We did some more work collecting information for the Catalog of Behavior for the Logistic Map function we introduced on Monday, getting a clearer idea on the changes in behavior as *a* increases towards 4.0. The patterns we observed raised a few questions:

- Somewhere within the interval 3.0 <
*a*< 3.1, the single fixed point attractor “bifurcates” (i.e., splits) into a 2 cycle. Where exactly does this happen? - Later, the 2-cycle becomes a 4-cycle. Do all points of the cycle bifurcate simultaneously, or can one split before another? In other words, is there a 3-cycle within the interval 3.4 <
*a*< 3.5, or does the 2-cycle split directly to a 4-cycle? - Once chaos appears past
*a*= 3.6, is that it? Or is there anything more to be found there?

Continue your explorations of this function to try and answer these questions. Use the applets posted yesterday. I have a special prize for the first person who can find a 3-cycle…