aren't.

And they don't have to be all that complex: Consider this example. For any 0< x< 1, double it, then, if that result is greater than 1, drop the integer part.

For example, if x= 1/3, doubling gives 2/3, doubling again 4/3= 1+ 1/3 which reduces to 1/3 when we drop the integer part. Repeating just gives the sequence 1/3, 2/3, 1/3, 2/3, ... But if you use 0.33333333333 on a calculator, say, and do the same thing it won't be long until you are getting very different results.