Fibonacci Form and Beyond

摘要

This paper develops a context for the well-known Fibonacci sequence (1,1,2,3,5,8,13,...) in terms of self-referential forms and a basis for mathematics in terms of distinctions that is harmonious with G.Spencer-Brown's Laws of Form and Heinz von Foerster's notion of an eigenform.The paper begins with a new characterization of the infinite decomposition of a rectangle into squares that is characteristic of the golden rectangle.The paper discusses key reentry forms that include the Fibonacci form,and the paper ends with a discussion of the structure of the "Fibonacci anyons" a bit of mathematical physics that relates to the quantum theory of the self-interaction of the marked state of a distinction.