The MAs in Alligator are meant to closely resemble other type of more complicated calculation. So called balance lines, based on some kind of fractal mathematics calculations. It is described in Bill Williams' and his daughter's books.
I actually answered this earlier with a download link for one of the books, but it was a pirate site, so probably moderators have deleted my post.
Williams may have had good personal reasons to displace his lines but there is nothing in fractal geometry that reflects in his entire works - absolutely nothing. Fractal geometry does not in any way shape or form mix with "technical" analysis. You may read what professor Mandelbrot thinks about "technical" analysis in his book "The (Mis)Behaviour of Markets." Mandelbrot invented Fractal Geometry - and if you know anything about Chaos theory and Fractal Geometry (which is the geometry of Chaos) you would know that both disciplines have been severely abused by all persons trying to "fit" "technical" analysis into those sciences - you cannot do that. "Technical" analysis has no fit whatsoever with science - it is simply not compatible much in the same way as "Fundamental" analysis has no place whatsoever in positive economics (it is in the realm of normative economics which makes it not much better placed than for example voodoo or using phases of the moon to analyse markets. My statements here are firm facts and I have made them strongly for two reasons a) we as traders need to be educated about the utility of those two - "technical" and "fundamental" analysis and especially how baseless they both are in science, and b) the lack of education on how non-scientific they are hurts very much how we view and attempt to trade markets. Regardless, I offer that what I have stated here are incontrovertible facts and all you have to do is ask around any faculty (in any university at all) associated with the named sciences. Cheers
Mandelbrot didn't even invent the Mandelbrot Set, let alone Fractal Geometry.
The main problem professors have with both technical and fundamental analysis is nobody talks about speculative trading. Until both speculative trading and real asset exchange on the same market are defined with proper equations no actual geometry can be defined for technical analysis, fractal or non-fractal. Williams made many and big steps in that direction, but he's still far away from actual market math.