Robert P. Munafo, 2010 Sep 9.
The unique point on the boundary of a mu-atom of period P where two external angles of denominator 2P-1 meet.
The root of R2F(1/3B1)S is a cusp at approximately -0.154724+1.031047i.
Parameter rays RM(θ) are defined as preimages of straight
rays [...] When θ is periodic, then c is the root of a hyperbolic
component (see below)
Hyperbolic components of M consist of parameters, such that the corresponding polynomial [(referring to Z2+C)] has an attracting cycle. The root is the parameter on the boundary, such that the cycle has multiplier 1. The boundary of a hyperbolic component contains a dense set of roots of satellite components. [...]
Another example is from Milnor's 1999 paper "Periodic Orbits, Externals Rays and the Mandelbrot Set ..." in the figure 12. This shows R2F(1/3B1)S with external rays leading to the island's cusp and to the bond point where its cardioid R2F(1/3B1)Sa touches its north bulb R2F(1/3B1)S.1/3a. The 3/15 and 4/15 external arguments meet at the cusp, and the 820/4095 and 835/4095 external arguments meet at the bond point. The caption reads:
Detail of the Mandelbrot boundary, showing the rays landing at the root points of a primitive period 4 component and a satellite period 12 component.
From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2022. Mu-ency index
This page was written in the "embarrassingly readable" markup language RHTF, and was last updated on 2010 Sep 09. s.27