I have a very naïve question: can one find anywhere a combinatorial description of the Mandelbrot set?

Let me try to be a bit more precise: is it possible to encode each of its "bulbs" by some sort of finite sequence of numbers (or more complicated combinatorial data), and then give a simple combinatorial description of how each of these bulbs connects to the other ones, and (if possible) some sort of formula giving the equation of each bulb in terms of its "code"?

I suppose the mathematical community in general should know the answer. A partial construction of this sort is given here: https://en.wikipedia.org/wiki/Mandelbrot_set#Main_cardioid_and_period_bulbs ; and hints of a bigger picture are given for example in this answer: The deep significance of the question of the Mandelbrot set's local connectedness? . But there is so much literature about the Mandelbrot set that searching for a precise reference is somewhat hard.

Could by chance anyone point me to some book that systematically expounds the answer to that question?

In fact, more generally, I would like to learn "how the Mandelbrot set works". So basically, I am looking for some nice introductory book to the Mandelbrot set. I have tried to ask a more specific question (whose answer, in my opinion, should occupy a central place in such a book), but it is necessarily somewhat vague - precisely because I know very little about this subject. So what reading would you recommend?