Mysterious Function

A few days ago in my COGS401 class our professor wrote a formula on the board. I hadn't been paying attention up until that point in the lecture, so I have no idea why he wrote the formula, or how it was related to psychology in any way. He seemed pretty excited about it however, so I wrote it down in my notebook:

Yi+1 = a * (1-Yi) * Yi

i+1 and i are both subscripts to the variable Y.

I just finished a small Java program to plot the formula to see what it looks like. 'Yi' is on the y-axis and 'a' is on the x-axis. My program could only plot the function between 1 < a < 4:


Here is 3.5 < a < 3.75:


and 3.75 < a < 4:


Very mysterious...