There are two groups within the friends of roulette.
One looks for superior patterns or figures,
the other one does not believe in this and seeks for new roulette progressions.
As roulette progressions define the bets - usual after losses -
they can be seen as sequence of integer numbers:
1, 2, 4, 8, 16, 32, .... = Martingale
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, .... = Fibonacci
and so on
For an easy handling of loss progressions the
roulette simulator has a universal loss progression already built in.
Its called + on win.
When easy chances are bet, its like a Martingale.
The example of the Fibonacci sequence above wikipedia,
shows quite nice how mathematical approaches can be used for roulette.
But you can also go the reverse way and examine a
number sequence that you found at roulette for mathematical properties.
For this works the search function of the website OEIS http://oeis.org/ very well.
OEIS stands for "On-Line Encyclopedia of Integer Sequences"
where you can search for your own progressions.
You can grub in this extensive collection of number sequences and
get inspired for new roulette progressions.