  We give a new proof that all external rays of the Mandelbrot set at rational
angles land, and of the relation between the external angle of such a ray and
the dynamics at the landing point. Our proof is different from the original
one, given by Douady and Hubbard and refined by Lavaurs, in several ways: it
replaces analytic arguments by combinatorial ones; it does not use complex
analytic dependence of the polynomials with respect to parameters and can thus
be made to apply for non-complex analytic parameter spaces; this proof is also
technically simpler. Finally, we derive several corollaries about hyperbolic
components of the Mandelbrot set. Along the way, we introduce partitions of
dynamical and parameter planes which are of independent interest, and we
interpret the Mandelbrot set as a symbolic parameter space of kneading
sequences and internal addresses.
