Click on the Q button to select the logistic (quadratic) function. Look at iterations 1 through the higher numbers. Notice how the iterations above about i10 seem to look pretty much the same for gains less than 3. For gains between 3 and 3.45 they settle on one of two branches, from 3.45 to 3.54 they settle on one of four branches and above about 3.6 they are all over the place. You might want to slip back to the Attractor Demonstration display to try to understand this behavior before you leave this display.