A lot has already been said about this classic. I would just like to recommend two videos by the Numberphile channel on YouTube that greatly enhanced my enjoyment of the material covered in the book:
On the Feigenbaum constant https://www.youtube.com/watch?v=ETrYE4MdoLQ
On the chaos game (in the chapter “Images of Chaos”) https://www.youtube.com/watch?v=kbKtFN71Lfs&t
Konrad Senf 