In particular, rays allow us to characterize any particular location on the M-set by a single number, the ray arc angle. This web page provides tables and expressions for various interesting features on the Mandelbrot set. These tables should be used with the accompanying visual atlas , to visually locate the features given in the tables below.
Every bud is pinched off by a pair of rays.
The table below provides the ray angles for some of the buds on the main cardiod. The table presented above generalizes through the idea of 'codeword concatenation'. The basic idea is that for any given bud on the main cardiod, we can construct a binary string, a 'codeword', that is exactly equal to the ray angle. The codeword represents the periodicity of the points orbiting in that bud. So lets explain what we mean by this.