# spiral forward orbits of analytic functions near repelling fixed points

An anonymous referee informs me that forward orbits near fixed points of analytic functions, such that the members of the forward orbits lie on spirals, are well-known. His citation for this (p. 31 of "Complex Dynamics", Carleson and Gamelin, Springer 1993) does not mention such spirals explicitly. Is there a discussion of these spirals in the literature, especially of equations they satisfy?