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

Fibonacci(2) = 1

Fibonacci(n>2) = Fibonacci(n-1) + Fibonacci(n-2)

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:

1,1,2,3,5,8,13....

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.