Once again try to predict the effect of this "next x selection" rule. This technique of taking the output from a function and putting it back in as the input is called "iteration". For the gain, which is set in this display at 3.5, notice what happens after several iterations. Keep your eye on the values of x and y displayed at the bottom of the graph. After about 35 clicks of the Action button, only four different numbers ever show up. This is our first contact with what is called a period-four point attractor. We will learn more about this later.
In the language of control systems this business of putting the output of a system, or a portion of it, back into the input is called feedback. You have probably experienced the condition that arises when the amplification of a poorly designed sound system is pushed too far and the sound comes back through the microphone to be re-amplified, causing an unpleasant squealing sound. Reducing the gain on the amplifier will cure this. This is exactly the situation with our logistic function. We will also explore the sensitivity to gain of any attractors later.