oeis

[tester]

I don't know yet why I am looking for such sort of things, but here is an example:

http://oeis.org/

Patterns in numbers. How to define them? How to define them in random sets at non-random visual appearances? How to define relativity and density of pattern assignments? Things not measurable via distributions due to small sizes of snapshots.

[KG_is_back]

Maybe multidimensional least-squares method. I've used it to estimate coefficients of biquad filter.
[X_0] would be 1,2,3,4,... [Y] would be the patern
and [X_1]...[X_n] would be various functions of [X_n] and [Y] inducing delays and delays of the functions

so basically use LSM to find [a_n] of fuction

y(0)= a_1*x(0) + a_2*x(1) + a_2*x(0)^2 + a_3*y(1) + ... + a_n*1

the reliability of output would be dependent on the number of functions in the equation cos' it basically tells you which affect the pattern and which don't.
LSM is doable in flowstone and should be easy in ruby (especially if you use matrix libraries) even though program needs to solve matrices of linear equations of 10+ variables.

Another way would be to use some kind of iterative method to predict the pattern. something that can tell from {1,1,2,3,5,8,13,21} that it is { y(0)=y(1)+y(2) & y(-1)=0 & y(-2)=1 } somehow by refracting each step into most probable function or I don't know I'm guessing...