An Introduction to the Unpublished Book "Reflections on a Tube" by Mitchell J. Feigenbaum

Abstract

This paper is an adaptation of the introduction to a book project by the late Mitchell J. Feigenbaum (1944-2019). While Feigenbaum is certainly mostly known for his theory of period doubling cascades, he had a lifelong interest in optics. His book project is an extremely original discussion of the apparently very simple study of anamorphs, that is, the reflections of images on a cylindrical mirror. He observed that there are \emph{two images} to be seen in the tube, and discovered that the brain preferentially chooses one of them. I edited and wrote an introduction to this planned book. As the book is still not published, I have now adapted my introduction as a standalone version, so that some of Feigenbaum's remarkable work will be accessible to a larger audience