If the number of values on the attractor doubles at each split and there have been an infinite number of splits from gain 3 to 3.6, we might well expect the attractor to be severely fragmented at gain 3.6. That in fact is what we find. It appears that the attractor here has an infinite number of values all within certain bounds. Next set the gain at 3.6 and iterate for a long time. The function never settles down. Eventually you will completely fill part of the screen with iteration lines, but only part of the screen.
When the iteration lines completely fill in the space, just change color and continue. You will see that the y value of the function is just as unstable as it was at the beginning. In fact the y value will never precisely repeat for as long as you care to carry out iterations. Due to the limits on screen resolution, lines will fall on one another. If ever the actual value repeated however, it would then follow the same pattern forever. Think about it.