The Fibonacci sequence is a revolutionary sequence of integers first
proposed by a mathematician of the same name a few centuries ago (I
believe it was circa 1202, but I could be mistaken). The basic structure
of the Fibonacci sequence is as follows:
Fibonacci(1) = 1
The resultant sequence is a non-terminating, non-negative, increasing sequence. Many students in elementary or middle school are introduced to the opening of the Fibonacci sequence:
And it's a part of your basic college-level course in discrete mathematics and mathematical reasoning to dissolve the Fibonacci sequence as part of an exercise in recursion (the case where a function is self-referential...the Fibonacci sequence is possibly the most famous recursively created sequence...the Ackerman sequence holds a close second).
What makes the Fibonacci sequence so useful (and what made it revolutionary at the time...aside from recursion being a new concept) is that is has a plethora of uses for modelling nature, including the modelling of a flower's blossom, the structure of seed heads on a plant, the proportion of chambers in a nautilus shell (and many other univalve mollusks), size and structures of a family tree, populations in beehives, and rabbit breeding patterns.
It's capable of modelling these patterns efficiently because of its unique application in geometry- it models the growth of many different forms of spirals.
As for the application this could lead to with an aesthetic pursuit- the function for Fibonacci ratios is given here:
Fibratio(x>2) = Fibonacci(x)/(Fibonacci(x-1)
After Fibratio(2), this function converges at 1.61804, a number frequently referred to in mathematics as Phi. However, it also has a more common name- it's referred to as the golden ratio, golden mean, or golden number. The ancient Greeks recognized this number as having paramount use in aesthetics, and used it for everything from their architecture to their music.
So, where does that leave us? Well, the human brain is built to do two things at its most core- associate stimui and project trends. Thus, using mathematical trends to structure your music can create specific effects inside a person's mind. It's a case of influencing the actions of the mind through the stimuli provided, and it's what all good artists do.
Score one to Manson for providing a little insight into the mathematical basis of his work.
BTW, I've knocked out most of the spiritual and magickal significances of this sequence and the numbers it produces.