The iterates beyond the first few look pretty much alike for all three functions. The "S" button calls the sinusoidal function, the "G" button the Gaussian function. The "Q" button recalls the quadratic function. First try the "S" button. You will notice that the gains at which things happen are different. Next try the "G" button in the same way.
Now go back to the quadratic function at iteration 100 and gain of 3.73. Advance the gain to 3.74 and then to 3.75. Notice how the character of the graph changes. It is extremely ragged in appearance at 3.73. It becomes more regular at 3.74. At 3.75 it is ragged again. That raggedness you will come to recognize as chaos. The regular behavior shows that at some gains the function has windows of order in the midst of chaos. In a few seconds you have been able to see what the pioneers in the field, without computers, took a lifetime to discover.