# Chapter 9, Exploration 11

You know that an attracting period 2 orbit exists for $$a$$ slightly bigger than 3 because we have shown that a period-doubling bifurcation occurs at $$a=3.$$ Use the logistic bifurcation tool to answer the following questions.

• At approximately what value of $$a$$ does the period 2 orbit bifurcate to a period 4 orbit?
• At approximately what value of $$a$$ does the period 4 orbit bifurcate to a period 8 orbit?
• At approximately what value of $$a$$ does the period 8 orbit bifurcate to a period 16 orbit?
What is happening to the lengths of these intervals?