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MLC stands for "Mandelbrot Locally Connected". It's not obvious, but this is equivalent to the bulbs of the Mandelbrot set (the domains of parameters where almost all points get attracted toward periodic orbits) are dense in the Mandelbrot set. Everyone believes it to be true.

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Yes, but how exactly are the bulbs arranged? Wikipedia says 'Not every hyperbolic component can be reached by a sequence of direct bifurcations from the main cardioid of the Mandelbrot set. Such a component can be reached by a sequence of direct bifurcations from the main cardioid of a little Mandelbrot copy'. Which sequences of bulbs have little copies at the end of them? And how do the little copies attach?

The combinatorics of how the Mandelbrot set is put together is well-studied, and rather independent of MLC. The arrangement of the bulbs on the boundary of the "main cardiod" (which is where there is an attracting fixed point) is described here: https://en.wikipedia.org/wiki/Mandelbrot_set#Main_cardioid_a.... Generally, the patterns are given by something called Lavaur's Algorithm; see https://en.wikibooks.org/wiki/Fractals/Iterations_in_the_com... for some explanation. Attachment points are always at the "root" of the Mandelbrot set, which is the cusp of the main cardioid.

A consequence of MLC is that the combinatorial picture given by Lavaur's algorithm and related analyses is "complete" -- all dynamical information is available from the combinatorial models.

Thank you, that's very helpful!

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