Tinkering around logistic map

I was tinkering around logistic map today, I accidentally discovered a property of it. That is, if you look at histogram of the sequence generated by it, it will be same independent of the input. This immediately hit me that there may be an underlying probability density of this map. In fact, after Googled, I found out that Ulam and von Neumann studied this! So here we go.


Monte Carlo as Intuition

I am doing teaching assistantship for Monte Carlo methods course. I explained the following exercise as an application of the Monte Carlo principle. It is nice because it coincides with a very intuitive guess.